VCD Vertical Column Density W WACCM Whole Atmosphere Community Climate Model

Keywords: Laser heterodyne radiometer (LHR), Ground-based remote sensing, Externalcavity quantum cascade laser (EC-QCL), Mid-infrared (mid-IR), Polycrystalline IR fiber

The measurement of vertical concentration profiles of atmospheric trace gases provides a better insight into air pollution, ozone destruction and climate change as well as a way to validate chemical models and satellite observations. To that end, laser heterodyne radiometer (LHR) offers significant benefits in terms of high spectral resolution, high sensitivity and high vertical resolution in conjunction with a compact instrumental size deployable for field applications.

The aim of this thesis is to develop a fully transportable mid-infrared (mid-IR) LHR instrument for ground-based remote sensing of key trace gases in the atmospheric column.

) mid-IR LHR receiver was first developed. Its field test was carried out on the QualAir platform of the Université Pierre et Marie Curie (UPMC) with the help of a heliostat of the TCCON-Paris station (TCCON : Total Carbon Column Observing Network). LHR absorption spectrum of CH 4 in the atmospheric column was extracted from the solar radiation using the developed ground-based LHR receiver and it is in good agreement with the spectrum measured by the TCCON-Paris station. After this field test validation, a fully transportable mid-IR LHR instrument was developed and deployed on the roof of the IRENE platform of the Université du Littoral Côte d'Opale (ULCO) in Dunkerque. LHR spectrum of CH 4 and N 2 O in the atmospheric column was measured and in good agreement with the TCCON FT-IR spectrum of CH 4 and N 2 O, as well as in good agreement with the atmospheric transmission modelling. The fully transportable mid-IR LHR instrument developed in this PhD work has high potential for use in measurement of vertical concentration profiles of key atmospheric species on spacecraft, on airborne or on ground-based platform.

director, for giving me the opportunity to do my PhD in LPCA. My progress on my PhD work would not have been possible without his insight and guidance, including the attention to all of the little details which sometimes passed me by. He has taught me how to think like a scientist.

I would like to give my sincere acknowledgement to the members of the jury who have accepted to evaluate my thesis work. Thanks to Mr. Bertrand PARVITTE and Mrs. Martina WIEDNER for being my reporters and giving me some valuable comments and advices. Thanks to Mrs. Aurore VICET for chairing my defense as well as being my examiner. Thank to Mr. Gunther ROELKENS for being my examiner and providing me some valuable comments.

I would like to thank Mr. Eric FERTAIN, who worked closely with me at the beginning of my experimental stage and always help me when I have problems in life.

I would like to express my sincere gratitude to Mr. Yao TE for his help in the field measurement at the Université Pierre-et-Marie-Curie (UPMC) as well as providing corrections and comments related to retrieval algorithm in my thesis.

I would like to sincerely appreciate to Dong CHEN for his care, his patient guidance and his distance mentorship during my PhD study and tough life. He is not only my mentor, my friend, but also my father.

Additional acknowledgments go out to Gaoxuan WANG, a post-doctor who always worked together with me when I was in troubles. In daily life, he treats me as his little sister, always tolerates me and has been really good to me for my tough five years in France.

I do really appreiciate Tu TAN for his help in the last year of my thesis, and always tried to enlighten me when I was in a bad mood.

ii I feel very grateful to my Chinese master supervisor Mr. Fengzhong DONG. Thank you for your patience and careful guidance during my master's study and life in China. The biggest regret in my life is not seeing you for the last time and not attending your funeral. I hope you will feel happy and proud of me in heaven when you see me graduate successfully. I acknowledge all of my best friends in France including Khaoula KARROUM, Layal FAYAD, and Ghidda BADRAN for their sincere love and support which let me never give up. They are really very warm and lovely, and their enthusiasm has infected me, which makes my tough and boring life in France full of happiness, surprise and expectation. When I return to China, I will remember this foreign friendship forever and hope that one day we will meet again somewhere in the world. I don't want the last goodbye in France to be the last goodbye in our lives.

Thanks to my team members including Tong and Lingshuo. Thanks to my friends in LPCA and UCEIV including Rayan, Hadi, Tinehinane, Bouthayna, Jonas, Lamia, Sté phanie, Alla, and Allen.

Thanks to my Chinese friends Jie ZHANG, Luo HAN, Huili ZHANG, Pengshuai SUN, Jingjing WANG, Huadong WANG, Wei WANG, Yan XIANG, and Jiajin CHEN, My parents, my elder brother, my sister-in-law, my niece (Zhongchenxi SHEN) and my nephew (Hongyi SHEN) deserve special thanks for their love and support throughout this process. It's safe to say that I wouldn't be here if they hadn't guided me through my life, including the tough times.

And finally, I could probably go on and list countless more people, but I'm afraid I only have so much space to work with. Please contact me if I have left you out. This introductive chapter describes the motivation behind developing LHR as well as other passive remote sensing techniques for the measurements of vertical concentration profile.

List of Figures

This chapter will provide a brief history review of LHR techniques and outline the currently state-of-the-art LHRs. At the end of this chapter, the composition of this dissertation is introduced.

I. Remote sensing of vertical concentration profiles of atmospheric trace gases

Vertical concentration profiles of atmospheric trace gases, such as nitrous oxide (N 2 O), methane (CH 4 ), water vapor (H 2 O), ozone (O 3 ), carbon dioxide (CO 2 ), and dichlorodifluoromethane (CCl 2 F 2 ) [1], are of significant interest, because of their crucial roles in air pollution, ozone depletion, and climate change [2].

As is well known, vertical concentration variation of any trace gas strongly depends on vertical air transport. As a point of reference, the vertical air transport (Fig. 1 left) in the troposphere is faster than the horizontal transport (Fig. 1 right). Comparing with horizontal variations of trace gas concentrations, their vertical concentration variations are thus larger.

The vertical air transport from the surface to the tropopause (~10 km) takes about one month on average. Trace gases with lifetimes longer than one month tend to mix well vertically in the troposphere, while trace gases with shorter lifetimes show great vertical concentration variation. Under planet boundary layer (PBL), it takes even 1-2 days for air transport from the PBL down to the surface. Due to the temperature inversion in the stratosphere, the air exchange between the troposphere and the stratosphere is much slower than the mixing of the troposphere. It takes 5-10 years for air transport from the troposphere to the stratosphere, and 1-2 years from the stratosphere down to the troposphere (Fig. 1 left) [3]. Therefore, trace gases with atmospheric lifetimes (t) longer than 10 years show little vertical variation within the troposphere [5]. Both nitrous oxide (t~120 years) and methane (t~10 years) have uniform vertical distributions throughout the troposphere due to their long atmospheric lifetimes and are regulated under the Kyoto Protocol because of their contributions to global warming [5][6][7].

Compared to other tropospheric greenhouse gases (GHGs), although nitrous oxide has a smaller concentration (~320 ppbv for parts per billion by volume), it is an influential global warming molecule due to its particularly long lifetime [5]. Meanwhile nitrous oxide is rather inert in the troposphere, the reduction in its concentration occurs in the stratosphere due to photodissociation [8]. In addition, nitrous oxide is the dominant source of nitrogen oxides active in stratospheric ozone depletion [9].

Similar to nitrous oxide, methane is also well-mixed throughout the troposphere (∼1.8

ppmv for parts per million by volume) [10]. A combination of slower transport from the troposphere to the stratosphere and reactions with OH generates lower methane concentrations at stratospheric altitudes [11,12].

Water vapor in the troposphere is the most important greenhouse gas [13] and plays a crucial role in climate change as a dominant feedback variable in association with radiative effects and moist dynamics. In the lower troposphere, water vapor acts as the main resource for precipitation in all weather systems, providing latent heating in the process and dominating the structure of diabatic heating in the troposphere [5,14].

Ozone plays an important role in the chemical reaction occurring in the atmosphere, as well as on the climate change [15,16,18]. On average, about 90% of the total ozone vertical column is present in the stratosphere and only 10% exists in the troposphere. However, important variations in the vertical distribution of ozone can be the result of photochemical and dynamic processes. The tropospheric ozone concentration is particularly highly variable in space and time [19]. In the boundary layer, photochemically produced ozone is a polluting oxidant with major implications for human health starting at mixing ratios below 0.2 ppmv [17].

Dichlorodifluoromethane (CCl 2 F 2 , commonly known as Freon-12), which originates from ground-level anthropogenic sources and is photodissociated in the stratosphere, can deplete the protective stratospheric ozone layer via a catalytic photochemical cycle reducing ozone to oxygen [20] and has therefore been banned under the Montreal Protocol [21]. The highest Freon-12 concentration (∼500 pptv for parts per trillion by volume) is found in the troposphere where it is evenly distributed due to its long lifetime (~100 years) [21][22][23]. In addition, the long lifetime of Freon-12 [24] makes it an ideal tracer for dynamic processes, such as subsidence [25], horizontal transport, and mixing [26].

The accelerating rise of global levels of carbon dioxide in the atmosphere, most likely due to human activity and anthropogenic emissions, is believed to be the main driver of (anthropogenic) climate change [27,28]. Carbon dioxide production and reduction primarily occur on the ground and these variations are quite low in the atmosphere [29], where the variation of CO 2 is likely to be the result of dispersion and transportation controlled by meteorological factors [30]. In the free troposphere, CO 2 has been used as a tracer gas to study the vertical transportation of air pollutants [31,32].

It is, therefore, important to measure the vertical concentration profiles of the key atmospheric trace gases, which helps us to understand pollutant transport, climate change [20,[22][23][24][25][26][33][34][35][36], globally environmental parameters [37], and anthropogenic effects on atmospheric chemistry [2]. Moreover, vertical concentration profiles provide a powerful means for validating various atmospheric chemical and transport models and satellite observations. Meanwhile, such profiles can also give a scientific and comprehensive basis for environment assessment and the formulation of related policies. For these and other reasons the study of atmospheric trace gas concentrations and their vertical profiles has been of longstanding interest to atmospheric scientists, and over the years these studies have generated plenty of data on vertical concentration profiles of atmospheric trace gases.

Atmospheric trace gas concentrations can be generally measured by local point measurement and vertical profile remote sensing, respectively. In local point measurement of trace gas concentrations, instrumentation is located directly at the point of interest and in contact with the trace gas of interest. While vertical profile remote sensing can provide us not only the concentration but also its vertical distribution.

II. Techniques of passive remote sensing of vertical concentration profile

Global measurements performed from satellite platforms and localized measurements from balloon/aircraft and ground-based platforms can be used for passive remote sensing of vertical concentration profiles of atmospheric trace gases [10,38,[START_REF] Washenfelder | Carbon dioxide column abundances at the Wisconsin Tall Tower site[END_REF]. These techniques based on three different platforms are complementary to each other to form a complete observation system for atmospheric vertical profile sensing.

(

1) Global measurements on satellite platforms

The satellite measurement platforms work in different modes including backscatter ultraviolet (BUV), occultation, limb emission, and limb scattering modes. Each mode involves a different viewing geometry that affects measurements of the atmospheric radiation and vertical resolution.

(1-1) In BUV mode (Fig. 2), satellite-platform instruments directly measure the upwelling solar UV light that is either reflected from the Earth's surface or scattered back from the atmosphere based on Nadir viewing geometry [40]. Nadir viewing describes a vertical direction viewing on the Earth's surface directly below the satellite [START_REF] Clough | Atmospheric radiative transfer modeling : a summary of the AER codes, Short Communication[END_REF]. BUV mode is widely used for measuring ozone vertical profile. Ozone has a strong absorption at short UV wavelength, which results in UV light at long wavelength being able to penetrate far into the atmosphere. The radiation at short UV wavelengths is significantly absorbed at higher altitudes, so the backscattered radiation at specific UV wavelengths can only be scattered from above a particular height. Below this level, all the radiation is absorbed and there is no backscattered radiation. This allows satellite-platform instruments in BUV mode to obtain ozone vertical profile by measuring radiation at a series of wavelengths.

In addition, this mode can be used to infer information on the concentration of other trace species which absorb in the same wavelength region. Disadvantages of this mode are that it cannot be used at night including the polar night and its vertical resolution is poor (~5-10 km). bromine monoxide, and other trace constituents as well as the related cloud information [START_REF] Clough | Atmospheric radiative transfer modeling : a summary of the AER codes, Short Communication[END_REF].

GOME (Global

(1-2) In occultation mode, one measures absorption amount of solar, lunar, and even stellar radiation directly through the limb of the atmosphere at different wavelengths (e.g. UV, visible, infrared (IR)) as the Sun, the Moon, and the stars rise and set (depending on which celestial radiator is being used by the satellite instrument). In solar occultation mode (Fig. 3) transmission of sunlight through the Earth's atmosphere is measured and ratioed to exoatmospheric measurements (solar measurements recorded with no atmospheric attenuation). This is carried out at a series of tangent altitudes (the altitude to which the instrument can see), increasing in altitude during a sunrise or decreasing in altitude during a sunset. From each of the atmospheric measurements a slant column is calculated which can contain contributions from multiple atmospheric layers. and layer n, respectively. These attenuated solar radiations are recorded by the instruments on the satellite in a set of tangent altitudes during an occultation [43].

(1-3) Limb scattering mode (Fig. 4) is a part of limb-sounding mode, whose viewing geometry is similar to that of both limb emission (see (1)(2)(3)(4)) and occultation modes. In limb scattering mode, the UV-visible-NIR radiance from the Sun is scattered by the atmosphere into the FoV of the instrument along the line of sight (LOS) [START_REF] Kaiser | Fast weighting functions for retrievals from limb scattering measurements[END_REF]. In each scan of the atmosphere, instrument in this mode observes the atmosphere above the Earth's horizon and records spectra at different tangent altitudes to which the instrument can see. The objective of this type of measurements is to determine vertical profiles of trace gases, aerosols and atmospheric parameters (such as temperature and pressure). Satellite measurement in limb scattering mode combines high intrinsic vertical resolution (similar to that of measurements in occultation mode) and rapid global coverage (comparable in BUV mode). But the viewing geometry in limb scattering mode is more complex and the horizontal resolution is poor comparing with other modes.

Figure 4

Limb scattering viewing geometry with single scattering, surface reflection, and second order of scattering, respectively (the atmosphere's curvature is exaggerated) [45].

SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric

CHartographY) instrument on-board ENVISAT (ENVIronmental SATellite) [45] is an imaging spectrometer operated in limb scattering mode. The solar radiation transmitted in, back scattered by and reflected from the Earth's atmosphere or surface is recorded with SCIAMACHY at relatively high spectral resolution (0.2-0.5 nm) in the spectral region of 240-1700 nm and 2000-2400 nm [START_REF]European Centre for Medium-range Weather Forecasts[END_REF]48]. The high spectral resolution and the wide wavelength range of SCIAMACHY make it possible to detect different trace gases as well as detecting clouds and aerosols.

(1-4) Limb emission mode (Fig. 5), another limb-sounding mode, is used to retrieve vertical profiles of atmospheric trace gases with an improved vertical resolution and increased sensitivity for higher altitude and minor species [49]. Instruments in limb emission mode measure long-wave (IR or microwave) radiation thermally emitted in the atmosphere along the LOS of the instrument. Vertical profiles of the incoming limb radiances can be measured by changing the elevation angle of the LOS of the instrument such that vertical scans through the atmosphere are performed [50]. The measurements in limb emission mode do not require background radiation source, and the Earth's atmosphere itself is the radiation emitter. Meanwhile, such measurements are independent on the satellite position relative to the radiation source and can provide daytime and nighttime measurements over the full globe (depending on inclination angle). Due to lower temperatures of the atmosphere compared to stars, the Planck function's peak is far lower, and the peak position is shifted to longer wavelengths with lower SNR (signal-to-noise ratio). The accuracy in this mode is slightly less than BUV mode, and the horizontal path is quite long compared to the tangent altitude.

MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) instrument on-

board ENVISAT [45] based on a Fourier transform spectrometer (FTS) is designed for measurement in limb emission mode to detect the middle and upper atmosphere in a wide spectral interval throughout the mid-IR region (4.15-14.6 µm) [51,52]. The detected features can be spectroscopically identified and used as inputs to suitable algorithms for extracting atmospheric vertical profiles of a number of target species.

Since passive remote sensing techniques using satellite platforms can cover the entire Earth or any designated area for a long time, and they can be used to facilitate the remote observation of vertical concentration profiles of the tropospheric trace gases, which would allow us to better understand the source, trends and global distribution of atmospheric species [53]. However, satellite-platform instruments involve complex instrumental characteristics and physical processes [54], and the measured data must be validated to determine its reliability and uncertainty before it can be used to solve practical scientific problems [55][56][57].

Meanwhile, satellite-plateform instruments have a high overhead cost and typically lose sensitivity at lower altitudes [58].

( It observes scattered sunlight at various slant elevation angles, where solar radiation travels longer absorption paths [START_REF] Wang | Vertical profiles of NO 2 , SO2 , HONO, HCHO, CHOCHO and aerosols derived from MAX-DOAS measurements at a rural site in the central western 30 North China Plain and their relation to emission sources and effects of regional transport[END_REF]. Fig. 6 shows the principle of MAX-DOAS measurement. Most often, the scattering event occurs in the lower troposphere due to higher air density and higher particle loadings. For most MAX-DOAS observations, they can be assumed that the stratospheric absorption is the same in all spectra taken during one elevation sequence measurement. The MAX-DOAS technique analyses the recorded spectra using a DOAS method that separates the spectra as fast and slow varying spectral structures using a Levenberg-Marquardt (LM) fit. In the spectral fit, the rapidly varying part corresponds to the trace gas absorption features, and the slowly varying part is caused by Rayleigh and Mie scatterings.

O

Usually the output of the MAX-DOAS spectral analysis is a slant column density (SCD), i.e.

the integrated trace gas concentration along the light path through the atmosphere. To derive the trace gas vertical column density (VCD), a so called air mass factor (AMF) is applied, which is defined as [START_REF] Solomon | On the interpretation of zenith sky absorption measurements[END_REF] :

SCD AMF VCD  (1)
The AMF is usually derived from numerical simulations of the atmospheric radiative transfer. For MAX-DOAS observations, one basic prerequisite is the assumption that the same air parcels are probed by the different viewing directions for accurate analysis of tropospheric species. The MAX-DOAS data analysis can lead to large errors due to rapid change of air masses, in extreme cases even 'negative concentrations' might be retrieved, which is a major problem in the MAX-DOAS technique.

In the MAX-DOAS spectral analysis process, several trace gas absorption cross sections (rapidly varying part), a polynomial of 2-5 orders (slowly varying part), a Fraunhofer reference spectrum (FRS) and a Ring spectrum are involved. Here FRS is introduced to correct for the solar Fraunhofer structure that is due to absorption in solar atmosphere (c.f. Appendix 4). In most cases, spectra recorded at zenith direction of 90˚ have been used as background FRS. The Ring spectrum is used to correct the Ring effect named by J. F. [START_REF] Grainger | Anomalous Fraunhofer line profiles[END_REF] [START_REF] Grainger | Anomalous Fraunhofer line profiles[END_REF]. The Ring effect is mainly caused by rotational Raman scattering and manifests itself by reducing the optical density of the observed Fraunhofer lines observed at large SZA. This reduction is on the order of a few percents. The Ring spectrum can be modeled, as the main constituents of the atmosphere are nitrogen and oxygen with known rotational states [START_REF] Aben | The ring effect in skylight polarization[END_REF].

The MAX-DOAS technique has been widely used for measuring atmospheric vertical profiles of halogen oxide (BrO, IO, OIO, ClO), O 3 , NO 3 , NO 2 , SO 2 , HCHO and atmospheric aerosols in the past decades. MAX-DOAS observations are not only limited to ground-based applications, but also can be performed on different mobile platforms like cars, ships and airplane. For car measurements, the view at low elevation angles (i.e. at a few degrees) is often blocked by obstacles like buildings or trees. For airborne and ship observations, viewing angles close to the horizon might be used. For ship MAX-DOAS observations, vertical profile retrievals should be in general possible, but for airborne MAX-DOAS observations, vertical profile retrievals might be possible outside from polluted regions or at higher altitudes [START_REF] Wagner | Interactive comment on "Mobile MAX-DOAS observations of tropospheric trace gases[END_REF].

(2-2) Ground-based SAOZ SAOZ spectrometer is a passive remote sensing instrument that was developed in the mid-1980s [START_REF] Pommereau | O 3 and NO 2 ground-based measurements by visible spectrometry during Arctic winter and spring 1988[END_REF] to measure total vertical column amounts of O 3 and NO 2 at latitudes up to the polar circle [START_REF] Goutail | Total nitrogen dioxide at the Arctic Polar Circle since 1990[END_REF]. The SAOZ instrument is part of the international Network for the Detection of Atmospheric Composition Change (NDACC). It consists of a conical mirror used for sunlight collection, a commercial JobinYvon flat field spectrometer equipped with a concave holographic grating, and a detector operated at ambient temperature comprising a Hamamatsu 512 or 1024 diode array with a 25 or 50 mm entrance slit, respectively. The optical scheme of the SAOZ instrument is shown in Fig. 7. The spectral range is 300-600 nm with a spectral resolution of ~1 nm [START_REF] Vaughan | SAOZ measurements of NO 2 at Aberystwyth[END_REF]. The SAOZ observes the zenith sky with a FoV of ~30˚, measuring light scattered downwards from a range of altitudes. At twilight (SZA ~90˚) the zenith sky is illuminated mainly by molecular scattering from high altitudes, which travels a longer path through the stratosphere compared to a very short vertical path in the troposphere. Therefore, absorption features in the spectra measured at this position are heavily biased towards the stratosphere. This makes zenith-sky spectroscopy ideal for distinguishing stratospheric NO 2 from boundary-layer pollution. SAOZ technique uses the DOAS method to analyse the recorded spectra in order to retrieve vertical concentration profiles.

Conical mirror

Figure 7 Optical scheme of SAOZ instrument [START_REF] Vaughan | SAOZ measurements of NO 2 at Aberystwyth[END_REF].

The SAOZ can be also used for on-board balloon and satellite measurements. However, the SAOZ can only retrieve vertical columns of trace gases in the stratosphere, and is insensitive to the concentration variations of trace gases in the troposphere [START_REF] Pommereau | Stratospheric O 3 and NO 2 observations at the southern polar circle in summer and fall[END_REF].

Ground-based MAX-DOAS and SAOZ discussed above both only work in the UVvisible range, for IR applications, other ground-based techniques will be presented below.

(2-3) Ground-based FTS

A sun-tracker collects and couples the solar radiation after transmission through the atmosphere to a Michelson interferometer-based FTS (Fig. 8). An interferogram containing sunlight absorption information by atmospheric trace gases is recorded. Infrared absorption spectra of trace gases in the atmospheric column can be retrieved from Fourier transform of the interferogram [START_REF] Drissen | Imaging Fourier transform spectroscopy for astronomy[END_REF] and then the vertical concentration profiles of these atmospheric constituents can be retrieved from the atmospheric trace gas column absorption spectra with appropriate retrieval algorithms [START_REF] Rinsland | Long-term trend of CH4 at northern mid-latitudes comparison between ground based infrared solar and surface sampling measurements[END_REF][START_REF] Wunch | University of Toronto's balloon-borne Fourier transform spectrometer[END_REF][START_REF] Sussmann | Stratospheric and tropospheric NO 2 variability on the diurnal and annual scale : A combined retrieval from ENVISAT/SCIAMACHY and solar FTIR at the Permanent Ground-Truthing Facility Zugspitze/Garmisch[END_REF][START_REF] Hase | Intercomparison of retrieval codes used for the analysis of high-resolution: Ground-based FTIR measurements[END_REF][START_REF] Barret | Ground-based FTIR measurements of CO from the Jungfraujoch: Characterisation and comparison with in situ surface and MOPITT data[END_REF][START_REF] Zhao | Carbon monoxide column abundances and tropospheric concentrations retrieved from high resolution ground-based infrared solar spectra at 43.58N over Japan[END_REF]. Currently, there are two well-known international networks established for measuring vertical concentration profiles of atmospheric trace gases using ground-based solar FT-IR instruments : the Total Carbon Column Observing Network (TCCON) [76-78] established in 2004 [START_REF] Wunch | A method for evaluating bias in global measurements of CO 2 total columns from space[END_REF] and the Network for the Detection of Atmospheric Composition Change (NDACC) established in 1991 [START_REF] De Maziè Re | The Network for the Detection of Atmospheric Composition Change (NDACC): history, status and perspectives[END_REF]. TCCON uses the FTS to record near-IR broadband solar absorption spectra to determine column-averaged abundances of trace gases, such as CO 2 , CH 4 , N 2 O, HF, CO, H 2 O, and HDO, with a spectral resolution up to 0.02 cm -1 [START_REF] Wunch | A method for evaluating bias in global measurements of CO 2 total columns from space[END_REF]. Today there are around 26 operational TCCON sites (Fig. 9 upper). Their data can be used for validating data obtained from GOSAT (Greenhouse gases observing satellite) [START_REF]greenhouse gases observing satellite[END_REF], OCO-2 (Orbiting Carbon Observatory-2) [START_REF] Wu | Carbon dioxide retrieval from OCO-2 satellite observations using the RemoTeC algorithm and validation with TCCON measurements[END_REF], etc. The NDACC data is obtained from solar FTS spectra recorded in the mid-IR spectral range for the measurements of various constituents throughout the troposphere and stratosphere up to the lower mesosphere. The NDACC currently consists of 23 sites (Fig. 9 lower) with measurements dating back up to 2 decades. The NDACC data can also be used to validate atmospheric measurements from satellites, such as SCIMACHY aboard ENVISAT and TANSO (Thermal And Near-infrared Sensor for carbon Observation) on GOSAT [START_REF] Ostler | Multistation intercomparison of column-averaged methane from NDACC and TCCON: impact of dynamical variability[END_REF][START_REF] Sepúlveda | Tropospheric CH 4 signals as observed by NDACC FTIR at globally distributed sites and comparison to GAW surface in situ measurements[END_REF]. Compared to the ground-based MAX-DOAS and SAOZ measurements, the passive ground-based FTS simultaneously measures atmospheric components using their IR absorption spectra, while the measurements of ro-vibrational spectra in the IR request higher spectral resolution. FTS instruments typically sacrifice spectral resolution for more compact instrument size or for faster data collection time. Therefore, the amount of altitudinal information that can be retrieved from emission/absorption data collected with a FTS is limited.

Michelson interferometer

(3) Passive remote sensing technique based on aircraft and balloon platforms

Aircraft and balloon platforms refer to measurement instruments (such as MAX-DOAS, SAOZ and FTS) installed on aircraft [START_REF] Jacob | Validation of OMI tropospheric NO 2 observations during INTEX-B and application to constrain NOx emissions over the eastern United States and Mexico[END_REF] and balloon [START_REF] Durry | Atmospheric CH 4 and H 2 O monitoring with near-infrared InGaAs laser diodes by the SDLA, a balloon-borne spectrometer for tropospheric and stratospheric in situ measurements[END_REF] for high-altitude remote sensing.

The CARIBIC (Civil Aircraft for the Regular Investigation of the atmosphere Based on an Instrument Container) aircraft project is an approach to obtain detailed long-term observations over large sections of the globe [START_REF] Dix | Airborne multiaxis DOAS measurements of atmospheric trace gases on CARIBIC long-distance flights[END_REF], which uses the MAX-DOAS to measure vertical profiles. NO 2 vertical profiles have been retrieved in nadir slant viewing direction with a 100-200 m height resolution, and in both up and down viewing directions (±10˚) with a 400-800 m height resolution [START_REF] Dix | Airborne multiaxis DOAS measurements of atmospheric trace gases on CARIBIC long-distance flights[END_REF]. HIPPO (HIaper Pole-to-Pole Observations), another airplane campaign, includes a suite of sensitive sensors to measure vertical profiles of CH 4 and N 2 O on a flight path from the north pole to the south pole over the Pacific Ocean [10].

Balloon-based remote sensing instruments, such as balloon-based TELIS (TErahertz and submillimeter LImb Sounder) and balloon-based DOAS, can investigate stratospheric trace gas distributions with a vertical resolution of ~2-3 km below the balloon height [START_REF] Birk | TELIS: TErahertz and subMMW LImb Sounder-Project summary after first successful flight[END_REF].

Aircraft-based measurements can probe large latitudinal/longitudinal transsects in a short time without cloud interference. Vertical profile measurements by aircraft/balloon-based instruments are less affected by transport model errors, making them particularly useful in constraining surface fluxes. Aircraft/balloon-based techniques are valuable links between ground-based and satellite-based measurements [START_REF] Xu | Performance assessment of balloon-borne trace gas sounding with the Terahertz channel of TELIS[END_REF]. However, lower few hundred meters of the atmosphere, which contains a significant part of tropospheric species, are difficult to reach. Moreover, they could not provide continuous measurements due to limited flight missions.

In order to achieve flight-based measurement data at lower few hundred meters of the atmosphere, unconventional flight platforms can become very useful, like an unmanned aerial vehicle (UAV). UAVs are increasingly used in civilian applications, and a large variety of UAV platforms are now available as remote sensing platforms for scientific research [START_REF] Watts | Unmanned aircraft systems in remote sensing and scientific research: classification and considerations of use[END_REF].

UAV platforms offer great potential for collecting measurement data with high spatial and temporal resolutions.

Table 1 shows the comparisons among bove three kinds of platforms. In this context, ground-based measurement is high desirable.

III. Laser heterodyne radiometer

Laser heterodyne radiometer (LHR) is a ground-based passive instrument, like the FT-IR spectrometer, using sunlight as a spectral source for long-range, long-term and continuous remote measurements of trace gases in the atmospheric column. In comparison to the FTS, LHR is advantageous in terms of spectral resolution, sensitivity and transportability. This technique is particularly attractive in the mid-IR region, which corresponds to the emission or absorption spectra of many key atmospheric molecules. LHR technique exhibits the following merits :

(1) High spectral purity of laser emission line (~10 MHz), resulting in a high resolving power : /≈ 10 5 -10 7 , which makes that LHR's spectral resolution is not limited by the apparatus function, and only determined by the selected electronic filters. Commonly applicable higher spectral resolution (~10 -3 cm -1 ) would allow one to achieve high vertical resolution in vertical profile;

(2) Higher sensitivity (within a factor of 2-3 of the quantum limit), which allows lower detection limit of gas species with high precision;

(3) Higher vertical resolution due to very small coherent FoV, which makes LHR have ultrafine geographical coverage with less cloud interferences [START_REF] Weidmann | A fully integrated, miniaturized quantum cascade laser heterodyne radiometer for EO[END_REF];

(4) Compact instrumental dimension making LHR easy for field deployment. LHR (Fig. 10) is a kind of radiometer based on a heterodyne receiver that deals with input sunlight radiation collected from a telescope by mixing it with radiation of a local oscillator (laser) onto a photodetector used as a photomixer [START_REF] Smith | Evaluation of laser heterodyne radiometry for numerical weather prediction applications[END_REF]. The amplitude of the resulting beat signal from the photomixer varies with the absorption feature of atmospheric trace gases.

Scanning the local oscillator (LO) frequency across the absorption feature, atmospheric absorption spectrum can be obtained. The vertical concentration profiles of the target trace gases can be retrieved based on the measured absorption spectra in the atmospheric column with the help of an appropriate retrieval algorithm.

III.1 History of the LHR technique

Heterodyne history began in 1902 referring to R. Fessenden's patent for "wireless signalling" [START_REF] Fessenden | Wireless telephony[END_REF]. The term "heterodyne" was created by J. L. Hogan in 1913 when he published a paper entitled "The heterodyne receiving system and notes on recent Arlington-Salem tests" [START_REF] Hogan | The heterodyne receiving system and notes in the recent Arlington-Salem tests[END_REF] where it was suggested that only one wave was transmitted from the receiving station and a second frequency was then generated and this produced LO [START_REF] Jain | Laser heterodyne system for measurement of monir constituents in the atmosphere[END_REF]. For more than a century, heterodyning of electromagnetic waves, which produces a low-frequency beat note, has been widely used in radio wave engineering and instrumentation.

Heterodyning expanded in the field of optics even before the advent of lasers. As early as 1940s, A. T. ). The atmospheric ozone and CO 2 concentrations versus altitudes were obtained [START_REF] Courtois | Detection of thermal emission from atmospheric gases by laser heterodyne radiometry[END_REF][START_REF] Mouanda | Laboratory and atmospheric ozone measurements by infrared-laser heterodyne detection[END_REF].

A limitation of LHR systems using gas laser LOs as mentioned above is their highly restricted tunability. In contrast, TDLs providing much greater frequency coverage [START_REF] Hinkley | Long-path monitoring: advanced instrumentation with a tunable diode laser[END_REF] than gas lasers were very promising.

In 1971, emerging lead salt semiconductor TDLs were proposed to serve as tunable LOs for LHRs, hence allowing remote measurements of atmospheric species with greater frequency agility [START_REF] Hinkley | Detection of air pollutants with tunable diode lasers[END_REF]. Several early demonstrations were followed using gas cells in the laboratory. In 1977, R. T. Ku and D. L. Spears [START_REF] Ku | High-sensitivity infrared heterodyne radiometer using a tunable-diode-laser local oscillator[END_REF] Since the first experimental demonstration of a quantum cascade laser (QCL) emitting at 4.3 µm in 1994 [START_REF] Faist | Quantum cascade laser[END_REF], the laser's performance has greatly improved (wide operation wavelength range, high power level, room temperature operation [START_REF] Beck | Continuous wave operation of a mid-infrared semiconductor laser at room temperature[END_REF], and narrow spectral line width [START_REF] Williams | Kilohertz linewidth from frequency-stabilized mid-infrared quantum cascade lasers[END_REF][START_REF] Ganser | Investigation of the spectral width of quantum cascade laser emission near 5.2 μm by a heterodyne experiment[END_REF]). QCLs seem to have all the properties required for the development and the deployment of LHRs. The first heterodyne experiment with a QCL was carried out with the Köln tuneable heterodyne infrared spectrometer (THIS) [START_REF] Wirtz | THIS : a tuneable heterodyne infrared spectrometer[END_REF][START_REF] Sornig | Venus upper atmosphere winds from ground-based heterodyne spectroscopy of CO 2 at wavelength[END_REF].

These historical elements sketching the development of LHR techniques are by no means exhaustive, and starting from the mid 70's onwards, many works in the development and the deployment of LHRs have been reported. Progress has been continuously made toward the Earth's own atmosphere as well as astronomical atmosphere.

III.2 Local oscillator involved in LHR (a) Mid-IR LO

Laser LO is the key element in LHR. It's a limiting factor to the performance of the LHR.

The 3-5 μm and 8-12 μm atmospheric windows, which correspond to the emission or absorption resulting from strong fundamental ro-vibrational transition of numerous key atmospheric molecules, are very suitable for remote sensing of atmospheric trace gases.

Common laser sources being used as LOs in LHRs include color center lasers, CO and CO 2 gas lasers, lead-salt diode lasers, interband-transition diode lasers, and intraband-transition QCLs.

CO 2 gas laser is one of the earliest mid-IR lasers [START_REF] Menzies | Air Pollution : Remote detection of several pollutant gases with a laser heterodyne radiometer[END_REF] used as LOs for LHRs in the 1970s, with advantages of high laser power and narrower line width. However, CO 2 gas lasers were not continuously tunable in wavelength, which limits the heterodyne measurement at a small fraction (15%) of the CO 2 laser emission wavelength range in 9-12 μm. CO 2 gas lasers were also too bulky and large for field deployment.

Tunable lead-salt diode laser [134,[START_REF] Weidmann | Infrared 7.6 µm lead-salt diode laser heterodyne radiometry of water vapor in a CH 4 -air premixed flat flame[END_REF] was firstly used as a LO (at 10 µm ) in a LHR in 2002 to determine vertical stratospheric ozone distribution [START_REF] Sonnabend | Tunable heterodyne infrared spectrometer for atmospheric and astronomical studies[END_REF]. In 2003, D. Weidmann and co-workers used a 7.6 µm tunable lead-salt diode laser as a LO for on-line LHR measurement of high-temperature water vapor emission in a combustion process with high spectral resolution, which proves that LHR techniques are also relevant in combustion diagnostics [START_REF] Weidmann | Passive remote detection in a combustion system with a tunable heterodyne receiver : application to sulfur dioxide[END_REF]. However, the lead-salt diode laser requires cryogenic cooling to achieve single-mode operation, and the output optical power is relatively low, only about 0.1-0.5 mW. Thermal cycling and aging can easily cause changes in laser frequency. Meanwhile, the mode-hop-free spectral range of the lead-salt diode laser is very limited with a single laser.

The birth of QCL in 1994 [START_REF] Faist | Quantum cascade laser : Temperature dependence of the performance characteristics and high T 0 operation[END_REF] was a milestone for the development of modern LHRs [START_REF] Weidmann | Infrared heterodyne radiometry using quantum cascade laser as tunable local oscillator : application to atmospheric studies[END_REF][START_REF] Weidmann | Ground-based prototype quantum cascade laser heterodyne radiometer for atmospheric studies[END_REF] In the mid-IR, CW DFB QCL can cover more than 1% of the wavenumber around the laser center frequency (corresponding to a tuning range of a few cm -1 ) with output power up to 100 mW [START_REF] Darvish | Room-temperature, high-power, and continuous-wave operation of distributed-feedback quantum-cascade lasers at λ∼9.6μm[END_REF]. Recent advances on EC-QCLs have dramatically increased the accessible frequency range. Tuning ranges of ∼200 cm -1 have been demonstrated [START_REF] Wysocki | Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing[END_REF], and up to ∼400 cm -1 is within reach via the development of broad-gain QCL structures [START_REF] Capasso | High-performance midinfrared quantum cascade lasers[END_REF]. A LHR with an EC-QCL as a LO has been demonstrated in the laboratory to operate over a range larger than 100 cm -1 [START_REF] Weidmann | High-resolution broadband (>100 cm -1 ) infrared heterodyne spectro-radiometry using an external cavity quantum cascade laser[END_REF][START_REF] Tsai | Atmospheric vertical profiles of O 3 , N 2 O, CH 4 , CCl 2 F 2 , and H 2 O retrieved from external-cavity quantum-cascade laser heterodyne radiometer measurements[END_REF][START_REF] Weidmann | Hollow waveguide photomixing for quantum cascade laser heterodyne spectro-radiometry[END_REF]. This wide frequency tunning range is highly desirable for measurements of atmospheric multi-component. In additon, EC-QCLs can provide high optical output power up to 70 mW through distributed Bragg gratings for single-mode operation [START_REF] Chao | 633-nm tunable external-cavity diode laser with an intra-cavity glass plate as the fine-tuning device[END_REF].

Therefore, EC-QCLs with wide and fast frequency tuning capacity, high optical output power, compactness, long life time and room temperature operation [START_REF] Tsai | Atmospheric vertical profiles of O 3 , N 2 O, CH 4 , CCl 2 F 2 , and H 2 O retrieved from external-cavity quantum-cascade laser heterodyne radiometer measurements[END_REF][START_REF] Tsai | External-cavity quantum cascade lasers with fast wavelength scanning[END_REF][START_REF] Stupar | Fully reflective external-cavity setup for quantum cascade lasers as a local oscillator in mid-infrared wavelength heterodyne spectroscopy[END_REF] can be excellent LOs in LHRs.

(b) Near-IR LO

Though in the near-IR range, the overall line-intensities of target molecules are usually lower than those in the mid-IR (and the detectable species are less too). For some key species (such as CH 4 , CO 2 , H 2 O, etc.), the corresponding line-strengths are still strong enough. Meanwhile, in the near-IR owing to the progress in the telecommunications industry [START_REF] Weidmann | Atmospheric observations of multiple molecular species using ultra-high-resolution external cavity quantum cascade laser heterodyne radiometry[END_REF], high performance DFB lasers and photodetectors, fiber optic components, and fiber collimating optics are very attractive in developing compact and portable miniaturized LHRs for field applications (on ground, on aircraft, on balloon, etc.).

III.3 State of the art

The development of modern LHRs since 2010 is overviewed below :

In in the atmospheric column with a measurement accuracy of 8 ppm [START_REF] Wilson | Miniaturized laser heterodyne radiometer for measurements of CO 2 in the atmospheric column[END_REF] (Fig. 12). The incoming sunlight is modulated with an optical chopper and injected into the LHR receiver through a single-mode optical fiber. The sunlight is then superimposed with the light from the DFB laser (LO) in a 50/50 single-mode fiber coupler. The superimposed lights are photomixed in an InGaAs photodiode with a bandwidth of 5 GHz to generate a heterodyne signal. The use of optical fiber greatly reduces the difficulty of optical coupling alignment in free space and also the LHR system volume. reported a compact and lightweight 1.65 µm DFB laser-based LHR with a FoV of 0.005˚ [START_REF] Rodin | High resolution heterodyne spectroscopy of atmospheric methane NIR absorption[END_REF]. A single-mode silica fiber Y-coupler is served as a diplexer to combine the sunlight and the LO light, the beams mixed in the single-mode fiber are detected by using balanced detection, as shown in Fig. 13. LHR spectra of CO 2 and CH 4 were recorded with a spectral resolution of 2.5 MHz. Inversion algorithm applied to the spectrum of CH 4 resulted in a maximum mixing ratio of 2148±10 ppbv near the surface and a column density of (4.59±0.02)

×10 22 cm -2 .

IV. Aim of this work

The objective of the present PhD work is to develop a fully transportable mid-IR LHR for ground-based in situ measurement of trace gases in the atmospheric column.

Chapter 1 depicts the principle of LHR (Sections 1.1 and 1.2 This heterodyne signal is then square-law detected and fed into a lock-in amplifier (LIA), the output of the LIA is sampled by a laptop for further data processing.

Heterodyne absorption spectrum of atmospheric species can be recovered by scanning the LO frequency across the absorption feature (leading to change in intensity of the resulting radio frequency (RF) beat signal). The shape of the ground-recovered atmospheric absorption spectrum contains information on vertical distributions of the target absorbers. It is possible to retrieve trace gas abundances at different altitudes through a retrieval algorithm based on an appropriate inversion model [1,2].

The principle of LHR is schematically shown in Fig. 1.1, which mainly includes four parts : sunlight collection, photomixer, RF receiver and LIA.

Sunlight collection

An optical heterodyne receiver is, in effect, both a receiver and an antenna, which is constrained by antenna property [3]. In heterodyne detection, only a fraction of sunlight radiation contributes to heterodying. Indeed, only the part of the same extended sunlight beam that superimposes with the LO will contribute to the heterodyne power. The rest of the illuminating power will contribute to the continuous component and noise [3,4], as shown in For the simple case of a single flat mixing element, it is obviously necessary to maintain the wavefronts of both sunlight and LO in phase over the photosensitive area if efficient mixing is to be achieved. If an effective aperture of a mixer A T is illuminated normally by a plane wave LO, effective heterodyning will only occur for sunlight arriving from within a solid angle Ω S about the normal, given by antenna theory [3] :

2     S T A (1.1)
where λ is the radiation wavelength. The throughput is limited by the operating wavelength when the diameter of the collecting optics is fixed. If the effective aperture of the mixing element is known, the solid angle increases with the radiation wavelength, as shown in Fig. 1.2 (right). In the case of a LHR instrument which includes an optical system for collecting sunlight, the geometric restriction of the antenna theory can be modified as Fig. 1.3, which always follows the antenna theory [3]. Here, the solid angle through which a detector is sensitive to electromagnetic radiation is usually expressed by FoV. From Fig. 1.3, the geometric expressions of the solid angle Ω S and FoV in a LHR system can be approximately written as :

2 2 2 f R f A L S      (1.2) f R FoV   2 (1.3)
where f is the focal length of the collecting optics, R and A L are the radius and the area of the optics used for collecting sunlight radiation, respectively.

From Eqs. (1.1), (1.2), and (1.3), the FoV of a LHR system can thus be expressed by [5] :

D FoV      4 (1.4)
where D = 2R is the diameter of the collecting optics.

A smaller FoV would be advantageous for monitoring localized phenomena and increasing the number of useful observations between scattered clouds. Meanwhile, a FoV smaller than the FoV (~0.5˚) of the Sun ensures that it does not drift off the Sun throughout the day [6].

Heterodyne receiver

A heterodyne receiver consists of four basic elements, as follows (Fig. 1.4) : (1) Photomixer,

(2) RF amplifier and band-pass filter, (3) Square law detector, (4) Lock-in amplifier.

Photomixer

RF Amplifier

Band-pass Filter

Square Law Detector

Lock-in Amp 4 Schematic diagram of a heterodyne receiver. i is the resulting photocurrent from the photomixer; i IF is the IF component of the photomixer current i; i IF-B is the IF signal after amplification and band-pass filtering; P HET is the resulting power from the square law detector; S is the demodulated heterodyne output from the LIA.

IF=| -L| Output i i RF P HET S i RF-B     ) cos( 0 t A t E S S          t A t E L L L L   cos 0  Figure 1.

Photomixer

Classically, the total electromagnetic field E(t) (in [V/m]) entering the photomixer, as shown in Fig. 1.5, is the sum of sunlight radiation E S (t) = A S0 (ω)cos(ωt) and the LO radiation E L (t) = A L0 (ω L )cos(ω L t), i.e. [6] :

          ) cos( ) cos( 0 0 t A t A t E t E t E L L L S L S         (1.5)
where A L0 (ω L ) and A S0 (ω) are the amplitudes of electric fields of the LO and the sunlight, respectively, ω L is the LO frequency, and ω is the optical frequency of the sunlight that beats with the LO light.

The resulting photocurrent i(t) from the photomixer is proportional to the total optical intensity, i.e. to the square of the total electric field amplitude E(t) [7,8] :

          2 0 0 2 ) cos( ) cos( t A t A h e t E h e t i L L L S                                                     t t A A t A t A A A h e L L L L S L L L S L L S ) ( cos ) ( cos ) 2 cos( 2 ) 2 cos( 2 2 0 0 2 0 2 0 2 0 2 0               (1.6)
where η is the quantum efficiency of the photomixer, e = 1.6×10 -19 C is the elementary electric charge, h = 6.62607×10 -34 J• s is the Planck constant, and ν is the frequency of the radiation falling onto the photomixer.

The high frequency components (at 2, 2 L and + L ) and the constant DC components are filtered out, leaving only the signal (beat note) at the intermediate frequency ( IF =|- L |) for heterodyne detection. The beat note has an amplitude proportional to the product of the electric field amplitudes (A L0 (ω L ) × A S0 (ω)).

          t A A h e t i L S L L IF            cos 0 0 (1.7) Solar radiation LO i IF (t)     ) cos( 0 t A t E S S          t A t E L L L L   cos 0  Beam splitter

RF amplifier and band-pass filter

The heterodyne beat signal at the intermediate frequency ( IF =|- L |), contains the spectral information of the sunlight that can be amplified, detected, and analysed with appropriate RF electronics. Typically, the intensity of the beat signal delivered by the photomixer is weak and must be amplified by a RF amplifier. Furthermore, the spectral resolution (B in [Hz]) of the LHR instrument can be defined by the used RF electrical filter bandwidth of B/2. B is then the double-sideband bandwidth of the heterodyne receiver, and a LHR system will respond to radiation signals in both IF sidebands of the LO frequency (Fig. Therefore, the IF signal after the amplifier and the band-pass filter (assuming its cut-off frequency b is zero) can be expressed by [9] :

b v L - b v L  2 B b v L   B/2 B/2 0 2 B b v L  

Band-pass filter i IF-B (t)

B/2     ) cos( 0 t A t E S S          t A t E L L L L   cos
          t A A G h e t i L S L L B IF              cos 0 0 when B B L L                2 2 (1.8)
where G is the gain of the amplifier. A careful choice of filter's pass-band will be discussed in Chapter 5.1.2.1 related to system noise analysis.

Square law detector

The square law detector is a nonlinear element whose output is proportional to the square of the input, associated with an averaging device, often a low-pass filter [10]. After RF quadratic detection, the resulting signal power P HET is thus given by [9] :

          t A A G h e t i P L L L S B IF HET                    2 2 0 2 0 2 2 2 - cos         t P P G h e L L L S                    2 2 2 cos 4         2 2 cos 1 4 2 2 t P P G h e L L L S                       (1.9)
where    

2 2 0   S S A P 
is the optical power of solar radiation,    

2 2 0 L L L L A P   
is the LO optical power. After the averaging device (low-pass filter), the resulting signal power P HET is given by :

    L L S HET P P G h e P                 2 2 2
(1.10)

From Eq. (1.10), the following expression can be obtained : Thus, the heterodyne signal power (P HET ) is proportional to the product of the sunlight power (P S (ω)) and the LO power (P L (ω L )) within the LHR instrument bandwidth B [4]. In general, the sunlight power is weak, and the LO power is several orders of magnitude greater than the sunlight. Eq. (1.11) therefore shows that heterodyne detection provides a form of amplification of the sunlight power by a gain of P L .

    L L
    ) cos( 0 t A t E S S          t A t E L L L L   cos

Lock-in amplifier

In LHR, lock-in amplifier [12,13] is usually used for sensitive measurement (c.f. Fig. 1.1).

The sunlight is modulated through a mechanical chopper [6,14] in free-space configuration or an optical switch [15] in fiber-coupling configuration at a modulation frequency  ref .

LIA, referenced to this frequency  ref , only detects the heterodyne signal with frequencies at the reference frequency using phase sensitive detection (PSD), noises at other frequencies are removed by a low-pass filter (with a time constant RC) in the PSD and weak heterodyne signal is then extracted from noise at this reference frequency.

The output of the LIA is proportional to the integrated P HET through the transfer function of the low-pass filter in the LIA,   IF j H  as follows [6] :

    IF HET j H P S     (1.12)
As a basic approximation, we consider the RC filter model, its transfer function is well approximated by :

     IF IF j j H   1 1 (1.13)
where the time constant  = RC of the low-pass filter, and the corresponding cut-off frequency f c =  c / 2 = 1 / (2). Eq. (1.12) can thus be expressed by :

        L L S IF IF HET P P j G h e j H P S                        1 2 2 2 (1.14)
Therefore, heterodyne detection allows an "amplification" of the weak incoming signal (although there is no optical amplification involved). The beat signal at the intermediate frequency within the bandwidth of the photomixer contains all spectral information, and is processed further with a RF receiver. Atmospheric species absorption spectrum can thus be recovered by scanning the LO frequency across the absorption feature.

Heterodyne efficiency

The heterodyne signal given in Eq. (1.7) is established for the ideal case of monochromatic plane waves, phase front perfectly aligned, beam spot size fully matched, and perfectly coaligned onto the photomixer surface with their polarization state matched [16]. The general form of the heterodyne efficiency is given in Eq. (1.15), which bears similarity to overlap integrals, with the added dependence on quantum efficiency of the photomixer η, including its spatial distribution dependence [16,17].

                          0 0 0 0 * 0 * 2 0 * r S S r L L r L S het dr r E r E dr r E r E r dr r E r E r    (1.15)
where E L (r) and E S (r) are the LO and the sunlight field amplitude distributions on the photomixer with a radius of r 0 , respectively, and η(r) is photomixer response distribution.

Therefore, the heterodyne efficiency of photomixing of the sunlight beam and the LO beam is strongly conditioned by three main criteria influencing each other including [17][18][19][20] :

(1) Spatial distribution of the beams being mixed;

(2) Polarization-sensitive photomixing;

(3) Coupling of the mixed beams to the mixer.

Spatial distribution of the beams being mixed

The effective photomixing efficiency depends explicitly on the spatial distribution of the beams being mixed. The complete theoretical analysis of this issue has been addressed by S. C. Cohen [17] and for more particular geometries by K. Tanaka [19]. Let us take S. C.

Cohen's results in the case closest to what will be ours, namely, an incoherent solar beam having an uniform distribution and a Gaussian LO beam which is linearly polarized [17].

Beam spot size

In quasi-optics, a Gaussian beam is a beam of monochromatic electromagnetic radiation whose transverse magnetic and electric field amplitude profiles are given by the Gaussian function. It implies a Gaussian intensity (irradiance) profile. Mathematical expression for the electric field amplitude is a solution to the paraxial Helmholtz equation [21]. Assuming polarization in the x direction and propagation in the +z direction, the electric field in complex notation is given by [21] :

                                              z z R r k z k i z w r z w w x A z r E 2 exp exp , 2 2 2 0 0 (1.16)
where x is the unit vector, r is the radial distance from the center axis of the beam, z is the axial distance from the beam waist, i is the imaginary unit, k = 2π/λ is the wave number (in radians per meter) for a wavelength λ, A 0 = E(0,0), the electric field amplitude (and phase) at the origin at time 0, w(z) is the Gaussian beam width at which the field amplitudes fall to 1/e of their axial values, at the plane z along the beam, w 0 = w(0) is the waist size at z = 0, R(z) is the radius of curvature of the beam's wavefronts at z, and ψ(z) is the Gouy phase at z, an extra phase term beyond that attributable to the phase velocity of light. Fig. 1.9 shows a Gaussian intensity profile. At a position z along the beam (measured from the waist), the spot size parameter w(z) is

given by [21]:

  2 0 1            R z z w z w (1.17) where   2 0 w z R   is called the Rayleigh range.
The curvature of the wavefronts is zero at the beam waist and also approaches zero as z → ±∞. It is equal to 1/R where R(z) is the radius of curvature as a function of position along the beam, given by [21] :

                  2 1 z z z z R R (1.18)
From Eqs. (1.17) and (1.18), the curvature of the wavefronts can be expressed by : The coupling efficiency of two Gaussian beams is given by [20] :

    1 2 2     n z w z R   (1.19)
1 2 2 1 2 2 1 2 2 1 1 2 1 1 4                                        R R w w w w w w K   (1.20)
In heterodyne experiment, the wavefronts of a Gaussian beam (w 1 , R 1 ) and a plane beam From this perspective, the curvature R 2 of the wavefront approaches +∞, so the coupling efficiency of a Gaussian beam and a plane beam can be written as :

  1 2 1 2 1 2 2 2 1 1 2 1 4                                n w w w w w w K (1.21)
where

01 1 1 w w n  for     1 2 1 2 1 1     n z w z R   .
n 1 =6 n 1 =5 n 1 =4 n 1 =3 n 1 =2 n 1 =1 w  w  K Figure 1.
12 Coupling efficiency of a Gaussian beam with a plane beam.

The calculation of the coupling efficiency between a Gaussian beam and a plane beam is shown in Fig. 1.12. The maximum coupling efficiency K can be obtained when :

2 1 w w  (n 1 =1) (1.22)
The condition for maximum coupling efficiency requires w 1 =w 2 and the maximum coupling efficiency decreases as the spot size of the Gaussian beam increases, i.e. the increase of n 1 (w 1 /w 01 , Fig. 1.12 green dot). Moreover, a larger n 1 needs a larger value of w 1 /w 2 for obtaining the maximum coupling efficiency.

Therefore, for the purpose of high-efficiency heterodyne mixing of two light beams, it is necessary to make the beam sizes of the sunlight and the LO as close as possible.

Phase front alignment

The quality of the superposition of the two beams on the photomixer greatly has a significant impact on the mixing efficiency. In order to obtain a maximum light-induced photocurrent, the iso-phase planes of the solar radiation and the LO light must coincide with each other as well as the photosensitive surface of the photomixer i. e. the wavefronts of the sunlight field and the LO field must be confused such that the photocurrents induced are in phase.

The following is an analysis of the influence of the misalignment of the two beams on the coherent detection. It is assumed that both the sunlight and the LO are plane waves, and there is an angle Θ between their wavefronts, as shown in the Fig. 1.13. It is assumed that the photosensitive surface of the photomixer is a square having a side length of d. In the analysis, it is assumed that the LO beam is incident in a direction perpendicular to the surface of the photomixer, so that the LO field can be written as :

Solar radiation LO

  t i L L L e A t E  0  (1.23)
The sunlight wavefront has a mismatch angle with the LO wavefront, the beam is obliquely incident on the surface of the photomixer, and the sunlight field can be written as :

  x k t i S S S e A t E     sin 0  (1.24) let   sin k 
, then the above formula is written as :

  x t i S S S e A t E      0 (1.25)
The total electric field incident on the surface of the photomixer is :

      t E t E t E L S   (1.26)
and the instantaneous IF photocurrent generated by the photomixer (c.f. Section 1.2.1) is written by :

    dxdy e A A t i d d x t i S L IF S L       2 , 2 0 0 2    52   2 2 sin 0 0 2           d d e A A d t i S L S L (1.27) Because       sin 2   
, the magnitude of the instantaneous IF photocurrent is related to the mismatch angle Θ. Obviously when the sinc function  :

1 2 2 sin        d d (1.28)
i.e. Θ = 0, the instantaneous IF photocurrent reaches a maximum value.

In practice, the mismatch angle Θ is difficult to adjust to 0. In order to get the maximum IF output as possible, it is highly desirable to set Θ = 0 as possible. To satisfy this condition, it would be : The effect of the mismatch angle on the output of the optical heterodyning is plotted in the Fig. 1.14. As can be seen, the photomixing efficiency dramatically decreases with increasing the mismatch angle. A photomixer with a smaller size has a larger mismatch angle and vice versa (Fig. 1.14 left). The shorter the wavelength is, the stricter the angular requirement is, i.e. smaller mismatch angle is needed (Fig. 1.14 right). Therefore, optimal spatial alignment for heterodyne detection is highly desired. Due to this strict spatial alignment requirement, stray light or background radiation that do not meet this requirement will not contribute to the optical heterodyning, heterodyne detection exhibits thus a good spatial filtering performance.

2   d << 1 (1.29) i.e.  sin << d    (1.30)

Polarization-sensitive photomixing

It is well known that the heterodyne detection is sensitive to polarization due to the fact that the beat occurs when the field component of the sunlight beam is parallel to the polarization of the LO beam [23,24]. Since we use an unpolarized/incoherent sunlight, optical power of sunlight that can contribute to the heterodyne signal is thus halved.

Coupling of the mixed beams to the mixer

The last criteria is the spatial distribution of the mixed light beams on the photomixer (Fig.

1 .15). That is, the focusing full-angle 2θ of the incident beam should be less than the FoV of the photomixer, and the focused beam size 2ω 0 on the photomixer should be less than its optical receiving area.

Detection chain noise

In a heterodyne system, the detection chain noises originating from a photomixer and preamplifiers, which are independent of the LO laser power (P L ), include : (1) Johnson noise,

(2) Background noise, (3) Dark noise.

Johnson noise

Johnson noise is produced regardless of an applied voltage, and is generated by the random thermal agitation of electrons inside a conductor of photomixer and amplifier at equilibrium [25]. The Johnson noise in the receiver band is expressed by the mean-square noise current 2 J i :

             A A M M J R M T R T B i 0 2 k 4 = (1.31)
where k = 1.38×10 -23 J/K is the Boltzmann; R M and R A are the load resistance of the photomixer and the resistance of the amplifier, respectively; T M and T A are the noise temperatures of the photomixer and the amplifier, respectively; M is a parameter (≤ 1)

expressing an impedance mismatch between the photomixer and the amplifier [26].

When the photomixer is cooled and its Johnson noise is negligible compared with the noise from the amplification system. Eq. (1.31) can thus become :

A A J R M T B i     0 2 k 4 =
(1.32)

Background noise

Thermal radiation outside of the receiving bandwidth of the heterodyne receiver, but inside the total spectral range over which the photomixer will give a photocurrent response. On the other hand, the thermal radiation inside the receiving bandwidth of the heterodyne receiver, but outside the FoV of the heterodyne receiver will induce the photomixer to produce noise currents. It follows that the optical power spectrally and spatially outside the heterodyne receiver will affect the photomixer and generate a photocurrent. This photocurrent will not be amplified by the heterodyne detection but it provides a continuous background noise to the detected signal. The background noise can be expressed by the mean-square noise

current 2 BG i : 0 2 2 2 B P h e i B BG        (1.33)
where h is the Planck constant,  is the frequency, η stands for the quantum efficiency, e is the electric charge, B 0 is the bandwidth of the photomixer, and P B is the thermal radiation power radiating onto the photomixer.

The influence of the background noise can be reduced by the addition of spectral and spatial filters in the optical path of the thermal source and the condition P B << P L is then achieved. Therefore, the background noise (∝ P B ) can be rendered negligible compared with laser induced-noise (∝ P L , see 1.4.2).

Dark current noise

Dark current noise is a constant current which is due to the random generation of electrons and holes within the depletion region of the photomixer when no photons are incident on the photomixer [27]. The dark current noise in the photomixer is expressed by the mean-square noise current 2 DK i :

0 2 2 B i e i DK DK     (1.34)
where i DK is the average dark current of the photomixer.

Typically, dark current noise can be significantly reduced at low temperature and therefore can be ignored.

Laser-induced noise

In a heterodyne system, laser-induced noises, which depend on the laser power (P L ), include :

(1) Laser-induced shot noise, (2) Coherently detected thermal noise, (3) Laser excess noise.

Laser-induced shot noise

Shot noise, also called quantum noise, is caused by fluctuations of the detected photons, which obeys Poisson statistic. In electronics shot noise originates from the discrete nature of electric charge, and in photon counting in optical devices, it is associated with the particle nature of light.

In a LHR system, laser-induced shot noise arises due to fluctuations in the rate of arrival of LO photons, but an expression for it can be obtained by considering the shot noise in the LO radiation-induced current in the photomixer [26]. This current is dominated by i dc , which is the response of the photomixer to the incident LO power, so that the mean square laserinduced shot noise current 2 LSN i is proportional to the LO power on the photomixer and is

given by [11,26,28] :

0 0 2 2 2 2 B i e B P h e i dc L LSN                     (1.35)
and

L dc P h e i       (1.36)
where h is the Planck constant,  is the frequency, η stands for the quantum efficiency, e is the electric charge , P L is the LO power, and B 0 is the bandwidth of the photomixer.

Coherently detected thermal noise

Radiation power from any unwanted thermal source (e.g. emission from the atmosphere in a ground-based experiment) located in the FoV of the heterodyne receiver is coherently detected and amplified by the usual heterodyne "amplification" process if within the bandwidth of the heterodyne receiver [26]. In this case, the coherently detected thermal noise must also be considered. For a thermal source of temperature T B filling the FoV of the heterodyne receiver, the coherently detected thermal noise has the same expression as heterodyne signal (c.f. Eq. (1.10)) and it can be expressed by the mean-square noise current 2 CDT i [11,26] :

L TB CDT P P h e i            2 2 2   (1.37) 0 2 B h P B TB       (1.38) and 1 1 exp                      B B T k h   (1.39)
Substituting Eqs. (1.38) and (1.39) into Eq. (1.37), then :

0 2 2 2 4 B P h e i L B CDT           (1.40)
where h is the Planck constant, is the frequency, η stands for the quantum efficiency, e is the electric charge, k is the Boltzmann constant, P L is the LO power, P TB is the radiation power from any unwanted thermal source, and B 0 is the bandwidth of the photomixer.

The contribution from the laser-induced shot noise (Eq. (1.35)) and the coherently detected thermal noise (Eq. (1.40)) measured at the photomixer output can thus be expressed by :

  B L CDT LSN B P h e i i                2 1 2 0 2 2 2 (1.41) if hν  kT B , then 0  B 
, the laser-induced shot noise (quantum noise) dominates the coherently detected thermal noise, and vice versa.

In an 8 µm EC-QCL-based LHR system, the temperature of the thermal source T B (Eq. 1.39) is usually equal to the room temperature (300 K), the radiation frequency ν is 3.75×10 13 Hz and the quantum efficiency of the photomixer η is 0.5. In Eq. (1.41), the term 2•η•δ B due to the coherently detected thermal noise is thus calculated to be 0.0024 which is far smaller than the term '1' resulted from the laser-induced shot noise. Therefore, coherently detected thermal noise can be neglected compared to the laser-induced shot noise in the 8 µm EC-QCL-based LHR system.

Laser excess noise

Laser excess noise depends on the transmitted laser power within the measurement bandwidth centred on the detection frequency. Both mode competition and optical feedback to the laser due to scattering from components in the optical system influence the laser excess noise. The mean square laser excess noise current 2 LEN i is proportional to the square of the LO power on the photomixer [29] and can be expressed approximately as :

0 2 2 2 B P h e i L LEN              (1.42)
where h is the Planck constant, is the frequency, η stands for the quantum efficiency, e is the electric charge, P L is the LO power, and B 0 is the bandwidth of the photomixer.

Signal-induced noise

In a heterodyne system, the signal-induced noises, which depend on the source power (P S ), include : (1) Signal-induced shot noise, (2) Signal excess noise.

.3.1 Signal-induced shot noise

In a LHR system, signal-induced shot noise arises due to fluctuations in the rate of arrival of source photons and it can be obtained by considering the shot noise in the source radiationinduced current in the photomixer [26]. This current is dominated by S dc i , which is the response of the photomixer to the incident source power, so that the mean square shot noise current 2

SSN i

is proportional to the source power on the photomixer and is given by [16,26] :

0 0 2 2 2 2 B i e B P h e i S dc S SSN                     (1.43) and S S dc P h e i       (1.44)
where h is the Planck constant,  is the frequency, η stands for the quantum efficiency, e is the electric charge, P S is the source power, and B 0 is the bandwidth of the photomixer.

Signal excess noise

The signal excess noise depends on the transmitted source power within the measurement bandwidth. The mean square signal excess noise current 2 SEN i is proportional to the square of the source power on the photomixer and is given by :

0 2 2 2 B P h e i S SEN              (1.45)
where h is the Planck constant, is the frequency, η stands for the quantum efficiency, e is the electric charge, P S is the source power, and B 0 is the bandwidth of the photomixer.

Comparing Eq. (1.35) with Eq. (1.43) and Eq. (1.42) with Eq. (1.45), for P S ˂˂ P L :

2 SSN i ˂˂ 2 LSN i (1.46) and 2 SEN i ˂˂ 2 LEN i (1.47)
Therefore, if LO power is high enough, the signal-induced noise can be rendered negligible.

In order to enhance sensitivity of the LHR system, i.e. to reach a shot-noise-limited

2 J i ˂˂ 2 LSN i (1.48) i.e. A A R M T B     0 k 4 ˂˂ 0 2 2 B P h e L                (1.49)
then the required lowest limit on P L is given by :

L P > A A R M e T h        2 k 2   (1.50)
With given parameters in an 8 µm EC-QCL-based LHR system, i.e. ν = 3.75×10 13 , η = 0.5, M = 1, R A = 50 Ω and T A = 300 K, P L must be greater than about 0.32 mW to ensure laserinduced shot-noise-limited operation. Meanwhile, LO power has an additional caveat that this power needs not to saturate the photomixer preamplifier either [16].

Based on the above introduction of the noise sources we are now discussing on instrument SNR and its sensitivity in the following section.

Instrument SNR and sensitivity (limit of detection, LoD)

To characterize the performance of a developed LHR, a blackbody source (with high cavity emissivity of ~0.99) is usually used. In this case, the BB source power P S received by the LHR system can be calculated by [5] :

  0 2 2 , 2 1 B T I P S S          (1.51) and   S c h T I        2 3 2 ,
, and

1 - 1 exp                     S S T k h   (1.52)
From Eqs. (1.51) and (1.52), the received source power P S can be expressed by :

S S B h P          0 2 (1.53)
where κ is the overall optical coupling efficiency defined as the fraction of the incoming blackbody radiation passed by all the optical components in the instrument, which mainly accounts for transmission efficiency of the optics. I (, T) is the Planck equation (spectral radiance) for a blackbody at temperature T S , and λ 2 is the throughput of a single spatial mode [5]. The one-half factor gives reason for heterodyne detection is inherently a polarization dependent technique [30].

The heterodyne power obtained in the LHR system (c.f. Eq. (1.10)) is expressed by [9] :

L S IF P P h e i            2 2 2   (1.54)
The ideal laser-induced shot-noise-limited SNR of the LHR system at the output of the photomixer preamplifier is given by :

S S LSN IF B h P i i SNR               2 0 2 2 (1.55)
From Eq. (1.55), the final SNR of the LHR signal at the output of the RF filter with the bandwidth B/2 (B˂B 0 ) and an integration time τ is given by [9,26] :

                      B B h P B i i SNR S S B B LSN B B IF LHR 0 0 2 2 / 2 (1.56)
where τ is often the time constant in case using a LIA, the theoretical SNR increases with τ. overall optical coupling efficiency of the blackbody radiation. As can be seen, under this condition, the SNR of the LHR increases with the wavelength, i.e. the mid-IR is theoretically more favorable than in the near infrared. In practice, optical losses, instabilities of the solar image on the photomixer, and atmospheric effects degrade this SNR. In LHR, in order to improve the SNR, pass-band of the RF filter must be carefully chosen to filter out low frequency noise. In addition, according to the analysis in Section 1.3.1, making spot sizes of two beams as close as possible and phase front misalignment angle as small as possible can improve effectively heterodyne efficiency (Eq. (1.15)), thus increase the actual SNR.

A noise equivalent power (NEP in W/Hz) is introduced as a measure of the sensitivity of a LHR system. Considering the source power before post-detection, the NEP corresponds to the P S that gives a SNR of unity, i. e. Eq. (1.55) is equal to 1, in a one hertz output bandwidth [9,30,31] :

      h B P NEP SNR S 0 1 (1.57)
The sensitivity of the LHR system in terms of minimum detectable sunlight power can be defined by the limit of detection (LoD) [32]. From Eqs. (1.53) and (1.56), the LoD, P S,min (in W) of the LHR can be expressed by [7,30] :

   B h SNR P P LHR S S    min , (1.58)
Assuming a quantum efficiency of 0.5 and an integration time of 1 ms, the P S,min for a 8 µm QCL-based LHR at different resolutions is shown in Fig. 1.17. When the atmosphere is transparent at a frequency corresponding to a wavelength near 8 µm, with a 485 MHz bandwidth and a 1 ms integration time, the corresponding theoretical sensitivity of the LHR to source radiation is about 0.0347 pW obtained from Fig. 1.17.

Extraction of heterodyne signal using a lock-in amplifier

In a LHR system, the heterodyne signal resulted from photomixing of a broadband incoherent sunlight with a coherent laser LO in a photomixer is proportional to the product of the intensities of the sunlight and LO. The heterodyne signal's frequency is the difference frequency between the sunlight and LO frequencies at RF frequency. Molecular spectral absorption information in the sunlight can be extracted by recording the heterodyne signal by scanning the LO frequency. The heterodyne signal can be detected with the help of lock-in amplifier.

LIA is an effective device capable of recovering weak signal buried in noise [33,34] through removing the 1/f noise by using modulation techniques to shift the input signal away from the base band and perform the detection at a relatively high frequency domain [35]. This is usually realized by modulating the input signal at a specific reference frequency. Phase sensitive detection is then carried out at this reference frequency for the demodulation of the modulated signal within a narrow lock-in pass-band to remove 1/f noise [12]. A low-pass filter with an appropriate cut-off frequency is used to extract the mean value of the amplified signal. Meanwhile, both of heterodyne spectral line-shape and spectral line center will be affected by the low-pass filter, which is determined by the LIA time constant. The details related to this issue will be discussed in the following chapters.

In LHR, the sunlight radiation modulated with a light modulator (such as mechanical chopper or optical switch) at a modulation frequency is synchronously detected by a LIA for demodulation.

The most reported LHRs using LIAs for efficiently extracting the heterodyne signal are shown in Fig. 1.18. In general, heterodyne signal can also be extracted using digital signal processing (DSP).

AC-coupling part of the output signal from the photomixer includes total noise of the LHR system (such as detection chain noise and laser-induced noise) and heterodyne signals. In this way, a high-speed acquisition card is used to directly digitalize the output signal from the photomixer, and the heterodyne signal ( 2Het  related to P HET ) is extracted by subtracting the variance of the system total noises ( 2 Noise  ) (when there is no sunlight injection) from the variance of the heterodyne signal plus system total noise ( 2 Sum  ) (when there is sunlight injection) using DSP, that is [36] :

2 Noise 2 Sum 2 Het -    (1.59)

Comparing the LHR with a Fourier Transform Spectrometer

It is interesting to briefly compare the LHR with a Fourier transform spectrometer, which should have large optical path differences in order to achieve a high spectral resolution (e.g. a Bruker IFS 125HR FTS (an optical path difference of 256 cm) with a spectral resolution of 0.02 cm -1 ).

The SNR of a FTS can be expressed as [37] :

  D FTS A D B U T I SNR           , (1.60)
where U is the FTS throughput, ξ is the efficiency, B is the resolution, D* is the detectivity, and A D is the physical area of the detector element. Dividing the SNR LHR (Eq. (1.56)) by the SNR for the FTS, quantitative comparison between them can be realized by :

B D U A c h SNR SNR D FTS LHR 3 2 1                       (1.61)
The term in the bracket is a constant related to the system parameters, and the term out of the bracket shows that LHR is more preferable at longer wavelength and higher resolution (smaller B). Typical specifications for a commercial FTS operating at a wavelength of 10 µm, are : A D = 1 mm 2 , U = 0.01 cm 2 sr, ξ = 0.1, and D* = 8 × 10 10 cm Hz W -1 , and assuming an ideal LHR with a quantum efficiency η of 1 and an overall optical coupling efficiency of the source radiation κ of 1, the quantitative comparison between them in the resolution ranging from 30 MHz to 360 MHz is plotted in Fig. 1. 19. It shows that with the given conditions, an ideal LHR at wavelengths longer than 7.7 µm and resolutions below 200 MHz has a greater SNR than a FTS.

From atmospheric column absorption spectrum to vertical profile concentration

The atmospheric transmission spectrum obtained by the ground-based measurement (Fig.

(b)

) is the integrated transmission spectrum from all species along the optical path in the atmosphere (Fig. 1.20 (a)). The measured atmospheric transmission spectrum contains information on the height distribution of the absorber up to altitudes (typically 35 km) [38] at which Doppler effects overwhelm pressure broadening. It is possible to retrieve trace gas abundance at different altitudes (Fig. 1.20 (c)) using a retrieval algorithm, given a decent knowledge of additional atmospheric parameters, such as solar angle, atmospheric temperature and pressure, atmospheric composition, and refractive index [2].

Retrieval principle

The retrieval algorithm is generally composed of two parts : atmospheric radiative transfer forward model and inversion method in atmospheric vertical profile . Atmospheric Signature CODE (FASCODE), etc [41].

The spectrum measured by the ground-based measurement has a high spectral resolution (~0.001 cm -1 ), the forward model used for calculating an atmospheric theoretical spectrum should have a same or higher spectral resolution than the measured spectrum. Therefore, LBLRTM with a higher spectral resolution of less than 0.001 cm -1 [START_REF] Clough | Atmospheric radiative transfer modeling : a summary of the AER codes, Short Communication[END_REF]43] is desirable.

Inversion method in atmospheric vertical profile

The data retrieval is performed employing the optimal estimation method (OEM), introduced by C. D. Rodgers [48,49], in which the Bayesian statistics theorem is used to find the Gaussian probability distribution function (PDF) of the state of interest. The atmospheric transmission spectrum of the solar radiance can be calculated using a radiative transfer model F(x), called forward model, which describes the instrumental output by considering the atmospheric transmission spectrum of the solar radiance and the instrumental model. The relationship between pre-processed measured data and the atmospheric state vectors is described as :

     c b a x F y , , , (1.62)
Where y is the measurement vector, i.e. atmospheric transmission spectrum measured with the ground-based measurement; x is the state vector, considered in the forward calculation; ε is the measurement error vector; A second order polynomial baseline (with coefficients of a, b and c) represents the non-selective absorption and uncorrected power contributions in the target spectral region [50].

To solve for x in Eq. (1.62), the OEM data retrieval algorithm uses an iterative Levenberg-Marquardt [51][52][53] approach to minimize the cost function, χ 2 , which is a measure of the convergence of the fit with the measured data and the a priori knowledge, as defined in the following equation [54] :

            T i a a i a T i i x x S x x x F y S x F y         1 1 2   (1.63)
where x a is a priori state vector with an a priori covariance matrix S a based on the error definitions, x i is the state vector at the i th iteration, and S ε is the measurement error covariance matrix based on the standard deviation of the measurement vector. The iterative state vector x i+1 is calculated using the following equation :

            i a a i i T i i T i a i i x x S x F y S K K S K S x x               1 1 1 1 1 1 1    (1.64)
where K is the Jacobian matrix (or weighting functions) describing the sensitivity of the forward model to the state vector, and λ is the LM parameter.

A flow chart for data retrieval is shown in Fig. 1.21, with the inputs of atmospheric parameters (i.e. vertical profiles of pressure, temperature, H 2 O continuum, and atmospheric species) [START_REF] Kaiser | Fast weighting functions for retrievals from limb scattering measurements[END_REF]45], the spectroscopic parameters (i.e. line position, line intensity, pressure line shift, and broadening parameters [46] those can be taken from the HITRAN 2016 database), the instrument parameters (i.e. noise performance, gain, and the ILS function), a priori state vector (i.e. an initial guess for the vertical profiles of target species that can be taken from ECMWF (European Center for Medium Range Weather Forecasts) [START_REF]European Centre for Medium-range Weather Forecasts[END_REF] or WACCM), and solar position (i.e. zenith angle for ray trace path calculation), the atmospheric transmission spectrum of the solar radiance (y 0 ) combined with a baseline and the corresponding weighting function (K) are calculated by the forward model. In the inversion model (OEM), given the measured and pre-processed measured spectrum (y), the a priori covariance matrix (S a ), and the error covariance matrix (S ε ), the forward model is iteratively called to minimize the cost function χ 2 (Eq. (1.63)) following LM algorithm (Eq. (1.64)). In a well-conditioned retrieval, the ultimate cost function (χ 2 ) should be close to the number of the measurement vector and the inversion program will yield a vertical concentration profile of target gas in the atmospheric column.

Baseline treatment

The solar spectra obtained by the measurement system include system background baseline, in order to obtain an absolute atmospheric absorption spectrum for retrieving vertical profile, the system background baseline should be determined.

In case of known regular laser scanning waveform (sine waveform or rectangular waveform), the baseline in the absence of absorption can be estimated (1) by selecting spectral points excluding absorption peaks and fitting these points with polynomial function;

(2) by fitting a baseline from near-by, non-absorbing wavelengths [14];

(3) in case of LHR baseline treatment, using a wavelength-modulated (WM) LO laser can (i) provide baseline-free spectra, a superior SNR (so lower limits of detection), and better precision and consistency than the conventional approach; (ii) open the door for cost-efficient wide spectral range LHR in the near future [55,56].

Vertical resolution

One of the basic parameters in an algorithm for atmospheric profile retrieval concerns the vertical resolution that is a measure of the smallest altitude over which an independent information can be obtained by the measurement system. In order to estimate the vertical resolution of the measurement system, an important quantity of the retrieval describing the sensitivity of the retrieved state x to the true state vector x t , i.e. averaging kernel (AK) matrix A is considered [57] :

    K S K K S K S x x A T T a t 1 1 1 1            (1.65)
Width of the AK can provide the vertical resolution of the measurement system at a certain altitude and it can be quantified using a spread function, which is well defined by G. Backus and F. Gilbert [58] and expressed by :

          2 2 2 ' ' , ' ' , ' 12     dz z z A dz z z A z z z s (1.66)
Substituting Eq. (1.65) into Eq. (1.66), the width of the AK at altitude z can be estimated [57],

therefore the vertical resolution of the retrieval is obtained.

The vertical resolution is closely associated with SNR and spectral resolution of the measurement system [59]. The system SNR influences the error covariance matrix S ε which is used for estimating the width of AK (c.f. Eq. (1.65)), thereby influencing the vertical resolution estimated by the width of AK. The spectral resolution of the measurement system influences the width of the weighting function (K) used in the retrieval algorithm, thereby affecting the vertical resolution generated by the algorithm. In addition, as the spectral resolution increases (instrument bandwidth (B) decreases), the SNR decreases (c.f. Eq.

(1.56)). In a realistic measurement system, a compromise between the spectral resolution and SNR should be made to achieve a vertical resolution as high as possible.

Conclusion

In this chapter, the principle of LHR has been presented. Through heterodyne detection, atmospheric absorption spectrum can be recovered by scanning the LO frequency across the absorption feature. Then, the heterodyne efficiency of two light beams in free-space LHR dependant on three optical criteria has been discussed in detail. The high heterodyne efficiency of the LO beam and sunlight beam can be obtained when phase fronts are perfectly aligned, beam spot sizes are fully matched, and beams are perfectly co-aligned onto the photomixer surface with their polarization state matched. Based on the analysis of the three major noise sources in a LHR, the LO power conditions for shot-noise-dominated heterodyne detection, shot-noise-dominated SNR and the corresponding instrument sensitivity have been discussed. SNR comparison of instrumental performance in terms of SNR between the LHR and the FT-IR has been made and it illustrates that the theoretical SNR of the LHR is more preferable over that of the FT-IR instrument at longer wavelengths and higher spectral resolutions with the given system condition. At the end of this chapter, vertical profile retrieval algorithm for retrieving vertical concentration profile from the measured atmospheric spectrum as well as the vertical resolution have been briefly described.

In the next chapter, practical instrumental considerations and the specifications of the devices involved in the LHR will be introduced and discussed.

Chapter 2 Mid-IR LHR instrumental consideration and configuration

Objective

In this chapter, practical instrumental considerations and specifications of the devices involved in our mid-IR LHR system (Fig. 2.1) are introduced and discussed.

Two systems for sunlight collection to the LHR receiver, including : (1) free-space telescope system, and (2) fiber coupling system, will be presented as well.

Key devices involved in a mid-IR LHR

Sun-tracker

Sun-tracker system is usually used in a LHR instrument to real-time follow the movement of the Sun for sunlight collection. The tracking mechanism of a sun-tracker is generally depicted in Fig. 2.2. The sun-tracker mainly composes of a servo system (including a 4-quadrant detector [1] (or a camera [2]) and a servo control loop), a zenith stepping motor (adjusting zenithal angle θ 2 ) and an azimuth stepping motor (adjusting azimuthal rotation angle θ 1 ).

During initial operation, the zenith and azimuth stepping motors coarsely point the tracker to the calculated position of the Sun (through a solar position algorithm based on the local GPS coordinates and time of day). Then a 4-quadrant detector generates an error signal as a result of an unbalanced solar power distribution and different sunlight beam shapes on four identical photodiodes which compose the 4-quadrant detector [3]. The servo control loop uses this error signal to drive the two stepping motors to center the Sun's spot on the center of the 4-quadrant photodetector with the help of an optical system consisting of two elliptical plane mirror 1 (M1) and mirror 2 (M2), as indicated in Fig. 2.2, in the sun-tracker. The zenithal and azimuthal angles are considered correct when the center of the Sun's spot is consistent with the center of the 4-quadrant photodiode.

Accurate and precise tracking of the Sun is required for remote sensing of the atmosphere in order to avoid significant bias at the data retrieval stage. Indeed, the retrieval of vertical profile of trace gas from an observed solar transmission spectrum is highly sensitive to the effective air mass sounded [4]. For LHR measurement it is also necessary to keep a stable sunlight power. So the center of the Sun's spot must be perceived on the servo system for a precise tracking, that is, the FoV of the sun-tracker is larger than the Sun's angular diameter (9 mrad), as shown in Fig. 2.2. Therefore, a sun-tracker with a high tracking accuracy and a large FoV is preferable. The Sun's spot is observed by a camera. An image processing software (called CamTracker [2]) calculates the position of the center of the Sun related to the input aperture of the collection system, and provides feedback signal to the sun-tracker stepping motors to point the optical system to the Sun center with a tracking accuracy of 0.0167˚. This kind of sun-tracker with a NA (Numerical Aperture) of 0.0087˚ is mostly designed for Bruker's FT-IR spectrometer for ground-based measurements of trace gases in the atmospheric column. The sun-tracker can be operated in two modes to follow the Sun's movement : (1) Calculation mode : when the sun-tracker is just starting up or the Sun is absent, tracking mode automatically changes to the calculation mode which will coarsely calculate the Sun's position (including zenith and azimuth angles) based on the received information from the GPS sensor on latitude, longitude, date and time. (2) Sun-sensor mode : once the Sun is within the FoV of the sun-tracker, tracking mode switches to this mode. A 4-quadrant detector and an internal learning track function will accurately detect the Sun's radiation (and hence its position) and will compensate for misalignment of the sun-tracker to the Sun position with the help of a closed-loop control system of the sun-sensor, even if the tracker is not oriented or levelled properly. In general, in order to maintain the highest tracking accuracy possible, two tracking modes will be automatically switched according to the solar radiation conditions. This sun-tracker is equipped with an adjustable instrument mount which allows fine optical alignment of the optical setup installed on this mount for sunlight collection.

Based on the specifications of above three kinds of sun-trackers, summarized in Table 2.1, the EKO sun-tracker is selected for use in the present work to collect sunlight with a higher tracking accuracy and lower price.

Local oscillator (LO)

The LO is the key device for a high-performance LHR. The characteristics of the laser source used as the LO determine the working spectral range (and thus the target molecule being measured) and the performance of the LHR. The following laser properties should be considered : emission frequency, output power, emission line width, frequency stability, single-mode tunability, and wavelength-dependent baseline.

In When the LO laser frequency is appropriately scanned across the target molecular absorption line, the changes in the resulting RF beat signal amplitude correspond to the molecular absorption feature that is thus restituted from the total absorption of the sunlight by all molecules in presence in the atmosphere. [6]; lower: absorption spectra of HONO [8] and N 2 O 5 [7].

Wide tuning range of more than some tens of cm -1 of the used EC-QCL as the LO is interesting, which offers the capacity of our LHR instrument to monitor multi-species or/and broadband absorption/emission. Fig. 2.11 shows major molecules present in the frequency tuning region of the used EC-QCL (based on the HITRAN database [6], the GEISA database [7] and our laboratory measurements [8]).

The performance of the EC-QCL source, in term of laser emission line width, single mode wavelength tunability and wavelength-dependent baseline, has been evaluated via concentration measurement of N 2 O produced in a chemical catalytical reaction process (described in Chapter 3).

Photomixer

Photomixer used for mixing LO radiation and sunlight to generate a heterodyne signal is a core component of the LHR. In order to sensitively detect weak mid-IR sunlight intensity (in the range of µW) with high SNR, the responsivity and the detectivity of the photomixer with a lower noise density must be as high as possible. Meanwhile, a photomixer with a wider bandwidth can provide not only a faster response time but also a high flexibility for the choice of filter pass-band of the RF receiver. In addition, a DC component output of the photomixer can be used to monitor baseline variation in heterodyne signal (mainly due to the variation in the LO power). Therefore a photomixer with both DC (for monitoring LO power variation) and AC (for heterodyne RF signal) components, which can be separated through a bias-T at the photomixer output, would be a favorable option. Currently, two photodetectors are potentially suitable for use as photomixer for 8-µm LHR.

(1) DC-coupled photovoltaic detector PVMI-4TE-8 (VIGO System S.A.) equiped with a four-stage thermoelectrical cooler and integrated with a preamplifier (MIP-DC-250M-F-M4) (Fig. 2.12 left). It has a FoV of 35˚. wavelength.

The upper 3 dB cut-off frequency is 195 MHz with a current responsivity of 0.226 A/W and a detectivity of 8.3E+9 cmHz 1/2 /W (at =8 µm), as shown in the Table 1. Fig. 2.12 (right)

shows its typical spectral performance.

(2) AC-coupled fast photovoltaic detector PVI-4TE-10.6 (VIGO System S.A.), four-stage thermoelectric cooled with a FoV of 35˚ (Fig. 2.13 left). The upper 3 dB cut-off frequency is 800 MHz with a current responsivity of 4.2 A/W and a detectivity of 5E+9 cmHz 1/2 /W (at =8 µm). The integrated preamplifier exhibits an electronic pass-band of 1 kHz-500 MHz.

RF receiver

Heterodyne signal at radio frequency from the photomixer is further processed by a back-end electronic RF receiver containing band-pass filter, RF amplifiers and a square law detector, as shown in Fig. 2.1.

Band-pass filter

Spectral resolution of the LHR system is in general determined by the bandwidth of the used band-pass filter, which may be easily changed to meet the spectral resolution requirements of particular measurements. Bandwidth and the cut-off frequency of the filter can be adjusted according to the noise density spectrum in the beat note, analyzed using a signal analyser (N9000B, CXA X-Series, Keysight, Inc It would be preferred to select an amplifier with a higher gain, a pass-band covering the bandwidth of the RF signal, and a NF as low as possible.

Square law detector

In order to rectify the RF beat signal, a square law detector is used, which plays a role of envelope detection. The filtered and amplified RF beat signal is passed to a Schottky diode (Model 8472B, Keysight Inc.), as called square law detector because its output is proportional

6 Lock-in amplifier

In order to improve the SNR of the LHR signal, lock-in amplifier is usually used. The key specifications of the used analog lock-in amplifier (Model 5110, AMETEK, Inc.) are listed in Table 2.5.

In order to perform phase-sensitive LIA detection, sunlight is mechanically modulated using a chopper. To avoid any truncation of sunlight by chopper slot aperture, sunlight beam size should be smaller than the slot aperture of the chopper. In our designed LHR system, the shaped sunlight beam size is about 12.5 mm. Therefore, a 10-slot blade with a widest aperture of about 13 mm is usable. An optical chopper (Model MC1F10HP, Thorlabs, Inc.) is used. It provides chopping frequencies ranging from 20 Hz to 1 kHz, with a frequency fluctuation of 20 ppm/˚C. As presented in Section 2.4, the used photomixer is AC-coupled with a frequency range of 1 kHz to 500 MHz, the chopper modulation frequency is set to 1 kHz to match the pass-band of the photomixer. [10]. Longer time constant τ can significantly filter out the noise, but it also results in blueshift of the spectral line center (shifting to the frequency scan direction / decrease in wavelength) and distort the line-shape (becoming broadened and asymmetric) [10,11].

The frequency shift δ can be approximately expressed by [12] :

     sc dt d   (2.2)
where dν/dt= sc (in [cm -1 /s]) is the frequency scanning speed, for frequency scan in continuous mode, it is the ratio of the frequency scanning range  scan to the scanning period T (in [s]) that is the reciprocal of the scanning frequency.

In order to avoid this unwanted effect, the LIA time constant  has to be appropriately chosen with respect to the time  scan needed for scanning through the halfwidth  HWHM of the absorption line profile, which depends upon the frequency scanning speed  sc .

Simulations of the impact of  have been performed in order to find optimal  with respect to the experimentally applied frequency scanning speed. The effective transfer function of a LIA can be equivalent to a LP filter [13], as shown in Figure 2.16. According to Kirchhoff's Laws and the definition of capacitance :

      dt t dVout RC t V t V out in   - (2.3)
where R is the resistance; C is the capacitance. For simplicity, assuming that samples of the input and output are taken at evenly spaced points in time separated by Δt, Eq. (2.3) can be expressed in terms of V out at time k, V in at time k and V out at time k-1 :

        t k V k V RC k V k V out out out in      1 - (2.4)
Rearranging terms in Eq. (2.4) gives a recurrence relation :

91                             t RC RC k V t RC t k V k V out in out 1 (2.5)
The first term on the right side of Eq. (2.5) is the contribution from the input, and the second term is the inertia from the previous output. This differential model of the LP filter described in Eq. (2.5) provides a way to determine the output data based on the input and the previous output values.

Based on Eq. (2.5), the effect of the LP filter is simulated by using a pseudocode algorithm with the help of Matlab. In the simulation, V in is a Hitran simulation spectrum of CH As can be seen from Fig. 2.17, when the scanning time ΔT scan ( HWHM / sc ) is 9-23 times of time constant the output spectrum (red) is consistent with the input spectrum (black).

The scanning time ΔT scan (Table 2.6 in blue bold) as a function of the time constant τ (Table 2.6 in red bold) is plotted (Fig. 2.18 square dot). The mathematical relationship between the time constant τ and the scanning time ΔT scan is obtained from a linear fit (r 2 =99.25), as shown in Fig. 2.18 :

        14 SC HWHM scan T (2.6)
Based on Eq. (2.6), with respect to the given frequency scanning speed in the continuous mode and to the halfwidth of the spectrum to scan, the reasonable scanning time ΔT scan should be approximately 14 times of the LIA time constant τ in order to efficiently reduce the noise without significant shift and distortion of the line-shape. In case of scanning laser frequency in point-by-point tuning mode, time-domain function characteristic of the low-pass filter at time k could be considered as follows :

         / exp 1 t t V t V in out     (2.7)
Plot of V out (t) versus V in (t) with time constant τ is shown in Fig. 2.19. As can be seen, when the time is 2.5 times time constant (τ), V out (t) is 91.8% of the input V in (t), while when the time is 6 times time constant (τ), V out (t) is 99.8% of the input V in (t). Therefore, when tuning laser frequency in point-by-point mode, a time interval (i.e. the time between two sampling points) longer than ~6 times of the LIA time constant  has to be used to avoid deformation of line-shape of the spectrum [14,15].

LHR configurations

The devices involved in a LHR have been introduced and characterized in the previous section, configurations of the PoC of mid-IR LHR being developed are discussed in this section. Fig. 2.20 shows two configurations used in the present work for the development of a LHR deployable for in situ ground-based measurements of vertical concentration profiles of atmospheric trace gases : (1) using heliostat located on a roof terrace (University Paris VI) to direct sunlight through a free-space telescope system to a developed LHR receiver which allows us to test, characterize and improve its performance in the first stage of the LHR development; (2) using an EKO sun-tracker to couple sunlight through a fiber to the LHR receiver, which makes the LHR truly transportable for in situ measurement anywhere.

95

Heliostat

LHR receiver

EKO sun-tracker

Fiber coupling system Free space telescope

Sunlight collection using a free-space telescope cage system

In order to well couple the sunlight coming from the heliostat (c.f. Chapter 4.3.1), a Thorlabs 60 mm cage assembly system is used to realize a free-space telescope (Fig. 2.21). For LHR measurement it is preferable to collect as much sunlight radiation as possible, therefore, a mirror reflector with a large aperture diameter of 50 mm is used to well collect sunlight from the heliostat (with a clear aperture of 78 mm) and then direct the collected sunlight to the LHR receiver. Whereas, if the sunlight beam size is too large, the focused beam size as well as the focusing angle by a lens will exceed the size and FoV of the used photomixer. In order to match the requirement for the size and FoV of the used photomixer (c.f. Chapters 1.3.3 and 2.2.1.2), the incoming sunlight with a beam size of 25 mm for heterodyne detection is chosen. A telescope in combination with an adjustable diaphragm (LCP50S) is designed to constrain the sunlight beam size while keeping enough sunlight power. The adjustable diaphragm located in front of the telescope is used as aperture stop for the lens 1, and the amount of reflected sunlight admitted is controlled by the opening diameter of the diaphragm. Sunlight beam emerging from lens 2 is directed to a beam splitter on which it is superimposed with the LO beam. The free-space telescope system with a 50 mm diameter mirror reflector collecting sunlight radiation at 8 μm provided a FoV of ~0.2 mrad (0.011˚) for LHR system.

Sunlight beam contraction and laser beam expander

The LO beam (Gaussian beam) from the EC-QCL has a pre-collimated size of 2.5 mm that is 10 times smaller than the sunlight beam size of 25 mm, which results in a beam coupling efficiency K of only 3.92% (c.f. Eq. (1.22)). In order to realize high-efficiency mixing of two light beams, it is necessary to match the beam size of the collimated sunlight to that of the collimated LO beam as close as possible (c.f. Chapter 1.3.1.1).

A 2× beam contraction of sunlight to reduce the sunlight beam size by a factor of 2 and a 5× beam expander to enlarge LO beam size by a factor of 5 are designed, which can make two light beams having the same beam size of about 12.5 mm, so as to ensure a maximum beam coupling efficiency. A sunlight beam contraction and a laser beam expander systems are designed using Kaplerian Telescopes. Kaplerian beam contraction/expander design consideration can be expressed by the following equations :

Magnification power 2 1 f f  (2.8)
Optical track length of the telescope 12 ff  (2.9)

where ƒ 1 and ƒ 2 are the focal length of two positive lenses, respectively. Design using two positive lenses meets the magnification requirements (Eq. (2.8)) without exceeding the designed overall system size (30 cm × 30 cm determined by Eq. (2.9). As illustrated further, these equations are first order equations, lens thickness and focus optimization might cause slight deviation from these ideal values.

Lens clear aperture also needs to be taken into account during the selection, as the lens size must be two times the incoming beam size in order to avoid any beam truncation.

(

1) Design of a 2× Kaplerian beam contraction and a 5× Kaplerian beam expander

A two-singlet Kaplerian telescope involving two lenses of f 1 =150 mm and f 2 =75 mm with a reasonable system size less than 300 mm long is designed for the 2× beam contraction.

Regarding the 5× beam expander, a Kaplerian telescope system using two lens of f 1 =20 mm and f 2 =100 mm is realized to meet the expander requirement.

It's worth noting, in a two singlet Kaplerian telescope system, wavefront quality would increase with increasing optical track, i.e. a combination of a 20-mm and a 100-mm lens would have a better wavefront quality than that of the combination of a 10-mm and a 50-mm lens for the same magnification power. In addition, the quality of the wavefront is improved by using a lens with a plane surface, such as plano-convex or plano-concave, rather than one with curvature on both surfaces. With plano lenses and a Kaplerian layout, orienting the convex surface towards the input beam tends to avoid the laser damage from the first plano surface, even if it's anti-reflection coated.

As the maximum beam size is also limited by the clear aperture of the lens, a 50 mm The distance between two lenses is optimized in two systems using Zemax in order to obtain the same emerging beam size of 12.5 mm (c.f. IMA semi-diameter in Tables 2.8 and 2.9) in both systems. 25 mm and 2.5 mm (c.f. STO semi-diameter in Tables 2.8 and 2.9, respectively) are set as input beam sizes with normal incident angle for sunlight beam contraction and for laser beam expander.

After optimization of the distance between two lenses (so called the thickness of surface 3), optimal distance between two lenses for the beam contraction and the beam expander are 282.2 mm and 144.1 mm, respectively.

Coupling of sunlight and LO beams to the mixer

According to the last criteria mentioned in chapter 1.3.3, the focusing angle 2θ (Fig. 2.24) of the light beam on the detector should be less than the FoV of the detector (35˚), and the focused size 2ω 0 would be less than the optical receiving area of the detector (0.5 mm × 0.5 mm). These parameters are both dependent upon the incoming sunlight beam size.

After optimization of beam expander and beam contraction with Zemax sequential mode, two optimal designs are integrated into Zemax non-sequential mode to make a final simulation and optimization of the entire system related with the optimal position. The lens editor and system layout are shown in Table 2.9 and Fig. 2.24, respectively. The optimal distance between the focusing lens and the photomixer detector is 52.3 mm. In order to make sure that the size and the focusing angle 2θ of the beams emerging from A portable EKO sun-tracker is used for the development of a fully transportable LHR. A mid-IR fiber is employed to couple solar radiation to the LHR receiver (Fig. 2.28). The mid-IR fiber coupling system, installed on the sun-tracker, includes lens 1 (in CaF 2 , f1=100 mm, D1=25.4 mm), associated with a Ge-filter to filter out radiation out of the spectral region of interest to minimize shot noise resulting from the signal source. Sunlight is focused by lens 1 into a polycrystalline fiber (NA=0.3 corresponding to an acceptance half-angle θ of 17.46˚ that is bigger than the half focusing angle of 7.47˚ of lens 1). The beam emerging from the fiber is collimated with lens 2 (in CaF 2 , f2=50 mm, D1=12.7 mm) and directed, in free-space, toward a beam splitter on which it is superimposed with the LO beam.

Test of the fiber coupling and sun-tracking performance

In order to test the coupling ability of the polycrystalline IR-fiber as well as to test the suntracker performance, measurement of the sunlight radiation was carried out over 5 hours on the roof of the IRENE (Innovation Recherche en Environnement) platform in Dunkerque (51.05˚N/2.34˚E).

μm) spectral regions, respectively. As can be seen, the trends of the two curves are roughly the same. In addition, the measured mid-IR solar radiation is around 38% of the global solar radiation, the difference from empirical value (43%) is mainly resulted from the PIR-fiber transmission of about 54% and optical coupling of the sunlight to the fiber. This experiment confirms the coupling ability of the polycrystalline IR-fiber and the tracking performance of the sun-tracker.

Conclusion

In this chapter, instrumental considerations and device specifications for design of a LHR, such as sun-tracker, blackbody, LO laser, photomixer, RF receiver (amplifier, band-pass filter, and square law detector), and LIA are introduced. Two sunlight collection configurations including free-space telescope cage system adapted to a heliostat and mid-IR fiber coupling system adapted to an EKO sun-tracker are considered and designed. The polycrystalline mid-IR fiber coupling sunlight system is tested and evaluated, which confirms the fiber coupling ability and the tracking performance of the sun-tracker.

Two LHR prototypes have been developed during this PhD works for field measurements : (1) a proof of concept mid-IR LHR involving a free-space cage system for sunlight coupling, and (2) a fully transportable LHR involving a polycrystalline IR-fiber coupling sunlight system.

because CO 2 is a valuable industrial gas for chemical industrial applications and power generation [1]. For this purpose, CO 2 should be as pure as possible. Purification of CO 2 can be performed through the oxyfuel-combustion which allows one to obtain a rich CO 2 stream with the highest purity (80%-98%) [2]. In an oxyfuel system, the combustion flow consists of O 2 and CO 2 . This Process emits also water vapor (H 2 O), unburned components such as carbon monoxide (CO) generated by incomplete combustion and nitrogen monoxide (NO) due to the oxidation of nitrogen (N 2 ) included in the fuel. Purifying CO 2 in an exhaust flow from the oxyfuel-combustion can be realized through the reduction of NO to N 2 by oxidizing CO into CO 2 over catalysts [2], as shown in Eq. (3.1) below [4] :

2 NO + 2 CO → 2 CO 2 + N 2 (expected process) (3.1)
However, products from the chemical process above is, like any chemical reaction, depending upon the reaction conditions (quantity of NO and CO, temperature, pressure, presence of oxygen and water vapor or not), kind of catalyst (active phase, metal dispersion, support type) and synthesis method, etc. N 2 O may be a by-product from the above NO-CO reaction [3] :

6 NO + 4 CO → 4 CO 2 + 2 N 2 + N 2 O (unexpected process) (3.2)
As N 2 O is a very powerful greenhouse gas with a global warming potential of 300 times greater than CO 2 , it is therefore necessary to optimize the catalytic reaction conditions to minimize the N 2 O production.

In the present work, tunable diode laser absorption spectroscopy (TDLAS) technique is applied to in situ monitor the production of N 2 O during the catalytic reaction of NO with CO.

Experimental details

N 2 O monitoring by long optical path absorption spectroscopy

The experimental setup is shown in Fig.

Frequency metrology and N 2 O absorption spectrum retrieval

The N 2 O absorption signal was recorded versus the data point number when scanning the EC-QCL frequency around 1261.0598 cm -1 using PZT scan mode. For the conversion of this absorption signal (a) to an absorption spectrum (d) (Fig. 3.3), interference fringes from a home-made Fabry-Perot etalon with a free spectral range (FSR) of 1 GHz (~0.0333 cm -1 )

were recorded (b) and used to determine the relationship between the data point number and the corresponding frequency in wavenumber (c). The absolute frequency was determined with the help of the N 2 O absorption frequency provided by the HITRAN database [5].

N 2 O concentration retrieval

N 2 O concentration can be determined based on the Beer-Lambert law using known spectral parameters (such as absorption frequency, line intensity, etc.). In the present work, the N 2 O concentration was deduced from a calibration curve of concentrations vs. integrated absorbances (over the scanned spectral range [6]). For this purpose, N 2 O samples with different standard concentrations were produced using a high-precision gas dilutor (Model PPA 2000M, Calibrage Inc.).

A N 2 O cylinder with a standard concentration of 1000 ppmv (C initial ) with different flow rates D 1 was mixed with N 2 gas (at a fixed flow rate D 2 ) in the gas dilutor. The concentration of the diluted N 2 O (C final ) was calculated using the following equations :

K C C initial final /  (3.3) 1 2 1 ) ( D D D K   (3.4)
where K is the dilution factor, and D The multi-pass cell was initially rinsed with pure nitrogen (N 2 ) before the measurements where k = 7.7656E-4.

Based on this calibration formula, the ambient N 2 O concentration was determined to be about 325±7 ppbv. The total relative uncertainty of about 4% is mainly attributed to the uncertainties in the linear fit (Δk/k ˂ 2 %) and in the Voigt profile fitting (ΔA I /A I ˂ 2 %).

Laser line width evaluation

The line width of the EC-QCL emission being used as a LO plays a key role in the spectral resolution of the LHR. This parameter was evaluated in the present work using spectroscopic method. As shown in Fig. 3.5, Voigt profile was fitted to an experimental absorption line of 6.13 ppm N 2 O at a pressure of 120 mbar. In Voigt fit, the line width w L is resulted from pressure induced collision broadening (Lorentzian line width, Δν L ), while the line width Δw G is the convolution of the Gaussian line width (Δν G ) due to Doppler effect and the line broadening related to instrument function (laser line width, Δν LA ). The Voigt line width (Δν V ) can be expressed as follows [11] :

  2 2 2 2 / 1 2 2 2166 . 0 5346 . 0 ) 2166 . 0 ( 5346 . 0 LA G L L G L L V v v w w w                   (3.6)
where the Lorentz line width, Δν L (FWHM, for Full Width at Half Maximum) was calculated to be 0.017035 cm -1 [5] at 120 mbar. The Gaussian line width, Δν G of 0.00236 cm -1 was calculated from Eq. (3.7) [9] :

M T G 0 7 - 10 16 . 7       (3.7)
with ν 0 the absorption center frequency (1261.0598 cm -1 ), T the working temperature (300 K), and M the molecular mass (44 g/mole).

Based on the fitted Δw G value of 0.00238 cm -1 , the laser line width Δν LA can be given approximately by [10] :

2 2 G G LA v w v      (3.

Measurement precision and limit of detection (LoD)

Stability of an analytical instrument is an important parameter that affects the detection sensitivity and the measurement precision. Signal averaging is usually used to improve the detection sensitivity and the measurement precision. However, due to the instability of the instrument (such as changes in light intensity, laser wavelength shifts and detector dark noise drifts, temperature drifts, moving fringes, changes in background spectra, etc.), any actual system is only stable for a limited time, i.e. an optimal averaging time should be determined via an Allan variance analysis [7] in order to determine the max. averaging number, i.e. the best measurement precision. shows the efficient white noise reduction by signal averaging within a maximum averaging time (system stability time) of about 236 s, which is mainly limited by the temperature and current stability of the QCL controller, but also constrained by other factors : stability of the optical setup (optical cell), or of the injected gas mixture. The corresponding measurement precision is 5.2 ppbv, leading to a relative uncertainty in measurement precision of 0.5%.

After 236 s, the Allan deviation increases (blue dashed line), i.e. the instabilities of the instrumental system nevertheless counterbalances the noise reduction given by timeconsuming average.

It's worth noting that this max. stabilization time of 236 s evinces also that the stability time of the used EC-QCL is at least as good as 236 s, which is very suitable for acquisition of LHR spectra (~ minute per spectrum). In the present work on monitoring a chemical reaction, a measurement precision of 10.8 ppbv (corresponding to a relative precision uncertainty of 1.1%) in 12 s was used to real-time track N 2 O production.

Experimental results and discussions

N 2 O evolution in catalytic reaction of NO with CO

The catalytic reaction of NO with CO over a Pt/SiO 2 catalyst in the temperature range of 50-500 ˚C was performed, N 2 O production was real-time monitored and analyzed using the developed EC-QCL sensor.

A typical N 2 O absorption spectrum recorded during the process of NO reaction with CO over a Pt/SiO 2 catalyst at 190 ˚C is shown in Fig. 3.9. It was recorded at a pressure of 120 mbar in the multi-pass cell with 240 spectral averages in 12 s. Based on the real-time monitoring of N 2 O concentration, optimal catalytic reaction condition for zero N 2 O production was experimentally determined [12].

Conclusion

In this chapter, the performance of an EC-QCL, that will be used as a LO in the LHR system, was evaluated in terms of laser emission line width, single-mode wavelength tunability, stabilization of the LO source and wavelength-dependent baseline. Based on the analysis of the measured N 2 O absorption spectra, the EC-QCL emission line width of 9.2 MHz was deduced. A stable operation time of the LO as good as 236 s was estimated using Allan variance analysis, it is suitable for LHR measurement of molecular absorption spectrum. The EC-QCL is mode-hop free continuously tunable with a smooth baseline. In fact, in a LHR instrument, spectral baseline is mainly determined by the laser (LO) power variation when scanning the laser wavelength across the target molecular absorption feature. It's thus highly desirable to have a laser power induced spectral baseline as smooth as possible in order to obtain high quality retrieval of atmospheric LHR spectrum. Radiation from a blackbody (BB, MODELS 67030, Newport Inc.) is collected and collimated with off-axis parabolic mirror (OAPM) 1 (f1 = 120 mm) and OAPM 2 (f2 = 75 mm). The BB beam is filtered by an optical filter (in Germanium in order to limit the bandwidth of the incident radiation and let only the transmission of the radiation at wavelengths longer than 7 µm and shorter than 12 in our case to minimize detected source shot noise [1]). Amplitude modulation of the injected BB beam is made at 1 kHz using a chopper located at the real focal point of OAPM2. It is then directed to a 5%R / 95%T beam splitter (in CaF 2 ). The BB beam will be superimposed with the LO beam from the EC-QCL (TLS-41000-MHF, Daylight solutions Inc.) which is size-expanded by two OAPMs (f3 = 12.7 mm and f4 = 38.1 mm), intensity-controlled and polarization-adjusted using a wideband IR polarizer (2 µm-12 µm, PGC-5, Innpho. Inc.). The combined beams are focused by OAPM 5 (f5 = 12.7 mm) onto a VIGO photomixer (PVI-4TE-10.6, VIGO System S.A.).

The beat note signal at |- L | in the radio frequency (RF) domain, generated from the photomixer, enters the RF receiver through a 27-33 MHz band-pass filter (Model 15542, Mini-Circuits ® ) followed by 2-stage low noise amplifiers (Model ZFL-500LN+, Mini-Circuits ® ) with a gain of 24 dB each. After that, the amplified beat signal is connected to a square-law Schottky diode (Model 8472B, Keysight Inc.) for power measurement of the RF signal that is proportional to the square of the input beat signal amplitude. The output signal from the square law detector is demodulated with a lock-in amplifier (LIA, Model 5110, AMETEK Inc.). A National Instruments data acquisition card (PCI 6251, NI Inc.) is used to digitalize the output signal from the LIA via a LabVIEW program. The data is then transferred to a laptop for further data processing.

LHR performance characterization

Beat signal generation

Beat signal was generated by mixing the blackbody (67030, Newport Inc.) radiation and the EC-QCL (LO) light (the frequency was set at a non-absorption position to avoid any air absorption within the optical path). Time series measurements of the RF signal from the lockin amplifier were carried out. During the experimental measurements, the effective LO power-induced amplitude measured with the photomixer was 2.5 V. Time constant of the lock-in amplifier was set at 1 s and using LP filters (12 dB/oct).

SNR of the beating signal

SNR of the generated beat signal was experimentally determined to investigate the quality of the generated beat signal. Based on the measurement of a beat note amplitude of 79.82 µV and a noise level (1 standard deviation) of 0.67µV in the beat note (Fig. 4.2), a SNR of ~119 was deduced for the generated beat signal. Blackbody temperature was set at T BB = 1000˚C. Throughout the optical system up to the photomixer, overall optical coupling efficiency (κ) of the blackbody radiation in the freespace LHR receiver is 0.82, and it is mainly resulted from a silver-plated OAPM (assumed reflectance ~0.97), two gold-plated OPAMs (assumed reflectance ~0.98), an optical filter (transmission ~0.975), a beam splitter (transmission ~0.95) and a BaF 2 wedged window in front of the photomixer (transmission ~0.95). The quantum efficiency of the photomixer η is 0.5 at 8 µm (provided by the manufacturer). The LHR double side bandwidth is 12 MHz and the time constant of the LIA is 1 s. Under these conditions, at fixed LO frequency (1242.3 cm -1 or 3.73×10 13 Hz), the calculated ideal SNR (c.f. Eq. 1.57 in Chapter 1.5) is :

1 exp ideal         kT h B SNR     356 (4.1)
This value is different from the experimentally deduced value of ~119. The reason for this kind of difference will be discussed in Chapter 5.1.2.1.

Beating level vs. the LO power

Beat signal level as a function of the LO (EC-QCL) power was experimentally investigated

Laser heterodyne spectrum of CH 4 4.2.2.1 CH 4 absorption line selection for sensitive and selective heterodyne measurement

Spectral interference between atmospheric species, in particular with ubiquitous water vapor (H 2 O) and carbon dioxide (CO 2 ) in the atmosphere, is a serious issue in a complex environment. Selection of suitable spectral lines for field test should be carefully addressed. Based on the comparison and analysis, the CH 4 absorption lines (shown in Table 4.1)

were selected in the present work for heterodyne measurement of atmospheric CH 4 absorption.

Laser heterodyne spectrum of CH 4 absorption at 8 µm

In order to validate the spectroscopic performance of the developed LHR receiver, laser heterodyne spectrum and direct absorption spectrum of CH 4 at 8 µm were simultaneously measured and compared.

In this work, laser heterodyne spectrum of CH 4 absorption at 1233.46 cm -1 was recorded with the experimental conditions as follows :

-

Frequency scanning speed vs. time constant of the LIA

The time constant (τ) in the LIA is a very critical parameter that impacts on noise suppression and absorption line-shape of the measured LHR spectrum. Longer time constant τ can significantly reduce the noise, but it also results in a shift of the spectral line center and distorts the line-shape [3]. In order to minimize such undesired effects, the time  scan for scanning through the halfwidth ν HWHM of the absorption line should be at least equal to 14 times of the time constant τ of the LIA (c.f. Chapter 2.1.6).

Experimental investigation on BB-based heterodyne spectra using different  and  sc combination was carried out. Heterodyne spectra of CH 4 were recorded using four combinations of different  and  sc (Table 4. As can be seen, selection of the LIA time constant should be well matched to the scanning speed of the LO frequency as well as the scanning time. When the time constant is too small, the noise will increase. While longer (than the optimal one) time constant would result in reduced absorption depth, in shift in absorption center frequency and in distortion of absorption line-shape.

Comparing above four optimal combinations for heterodyne detection, summarized in In principle, the relationship between the scanning time (ΔT scan ) and the LIA time constant (τ) should be (c.f. Chapter 2.1.6) :

        14 SC HWHM scan T (4.2)
According to ΔT scan and τ in Table 4.7, the combination of the scanning time of 137 ms and the time constant of 1 ms meets well Eq. ( 4.2) which can efficiently reduce the noise without causing obvious shift and distortion of the line-shape, and is consistent with our spectral analysis as discussed above. This combination was therefore selected for our further LHR measurements.

LHR involving a telescope system for free-space coupling of sunlight

In order to couple the sunlight, collected by the heliostat on the QualAir platform, to our LHR, a Thorlabs 60 mm cage assembly system was utilized for a free-space coupling telescope system. Cage assembly system using four rigid steel rods on which optical components can be mounted along a common optical axis, provides a convenient way to construct stable optomechanical systems with an established line of precision-machined building blocks designed for high flexibility and accurate alignment.

The used cage system for sunlight coupling consists of a mirror mounted in a rotating cube to reflect the sunlight from the heliostat to our LHR, a diaphragm used to control the sunlight beam size, and two lenses (in CaF 2 , f1 = 150 mm and f2 = 75 mm) used for 2× beam contraction, as shown in Fig. 4.13.

Preliminary field test results of the developed PoC LHR

LHR baseline treatment

To retrieve the atmospheric vertical column, baseline treatment is a key issue which needs to be seriously considered. Traditional baseline treatment in applied spectroscopy using an absorption cell/cavity is to vacuum the cell and then fill the cell with nitrogen or zero air in the same experimental conditions to measure target molecule-free baseline. This method is, however, no longer applicable for open-path remote sensing like LHR monitoring. According to the formula (P HET  P S × P L ), the heterodyne signal intensity (P HET ) is proportional to the product of the sunlight intensity (P S ) and the LO laser power (P L ). Since the frequency scanning range of the LO EC-QCL is very small (~1 cm -1 ), the sunlight power can be considered as a constant. The baseline feature of the LHR spectrum can be reasonably considered as determined by variation in the LO laser power during frequency scan.

In the present work, frequency scan of the used EC-QCL is realized by applying a sinewave signal to a PZT element that scans the laser external cavity. Compared to LHR working with a DFB laser as a LO whose frequency is scanned using a sawtooth-wave signal, the baseline feature in our case is more complex. In addition, structured baseline resulting from dysfunction of our used LO EC-QCL is inevitable at some frequencies of interest. Therefore it is unable to describe the baseline with a standard curve fitting. In this study, blackbody radiation was used to replace sunlight which allowed us to record the baseline (rather than LO laser power variation curve) of the heterodyne spectrum.

Sunlight-coupled heterodyne spectral signal was recorded (Fig. 4.16 (b)), and under the same experimental conditions (LO power), blackbody-coupled heterodyne spectral signal (baseline) was recorded (Fig. 4.16 (c)). As can be seen, both of these spectra have similar variation features and both are similar to the LO variation baseline (Fig. 4. 16 (a)) which shows that the LHR spectral baseline is mainly determined by the LO power variation when scanning the LO frequency. Fig. 4. 16 (a) shows also that the used LO power variation is not a regular sine-wave signal applied to the PZT.

Heterodyne measurement of atmospheric CH 4 absorption spectrum

Atmospheric CH 4 absorption signal was field extracted using the developed LHR. In this study, LHR receiver parameters were set as follows : LO (EC-QCL) was scanned using PZT scan mode around 1242.00 cm -1 with a scanning frequency of 250 mHz. The scanning voltage is 3.0 V with an offset of 1.6 V. Electronic filter bandwidth is 6 MHz (27-33 MHz), and sensitivity and time constant of the LIA are 100 mV and 1 ms,respectively.

In Fig. 4.17 In order to confirm this CH 4 LHR spectrum, under the same experiment conditions, the

Conclusion

In this chapter, a PoC mid-IR LHR was developed and its performance was evaluated and

Performance characterization of the LHR prototype

SNR of the beating signal I. SNR of the LHR using fiber coupling system

In order to characterize the LHR performance using a fiber coupling system for sunlight collection, investigation in terms of SNR of the LHR signal was performed using a calibrated blackbody source. In this study, the blackbody's temperature was set to 1000 ˚C. Time series The theoretical shot-noise-limited SNR of the LHR can be expressed by Eq. (5.1) [2] (c.f. Eq. 1.57 in Chapter 1.5). This equation can be used to assess the experimental LHR performance when referenced to the ideal shot-noise-limit. In other words, it corresponds to the expected performance of an ideal LHR in which shot noise is the sole noise [3] :

1 exp                     T k h B B h B P SNR het s het          (5.1)
where the overall optical coupling efficiency κ is defined as the fraction of the incoming signal radiation transmitted through all the optical components to the photomixer [3]. For the blackbody, this accounts for two CaF 2 lenses (transmission ~0.92 each), the polycrystalline IR-fiber (transmission ~0.54), the Germanium lens (transmission ~0.99), the beam splitter (transmission ~0.95), the silver-plated OAPM (assumed reflectance ~0.97) and the BaF 2 wedged window in front of the photomixer (transmission ~0.95) which results in an overall coupling efficiency of 0.396. The heterodyne efficiency η het of photomixing of the sunlight beam and the LO beam is considered to be 1 in the ideal case (c.f. Chapter 1.3), the quantum efficiency η of the photomixer provided by the manufacturer at this wavelength is 0.5. Under these conditions, given a LHR double side bandwidth of 485 MHz (for a RF pass band of 27.5-270 MHz) and 1 s time constant of the LIA at a LO frequency (1242.3 cm -1 or 3.73×10 13 Hz), a shot-noise-limited SNR of about 1430 was obtained. The theoretical shotnoise-limited SNR is 3.4 higher than the measured SNR at a photocurrent of 610 µA, or a factor of 0.29 in theoretical SNR is observed. The factor of 0.29 (=419/1430) may come from the unexpected performance of the developed LHR.

Please note that in the following experiment description, the LO and BB power will both be expressed as photocurrent (in [µA]).

I.1 Noise sources in LHR system

In order to understand the difference between the measured and the calculated ideal SNRs, the noises in various parts of the LHR system were investigated with the help of a signal analyzer (N9000B, CXA X-Series, Keysight, Inc.). In this study, the parameters of the signal analyzer were set as Table 5.1. where the RBW (Resolution BandWidth) is the frequency span of the final filter applied to the input signal in the signal analyzer. Smaller RBW provides finer frequency resolution. The VBW filtering is a time-domain low-pass filter, mathematically equivalent to the mean or average. The main effect of the VBW filter is to smooth the signal and decrease noise. The VBW (Video BandWidth) affects therefore the displayed signal quality.

In this study, the total noise density N total ( Hz nV /

) of the LHR system can be expressed by (c.f. Chapter 1.4) :

2 2 2 total SIN LIN Det N N N N    (5.2) 2 2 2 LEN LSN LIN N N N   (5.3) and 2 2 2 SEN SSN SIN N N N   (5.4)
where N Det , N LIN and N SIN are the noise from the detection chain , the laser-induced noise and signal-induced noise, respectively. The laser-induced noise includes laser-induced shot noise N LSN and laser excess noise N LEN , respectively. While the signal-induced noise includes signal-induced shot noise N SSN and signal excess noise N SEN .

The contribution of each type of noises in the above expressions is discussed below in detail.

(1) Noise from the detection chain (N Det )

As mentioned in Chapter 1.4.1, noise from the detection chain N Det includes the background noise, the Johnson noise resulted from the amplifier associated to the photodetector, and the dark noise. It can be measured when there is no light incident on the detector.

In order to identify noise sources, signals at the RF output of the photomixer were measured with the signal analyzer under different conditions :

(A) input of the signal analyzer directly connected to a resistance of 50 Ω (Fig. Noise from the RF output of the photomixer within its pass-band of 1kHz-500 MHz was analyzed using the signal analyzer, as shown in Fig. 5.6 upper, at different LO photocurrents (note : here the signal analyzer background noise has all been subtracted).

The system total noise density N total in [ Hz nV / ] (Fig. Based on the laser-induced noise N LIN deduced as shown in Fig. 5.7, laser-induced shot noise and laser excess noise are studied in detail.

(2.1) Laser-induced shot noise (N LSN )

Voltage V SN and current I SN of the laser-induced shot noise can be calculated with Eqs. (5.8) and (5.9), respectively [4] :

    A I R V V SN ti SN   (5.8)     B A I e A I DC SN      6 10 2



(5.9) and

    ti DC DC R V V A I / 10 6    (5.10)
where R ti = 6000 V/A is the transimpedance of the photomixer, e = 1.602×10 -19 C is the electric charge, B = 5×10 8 Hz is the bandwidth of the photomixer over which the noise is considered, I DC is the DC LO photocurrent induced by the LO laser power in the photomixer, V DC is the DC LO voltage induced by LO laser power monitored at the output of the photomixer and 10 6 represents the unit conversion from V to µV. From Eqs. (5.8) (5.9) and (5.10), the laser-induced shot noise density N LSN (in

[ Hz nV /
]) can be expressed as [5] : (5.11) where 10 9 represents the unit conversion from V to nV and 10 -6 represents the unit conversion from µA to A. 5.8, (1) red line) were 0.9 times and 0.9 times the laser-induced shot noise N LSN (Fig. 5.8, (4) black circle), respectively. The total noise of the LHR system N total exceeds thus the laserinduced shot noise N LSN by (using Eqs. (5.2) (5.3) and (5.4)) :

        A I R A I e B V V Hz nV N DC ti DC SN LSN              396 .
    LSN LSN LSN LSN LEN LSN Det total N N N N N N N N           62 . 1 9 . 0 9 . 0 2 2 2 2 2 2
(5.12)

The system total noise N total is 1.62 times laser-induced shot noise N LSN , a correction factor  1 of 0.62 (=1/1.62) is obtained for the theoretically calculated SNR under ideal shotnoise condition.

(2) The overall optical coupling efficiency κ of 0.40 for the blackbody radiation, based on the transmission of each optical component given by the manufacturer, would be overestimated. The measured overall optical coupling efficiency was about 0.27, and this difference between 0.27 and 0.40 in κ may be due to the long-time exposure of these optical components to a humid and salty environment at the seaside. An additional correction factor  2 of 0.68 (=0.27/0.40) was obtained.

(3) The heterodyne efficiency η het of 1 for the ideal case (c.f. Chapter 1.3) would be over estimated. The difference in shaped beam sizes of sunlight (12.5 mm) and LO light (7.5 mm) caused a heterodyne efficiency of ~0.8 (c.f. Fig. 1.12). As well the photomixer has a small photo-sensitive area of 0.5×0.5 mm 2 , even a small mismatch angle would result in a heterodyne efficiency of ~0.9 (c.f. Fig. 1.14 left). An additional correction factor  3 of 0.72 (= 0.8×0.9) was achieved.

Based on the above analysis, a total correction factor  exp for the theoretical SNR, resulted from the above reasons, is :

 exp = 1 × 2 × 3 = 0.30 (5.13)
This value is comparable to the factor of 0.29.

We dealt with the noise sources in Section I.1 and then the analysis for understanding the difference between the theoretical SNR and the experimentally measured SNR in section I.2.

In next section, the heterodyne signal and SNR of the LHR as function of LO power (in terms of photocurrent) will be discussed.

I.3 Heterodyne signal and SNR of the LHR vs. LO photocurrent

Based on the study performed on the noises as function of LO power-induced photocurrent, we now investigate the heterodyne signal and the corresponding SNR as the function of the LO photocurrent. The LO power was varied by adjusting a polarizer in front of the LO output, both the mean heterodyne signal and its standard deviation were measured from which, the corresponding SNR was derived. The results are shown in Fig. 5.9. that the maximum SNR of the LHR can be obtained with an optimum LO photocurrent. The optimum LO photocurrent is highly dependent on detector (used as photomixer) technology and characteristics [3]. For each type of detector the optimum LO photocurrent must be determined because saturation effects, detection chain noise and detector response homogeneity will affect the performance.

Therefore, the LO power should be precisely adjusted in order to significantly reduce the noise on heterodyne signal to achieve high SNR while without any device saturation.

Section I mainly analyzed the noise sources and SNR of the LHR system using fiber for sunlight coupling to the LHR receiver. The following section will compare the performance, in terms of SNR, of LHRs using free-space coupling and using fiber coupling for BB source collection.

II. SNR comparison between LHRs using free-space coupling and fiber coupling for sunlight collection

In the LHR using free-space coupling system, an experimental SNR of ~119 (with an injected BB power-induced photocurrent of 207 µA, an LO power-induced photocurrent of 417 µA, a LIA time constant of 1 s and a pass-band of 27-33 MHz) was obtained, in comparison with a calculated ideal SNR of ~356, as discussed in Chapter 4.

The experimental SNR of the LHR using fiber coupling was ~419 (with an injected BB power-induced photocurrent of 117 µA, an LO power-induced photocurrent of 610 µA, a LIA time constant of 1 s and a pass-band of 27.5-270 MHz) and it was about 3.52 times higher than that obtained in the free-space coupling configuration (~119). This difference is analyzed as follows.

(1) As SNR is proportional to the LHR double-sideband bandwidth (B) (c.f. Eq. (5.1)), the difference in SNR between these two optical coupling systems is mainly attributed to the difference in the bandwidths of the used RF filters in two system, a factor  1 of ~6.36

(= 12 485
where B fiber =485 MHz=2×(270-27.5) MHz for the fiber coupling system against B free-space =12 MHz=2×(33-27) MHz for the free-space coupling system) in favor of the fiber coupling LHR.

(2) As SNR is proportional to BB photocurrent (c.f. Eq. (5.1)), the difference in SNR is related to the difference in the BB photocurrent, a factor  2 of ~0.57 (= 117/207 the BB photocurrent ratio between two LHR systems).

The total difference in the SNRs due to above two reasons is :

 1 ×  2 = 6.36 × 0.57 = 3.63 (5.14)
which is comparable to the factor of 3.52.

Summarizing Section 5.1.1, the noise sources, heterodyne signal and SNR of the LHR prototype are analyzed, the optimum operating LO photocurrent (~610 µA) is experimentally obtained. Spectroscopic performance of the LHR system will be evaluated in the following section under the optimal LO photocurrent.

Spectroscopic performance

The capacity of the mid-IR optical fiber used to couple broadband source (BB or sunlight) was evaluated in this section. To that end, the same blackbody source as used in Chapter 4

was coupled to a direct absorption cell through the optical fiber. The common parameters were set as follows :

(1) temperature of the blackbody : 1000 ˚C;

(2) LO center frequency was scanned with a PZT driven by a sine-wave of 3.0 V with an offset of 1.6 V.

I. BB-laser heterodyne spectrum of CH 4 absorption at 8 µm

Two very adjacent absorption lines of CH 4 were chosen (centered at 1241.8632 cm -1 and 1241.9489 cm -1 with a line intensity of 6.590E-21 cm/molecule and 6.596E-21 cm/molecule, respectively [6]). Heterodyne spectrum of these CH 4 lines were recorded and compared with its direct laser absorption spectrum. The experimental parameters were set as follows :

(1) LO center frequency : 1242.00 cm -1 ;

(2) frequency scanning rate : 500 mHz;

(3) electronic filter pass-band : 27.5-270 MHz;

(4) LIA sensitivity and time constant : 10 mV and 10 ms, respectively.

In order to record direct absorption spectrum of CH 4 , one part of the EC-QCL radiation separated by a beam splitter was injected into a 12.5-cm long single-pass cell filled with a mixture of CH 4 in air at 260 mbar.

Using a PZT, driven by a sine-wave signal, to scan the external cavity of the LO laser and hence the laser frequency, direct laser absorption signal of CH 4 (Fig. It is seen that two adjacent CH 4 absorption lines of the LHR spectrum (Fig. 5.10 right)

were resolved and in good agreement with the CH 4 direct absorption spectrum (Fig. 5.10 left).

As can be observed in the spectral comparison, the heterodyne spectrum with a fitted Voigt linewidth (FWHM) of 0.0457 cm -1 (Fig. 5.10 right, green) is significantly broader than the direct absorption spectrum with a experimentally fitted Voigt linewidth of 0.0239 cm -1 (Fig.

left, green).

The theoretical Voigt line width ( V , FWHM) can be approximately expressed as follow (c.f. Chapter 3.2.5) [7] :

  2 2 2 2166 . 0 5346 . 0 INS G L L V v v             (5.15)
where the Lorentz linewidth  L is 0.0221 cm -1 [6] at 260 mbar, the instrument function of the LHR system INS is 0.0162 cm -1 mainly determined by the doubled RF filter bandwidth of 485 MHz (for the pass-band of 27.5-270 MHz), the INS for the direct absorption spectrum measurement is determined by the laser emission linewidth of 9.2 MHz (or 0.00031 cm -1 ), and the Gaussian linewidth  G of 0.00383 cm -1 is calculated from Eq. (3.7) [8] with ν 0 of 1241.8632 cm -1 , T of 300 K, and M of 16 g/mole.

With above parameters, the theoretical Voigt linewidths of the LHR and direct absorption spectra of 0.0314 cm -1 and 0.0228 cm -1 are calculated using Eq. (5.15), respectively. As can be seen, the significant broadening characteristic in heterodyne spectrum is due to the wider instrument function. The broadening reasons are addressed as follows :

(1) The used LIA time constant of 10 ms was not adapted to the scanning time of T scan =14 ms needed to scan across the halfwidth of the absorption line (i.e. the used time constant cannot meet

    14 scan T
), that would broaden the heterodyne spectral line width (c.f. 5.1.2.2 (III)), in this case the scanning speed of LO frequency  sc is 0.787 cm -1 /s and the  HWHM is 0.0111 cm -1 ).

(2) A uncertainty of ~15% in the pressure measurement resulting from the single-cell leakage would cause a broadening of 0.0033 cm -1 (corresponding to a P=39 mbar where the pressure-broadening coefficient  is 0.0861 cm -1 atm -1 [6]).

This work demonstrated that the 860-μm-core polycrystalline fiber is suitable for application of coupling mid-IR BB radiation to LHR. According to the analysis of the broadening effects, the impact of LHR instrument function (such as RF filter pass-band, LIA time constant with respect to the scanning speed of LO frequency, etc.) on LHR spectrum will be studied in the following sections.

II. Impact of RF pass-band on LHR spectrum

To investigate the impact of the RF filter pass-band on the LHR spectral signal, heterodyne absorption spectra of CH 4 in a single-pass cell were experimentally extracted and analysed with different pass-bands of RF filters. The experimental parameters were the same as those set above, except for :

(1) LO center frequency : 1255.00 cm -1 ;

(2) frequency scanning rate : 500 mHz;

(3) pressure of the CH 4 mixture in air in the single-pass cell : 280 mbar;

(4) LIA sensitivity and time constant : 5 mV and 10 ms, respectively.

LHR noise has been investigated at first. Fig. 5.11 shows a noise amplitude spectrum of LHR signal from the RF output of the photomixer recorded using a signal analyzer (with a RBW of 100 kHz). As can be seen, there are strong 1/f noises in the low frequency range which has to be filtered out. The noise densities within different pass-bands of the RF filters available in the present work were estimated by dividing the integral noise over each pass-band by both the bandwidth and the square root of the RBW (100 kHz) (Table 5.3). As shown in Table 5.3, the noise density of the RF filter with a pass-band of 27.5-270 MHz was lowest and the corresponding SNR was highest because of its wider filter bandwidth (at the cost of lower spectral resolution). LHR CH 4 absorption spectra were then recorded with these five available RF filters, as shown in Fig. 5.12. The LHR CH 4 absorption spectra measured with AC-coupling band-pass RF filters (Fig. 5.12 left), which can significantly filter out low frequency noises, have higher SNR and better spectral line-shape, while the spectra measured with DC-coupling low-pass RF filters (Fig. 5.12 right) are noisy resulted from high 1/f noise. It's seen that the noise level of the spectrum measured with the RF filter with a pass-band of 27.5-270 MHz (Fig. 5.12 left in black) is lower than that measured with a pass-band of 27-33 MHz (Fig. 5.12 left in red). Moreover, there is no obvious difference in spectral line widths between two LHR CH 4 absorption spectra. The reason is that the theoretical spectral line width (FWHM) of CH 4 absorption around 1255.00 cm -1 at 280 mbar is 0.034 cm -1 (1020 MHz [9] that is wider than the doubled RF filter bandwidths (12 MHz and 485 MHz) and therefore there is no any obvious effect of the RF filter bandwidths on the measured line widths.

Based on such analysis, the RF filter with a pass-band of 27.5-270 MHz was selected for the current LHR system.

III. LHR spectral line-shape vs. scanning speed of LO frequency

As discussed in Chapter 2.1.6 and Chapter 4.2.2.3, in order to obtain high-precision heterodyne spectrum (with minimized line shape shift and distortion), the scanning time ΔT scan across the halfwidth of the absorption line  HWHM (in [cm -1 ]), which is also dependent on the scanning speed of the LO frequency sc (in [cm -1 /s]), should be appropriately adapted to a LIA time constant τ such that

        14 SC HWHM scan T
. Experimental investigation on BB-based heterodyne spectra using different scanning speeds with a selected LIA time constant of 1 ms were carried out.

In this study, the experimental parameters were the same as those set above, except for :

(1) LO center frequency : 1242.00 cm -1 ;

(2) RF filter pass-band : 27.5-270 MHz;

(3) pressure of the CH 4 mixture in air in the single-pass cell : 280 mbar;

(4) LIA sensitivity : 2 mV (Model SR830, Stanford Research Inc.).

LHR CH 4 absorption spectra recorded by scanning the LO frequency at different speeds (see Table 5.4) using the same LIA time constant of 1 ms are plotted in Fig. 5.13. As can be seen, selection of the scanning speed of the LO frequency should be well matched to the applied LIA time constant. Comparing these four heterodyne absorption spectra of CH 4 , SNR, linewidth broadening Δν b (FWHM), line shift δνand noise level (1σ) of these heterodyne absorption spectra were analyzed based on Voigt profile fit (Fig. 5.13, blue) and summarized in Table 5.4. It is seen that the combination of 1 ms time constant and the 0.3935 cm -1 /s scanning speed (with a scanning time of 36 ms), the heterodyne spectrum has a lower noise level and a smaller line shift while keeping high spectral resolution (Fig. 5.13 (b) and Table 5.4 in bold). Meanwhile, it is generally considered that the scanning speed of the LO frequency  sc set to a slower value, which meets well

        14 SC HWHM scan T
, can limit the distortion of the line shape.

As can be seen from Table 5.4, at a LO frequency scanning speed of  cm -1 /s, the scanning time of 89 ms was far more than 14 times the applied LIA time constant of 1 ms. In this case, the measured line shift was smallest, the absorption depth was deepest, the linewidth  b (Table 5.4) was narrowest and close to the theoretical value of ~0.036 cm -1 calculated from Eq. 5.15 using  L of 0.028 cm -1  INS of 0.0162 cm -1 and  G of 0.0038 cm -1 (c.f. 5.1.2.2 (I)). However, the noise (1 σ : 0.0091) was highest and SNR (~12) was lowest (Table 5.4). A trade-off has to be made. Therefore at the LIA time constant of 1 ms, the scanning speed of the LO frequency of  cm -1 /s (the scanning time of 36 ms), with which the noise (1 σ : 0.0043) was relatively low, the SNR of system (~24) was relatively high, the line shift (~0.0004 cm -1 ) was relatively small and the achievable spectral resolution (spectral line width of ~0.042 cm -1 ) was relatively high, was thus selected for the LHR prototype measurement.

LHR prototype involving a mid-IR fiber to couple sunlight radiation

Instrumental description

The developed LHR prototype using a mid-IR polycrystalline fiber to couple sunlight to the LHR receiver is schematically shown in Fig. 5.14 and Fig. 5.15. The LHR prototype uses an EKO sun-tracker to real-time follow the Sun's movement. Collection of the sunlight in the atmospheric column into a mid-IR fiber is achieved through a lens associated with an optical filter in Germanium. The collection optics is installed on the instrument mount of the suntracker. The Ge-filter in front of the fiber is used to protect the fiber input terminal from damage caused by the direct exposure to the intense ultraviolet and visible part of the sunlight, and to limit the optical bandwidth of the incident radiation and let only the transmission of the solar radiation at wavelengths longer than 7 µm in our case to minimize shot noise resulting from the solar radiation [1].

The emerging sunlight from the fiber is collimated with a lens3 (in Germanium, AR coating (3-12 μm)) and injected into free-space. The sunlight is then amplitude modulated at a rate of about 1 kHz and directed to a beam splitter. The sunlight beam of 12.5 mm in diameter is superimposed on the beam splitter with a LO beam of 7.5 mm from the EC-QCL One part of the LO beam (transmitted LO power from the beam splitter) is directed to either a 12.5 cm single-pass cell filled with a CH 4 mixture in air for absolute frequency determination, or to a 12.5 cm long home-made Ge-etalon (FSR = 0.0333 cm -1 ) for relative frequency calibration when the LO frequency is tuned.

Heterodyne measurement of atmospheric CH 4 and N 2 O absorption spectrum

The developed LHR prototype was deployed on the roof of the ULCO-IRENE platform in Dunkerque (51.05˚N/2.34˚E) for ground-based remote sensing of trace gases in the atmospheric column. When checking the system noise at the RF output port of the photomixer with the signal analyzer, it was found that the system noise was enhanced within 110 MHz, and became especially significant around 100 MHz, as shown in Fig. 5.16. This enhanced system noise may be resulted from the instability of the external cavity of the laser due to frequent field deployments. Therefore the previously optimized RF filter pass-band of 27.5-270 MHz was no longer adapted, a new RF filter with a pass-band of 225-270 MHz was selected to remove this excess noise. The LHR operational parameters were set as follows :

(1) LO center frequency : 1262.00 cm -1 , scanned at a frequency of 250 mHz with a scanning voltage of 3.8 V and an offset of 2.0 V;

(2) LIA sensitivity and time constant : 10 mV and 1 ms, respectively;

(3) acquisition time per spectrum : 60 s;

(4) averaging number of spectra : 15.

The LO frequency was scanned around 1262.00 cm -1 using PZT scan mode, atmospheric CH 4 and N 2 O absorption spectrum was measured in the atmospheric column. Fig. 5.17 shows a heterodyne absorption spectrum of atmospheric CH 4 and N 2 O around 1262.00 cm -1 (left).

Fig. 5.17 also shows simulation spectra (right) for spectral identification. As can be seen in Fig. 5.18, the absorption line positions of CH 4 and N 2 O from the LHR spectrum were in good agreement with those of the FT-IR spectrum as well as with an atmospheric transmission modeling. As water vapor was interfering with the LHR spectrum of CH 4 -N 2 O (shown in Fig. 5.17), and the water vapor distribution changes with time and space [9][10][11], the line-shape of the LHR spectrum was slightly different from the FT-IR spectrum and the atmospheric transmission modelling spectrum, made at different locations and different time under different atmospheric conditions. The overall spectral line-shapes of all three spectra were consistent.

Comparing to the FT-IR spectrometer used for ground-based remote measurements of trace gases in the atmospheric column, LHR is advantageous in terms of room temperature operation, a compact size, portability, higher spectral resolution, and smaller FoV, as summarized in Table 5.5. which demonstrated that the developed portable LHR prototype could be used for groundbased atmospheric sounding measurements of GHGs in the atmospheric column.

In the future work, vertical profiles of GHGs in the atmospheric column will be retrieved from the ground-based measured LHR spectrum using a retrieval algorithm, given a decent technology. The objective is to realize a "on-chip" LHR receiver. It will make the NexLHR cost-effective, energy efficient, autonomous and ultra-portable. It will be most suitable for field deployment for the measurements of atmospheric vertical profiles of key atmospheric species through in situ ground-based measurements, aircraft and satellite observations, as well as for integration into currently operational worldwide observation networks. Meanwhile, the proposed infrared LHR instrument presents high potential for technology transfer and commercialization.

Ré sumé

La mesure des profils de concentration verticale des gaz traces dans l'atmosphè re est d'une grande importance pour comprendre la physique, la chimie, la dynamique et le budget de L'objectif de cette thè se consiste à dé velopper un instrument RHL entiè rement transportable pour la télédétection au sol, dans le domaine de l'infrarouge moyen (mi-IR), de gaz à l'é tat de traces pré sents dans la colonne atmosphé rique. ii. La contribution de chaque type de bruits dans les expressions ci-dessus est discuté e cidessous en dé tail.

( (3) L'efficacité hé té rododine η het de 1 pour le cas idé al (c.f. chapitre 1.3) serait surestimé e.

La diffé rence dans la taille des faisceaux en forme de la lumiè re du soleil (12,5 mm) et de la lumiè re OL (7,5 mm) a causé une efficacité hé té rodé rine de ~0,8 (c.f. Fig. 1.12). De plus, le photomixteur a une petite zone photo-sensible de 0,5×0,5 mm 2 , mê me un petit angle d'inadé quation se traduirait par une efficacité hé té rodine de ~0,9 (c.f. Fig. (1) tempé rature du corps noir : 1000 ˚C;

(2) la fré quence du centre OL a é té numé risé e avec un PZT entraî né par une onde sinuel de 3,0 V avec un dé calage de 1,6 V. (1) fré quence centrale OL : 1255,00 cm -1 ;

(2) taux de balayage de fré quence : 500 mHz;

(3) pression du mé lange CH 4 dans l'air dans la cellule à une passage unique : 280 mbar;

(4) LIA constante de temps : 10 ms, respectivement.

Le bruit de RHL a é té é tudié dans un premier temps. (1) fré quence centrale OL : 1242,00 cm -1 ;

( Pendant ce temps, il est gé né ralement considé ré que la vitesse de numé risation de la fré quence OL  sc est réglée à une valeur plus lente, qui s'accord avec bien

        14 SC HWHM scan T
, peut limiter la distorsion de la forme de la ligne.

Comme constaté à partir du tableau 5.4, à une vitesse de balayage de fré quence OL de  cm -1 /s, le temps de numé risation de 89 ms é tait beaucoup plus de 14 fois la constante de temps LIA appliqué e de 1 ms. Dans ce cas, le dé calage de ligne mesuré é tait le plus petit, la profondeur d'absorption é tait la plus profonde, la largeur de la ligne  b (tableau 5.4) é tait la plus é troite et proche de la valeur thé orique de ~0,036 cm -1 calculé e à partir de Éq. 5,15 à partir de :  L de 0,028 cm -1  INS de 0,0162 cm -1 et de 0,0038 cm -1 (c.f. (1) fré quence centrale OL : 1262,00 cm -1 , numé risé e à une fré quence de 250 mHz avec une tension de balayage de 3,8 V et un dé calage de 2,0 V;

(2) LIA constante de temps : 1 ms;

(3) temps d'acquisition par spectre : 60 s;

(4) nombre moyen de spectres : 15.

La fré quence OL a é té numé risé e autour de 1262,00 cm -1 à l'aide du mode de balayage

         a r J E r E m 1 0 0  (1)
where a r   0

. A Gaussian beam with a waist ω 0 can be expressed by :

    2 0 2 0 exp  r E r E   (2)
The power coupling efficiency of the incident beam to each HE 1m mode can be expressed by the overlap integral :

                             0 1 0 2 0 2 0 2 2 0 1 0 2 0 2 / 2 exp / exp rdr a r J rdr r rdr a r J r m a a m m      (3)
This equation describes the amount of light power coupled to the HE 1m modes in the fiber for a given light spot size to fiber core size ratio ω 0 /a. According to this equation, calculation was performed using MATLAB to obtain theoretical coupling efficiency curves of the first five HE 1m modes in 320-, and 1000-μm-core hollow-glass fiber, respectively (Figs. 2 and3). As can be seen in Figs. 2 and3, the highest coupling efficiency were obtained when : ω 0 /a = 0.64

for HE 11 mode in a 320-, and 1000-μm-core hollow-glass fiber, respectively

(2) Attenuation coefficients for the HE 1m modes inside the fiber For a hollow fiber with a single dielectric film, the minimum loss occurs when the films thickness d is given by [1] :

            4 2 1 2 1 tan 1 2 d d d n n n d   (5)
where n d is the wavelength-dependent refractive index of the dielectric films. The assumption is that there is no absorption in the films. Here :

  4 3 2 233 . 1 678 . 2 920 . 1 239 . 0 956 . 1           d n (6)
At 8 µm, n d () = 1.9512 which leads to a thickness of d = 43 µm. The attenuation coefficients of the various HE nm fiber modes can be expressed as :

                                     1 1 2 1 2 2 2 2 2 2 3 2 2 1 d d m nm n n n n a      , HE 1m modes (7)
where n and  are the real and imaginary parts of the complex index of the metallic guide, µ 1m is the mth root of the zero-order Bessel function,  is the wavelength, and a is the core radius. The µ 1m values for the first five HE 1m modes are given in Table 1. Calculation of the attenuation coefficients for the first four HE 1m modes in an Ag/AgI hollow-glass fiber is made according to Eq. ( 9). These four curves show the 1/a 3 , dependence of loss as well as the dramatic increase in loss for the higher order modes (Fig. 4). As can be seen in Fig. 4, the HE 11 mode will have the smallest attenuation coefficients, i.e.

the lowest transmission loss.

(

3) Total loss in hollow fibers

To make an estimation on the theoretical transmission losses in a hollow fiber, one needs to take into account both the attenuation and coupling efficiency to each of the modes.

Accordingly, the transmission in a length z, P z , can be expressed as :

) 2 exp( z z P m m m      (8)
where the factor 2 is resulted from squaring the electric field to get the intensity. It is particularly important to sum over all possible modes when calculating a theoretical loss for fiber used under poor launch conditions since it may excite many higher order modes. The theoretical total loss L z can be expressed as : For 320-µm-core hollow fiber : ƒ -number = ƒ/20, that is : ω 0 / a ≈ 0.62;

For 1000-µm-core hollow fiber : ƒ -number =ƒ/51, that is : ω 0 / a ≈ 0.52. As indicated by the simulation results, the launch condition for maximum transmission (min-loss) requires a smaller value of   /a than that for optimal coupling to the HE 11 mode (ω 0 /a = 0.64). The difference depends on fiber core size and is more severe for the larger core fibers. As can be seen in Figs. 2 and3, more power is coupled to the higher order modes at smaller f-numbers (ω 0 /a ˂ 0.64) (Fig. 6 (a)), and the focused spot becomes larger than the fiber core diameter (2a) at larger f-numbers (ω 0 /a  0.64) (Fig. 6 (c)). In this case, the beam is clipped by the fiber walls.

In a large-bore fiber, attenuation to the higher order modes is not significantly greater than that of the HE 11 mode (Fig. 4), so the elimination of beam clipping by reducing the input beam spot size does not have an obvious effect on the total loss. In addition, for high-power applications, laser energy cannot hit the fiber walls to avoid any damage. Thus, the possibility of damaging the input can be eliminated by reducing the input beam spot size with the help of the smaller f-number (ω 0 /a ˂ 0.64) launch.

(4) Output beam divergence

The divergence of the beam emerging from the hollow fiber depends on the modes propagating in the fiber as well as on the core size. The HE 1m modes will couple to free-space modes with a half-angle beam divergence θ given by [2] :

201 a 2 sin 1      m m   (10)
Calculations for the beam divergence of the first four HE 1m modes as a function of core size are given in Fig. 7. As expected, the lowest order mode gives the smallest beam divergence, as shown in Fig. 7. (5) Fiber-coupled LHR system A fiber-coupled optical assembly is shown in Fig. 8, two single lenses are used to couple sunlight and laser light into the hollow fibers, respectively, and then a 2 to 1 hollow core fiber coupler is used to realize beams overlapping.

The design work mainly focuses on improving the fiber coupling efficiency issues. From above theoretical analysis,the coupling efficiency of a fiber-coupled LHR system depends on the light beam mode coupling to the hollow fibers. The efficiency of light coupling to the fiber is limited by two facts, e.g. the focused spot size and the beam focusing angle after the light coupling lens. Normally, coupling light into a hollow fiber is relatively simple, given the relatively large core. However, both transmission and beam quality can be adversely affected if the proper focal length optic is not used. In general, the beam should enter straight into the fiber with a relatively gradual focus. The curves drawn in Figs. 2 and3 show that optimal coupling into the lowest order mode occurs when the ratio of the focused spot size (2ω 0 ) to the fiber core diameter (2a) : ω 0 / a ≈ 0.64 (where

       D f    2 0
). The beam quality that coupled into the fiber will be highest with the lowest loss. So the calculation for an optimal focus (

             D a f 2 16
. 0 opt ) assumes an ideal collimated Gaussian input beam, and a non-ideal beam will have a larger focused spot. For this reason, selecting a focal length that is either equal to or less than the optimal focal length is recommended, which can in turn satisfy the smaller f-number (ω 0 /a ˂ 0.64) launch condition.

Due to the core size limitation of the 2 to 1 hollow fiber (the maximum option of the core diameter is 1000 μm in our case), so the maximum size of each single fiber core for coupling sunlight/LO is 320 μm.

In our LHR prototype system, the sunlight is collected and collimated with a telescope, the output beam size is specially filtered by a diaphragm, and the final beam size of sunlight is D=12.5 mm. Hence, the ƒ opt for coupling the sunlight into the fiber should be equal to or less than 250 mm.

As we know, hollow fibers utilize total internal reflection (TIR) in order to confine and guide light within a solid or liquid structure. Within the fiber, a critical angle of incidence exists such that light will reflect off the core/cladding interface rather than refract into the surrounding medium. To fulfill the TIR conditions in a fiber, the incidence angle of the light launched into a fiber must be as close as possible to the acceptance half-angle θ of the fiber.

The numerical aperture (NA) is a dimensionless quantity used by fiber manufacturers to specify the acceptance angle of an optical fiber and is defined as :

  sin sin   n NA   1   air n n ( 11
)
For the 320-μm-core hollow fiber, the acceptance full-angle is 2.29˚. Because the focusing angle increases with the decrease of the focal length of the coupling lens, we use Zemax to make a simulation of the coupling lens, the focusing full-angle θ 1 after the coupling lens is about 2.3˚ when the coupling lens with 250 mm focal length is used, which is approaching the acceptance angle of the fiber. Therefore, the focal length 250 mm of the coupling lens is selected for coupling sunlight.

For a laser with a TEM00 output mode like our Daylight laser, it is sufficient to take into account only the contribution from the HE 11 mode, and to couple as much power as possible to the HE 11 mode (at ω 0 /a≈0.64) into a hollow fiber. Consistent with the fiber core size used for coupling sunlight, the fiber core size used for coupling the laser beam (with D=2.5 mm) is also 320 μm. The corresponding focal length ƒ opt of the coupling lens should be equal to and less than 50 mm. when the coupling lens with a 50 mm focal length is used, the result of the simulation shows that the focusing full-angle θ 2 after the coupling lens is about 2.88˚, which is a little larger than the acceptance full-angle of the fiber. Considering the focused spot size, the focal length 50 mm is still selected for coupling laser.

Two beams, transmitted by two 320-μm-core hollow fibers, separately, will be coupled into a 1000-μm-core fiber in which they are well overlapped. Finally, the output beam from the 1000-μm-core fiber will be focused into VIGO detector using a dual lens collimating/focusing assembly. The beam focusing full-angle after the dual lens collimating/focusing assembly should be less than the acceptance angle (35˚) of the VIGO detector. In order to verify this, the beam focusing full-angle is simulated by Zemax, the result is about 15.3˚ (as shown in Fig. 9), which is less than 35˚. Finally, the FoV of the fiber-coupled LHR system is calculated based on the Eq. (1.4).

The fiber system with a D=25 mm diameter lens collecting radiation at =8 μm would provide a FoV of ~0.4 mrad (0.023˚).

From above analysis, the elements of the fiber-coupled LHR system are as follows :

) ( ) ( V W E W V R V Intensity W Power    (2)
Here, the intensity is V det , then the power in function of the intensity is obtained by : (3) about 9%, 44%, and 47% of the total energy, respectively. The solar emission spectrum is a continuous spectrum, but when the visible light below the Sun's surface passes through the layers above the photosphere and chromosphere, some light at particular wavelengths is absorbed by atoms and ions and so it seems missing in the solar emission spectrum that we can see. When there is no light, it appears as black in the solar emission spectrum. These absorption lines are called Fraunhofer lines, and there are more than 2000 Fraunhofer lines of the solar atmosphere when the Sun is viewed from moderate to high resolution [1].

      V V E V in V

The conversion between the measured intensity (in [V]) and the radiation (in [W/m 2 ])

        V V E E V V E m Area W Power Radiation

Introduction

Carbon dioxide (CO 2 ) is responsible for 55-60% of anthropogenic radiative forcing on global warming. The vast majority of anthropogenic CO 2 emissions come from combustion of fossil fuels (principally coal, oil, and natural gas) [1]. To reduce CO 2 injected into the atmosphere, reuse of CO 2 represents a promising and alternative solution because CO 2 is a valuable industrial gas for chemical industrial applications and power generation [2]. For this purpose, CO 2 should be as pure as possible. Purification of CO 2 can be performed through the following methods: (1) pre-combustion [3], (2) post-combustion [4] and (3) oxyfuel-combustion. Compared to the first two methods, oxyfuel-combustion allows one to obtain a rich CO 2 stream with the highest purity (80%-98%) [5]. In an oxyfuel system, the combustion flow consists of O 2 and CO 2 . This Process emits also water (H 2 O) vapor, unburned components such as carbon monoxide (CO) generated by incomplete combustion and nitrogen monoxide (NO) due to the oxidation of nitrogen (N 2 ) included in the fuel. Because NO X (including NO and NO 2 ) is considered as one of the main environmental pollutants responsible for production of photochemical smog and acid rain, as well as for ozone layer depletion [6], its production should be minimized.

Purifying CO 2 in an exhaust flow from the oxyfuel-combustion can be realized through the reduction of NO to N 2 by oxidizing CO into CO 2 over catalysts [5]. Products from the chemical process of NO reduction via reaction with CO is, like any chemical reaction, depending upon the reaction conditions (quantity of NO and CO, temperature, pressure, presence of oxygen and water vapor or not), kind of catalyst (active phase, metal dispersion, support type) and synthesis method, etc. The main reactions are given by the following equations [7]: 2 NO + 2 CO → 2 CO 2 + N 2 (expected process)

(1)

6 NO + 4 CO → 4 CO 2 + 2 N 2 + N 2 O (unexpected process) (

As shown in Equation (2), in an unexpected process, N 2 O may be a by-product from the NO-CO reaction [6]. As N 2 O is a very powerful greenhouse gas with a global warming potential of 300 times greater than CO 2 , it is therefore necessary to optimize the catalytic reaction conditions to minimize the N 2 O production. In the present work, a N 2 O sensor based on a continuous-wave external-cavity quantum cascade laser (EC-QCL) has been developed for real-time on-line monitoring of N 2 O during the catalytic reduction process of NO by CO.

The analytical techniques currently used to measure N 2 O concentration are described as follows:

(1) Gas Chromatograph (GC) which separates different chemical components from a mixture based on the molecular-specific retention times in a separation column, the eluted analyte components from the column may be detected using a thermal conductivity detector (TCD) based on the fact that their thermal conductivities are different from that of the reference carrier gas. However, the retention time for N 2 O and CO 2 are almost the same. In case of a huge CO 2 amount in the gas composition, this cross-interference will result in hiding the small N 2 O signal [8], which makes GC technique unsuitable for quantifying N 2 O in this work.

(2) Mass Spectrometry (MS) in which the gas sample is firstly ionized to electrically charged fragments. By subjecting and accelerating them in an electric or magnetic field, they will be separated according to their mass-to-charge ratio (MCR) [9] which determines the deflection of the moving ion's trajectory inside the electric or magnetic field. They will be detected using an electron multiplier capable of detecting charged particles. The molecular species can thus be identified and quantified via the information on their MCR and the detected ion abundance [10]. As summarized in Table 1, the mass fragments of N 2 O are [START_REF] Kaiser | Fast weighting functions for retrievals from limb scattering measurements[END_REF]30,28,16 (in [kg/C]) that can be also found in CO 2 [START_REF] Kaiser | Fast weighting functions for retrievals from limb scattering measurements[END_REF]28,16) and in NO (30 and 16). These interferences will significantly impact N 2 O quantification using MS. (3) Tunable diode laser absorption spectroscopy (TDLAS) which identifies and quantifies gaseous species of a mixture based on the Beer-Lambert law. High spectral resolution TDLAS could enable in-situ, real-time, interference-free quantification of target molecular species with high-accuracy and without any sample preparation [11].

In this paper, we report on the development of a N 2 O sensor based on a continuous-wave (CW) external-cavity quantum cascade laser (EC-QCL) operating at ~ 8 µm, coupled to a modified-Herriot multi-pass cell. Working at an optimal gas pressure of 120 mbar, a 1σ (SNR = 1) limit of detection of 32.3 ppbv was achieved in 12 s averaging time with a relative uncertainty of 1.1% in measurement precision. Productions of N 2 O through catalytic reduction of NO by oxidizing CO into CO 2 over Pt/SiO 2 catalyst under different temperatures were experimentally monitored. N 2 O concentration of up to ~ 6.1 ppmv at 190 ˚C was observed and analyzed. The optimal catalytic reaction condition for zero N 2 O production was experimentally determined.

Experimental details

N 2 O monitoring by long optical path absorption spectroscopy

The experimental setup is shown in Fig. 1. An EC-QCL (TLS-41000-MHF, Daylight solutions Inc.) was coupled to a modified-Herriot multipass cell. The EC-QCL frequency was scanned across an appropriate N 2 O absorption line to determine its concentration-dependent integrated absorbance by fitting the experimental absorption spectrum to a Voigt profile model. The fine frequency tuning of the EC-QCL was realized by applying a 50 Hz sine-wave (with an amplitude of +3 V PP and an offset of +1.6 V DC ) from a function generator to the PZT (Piezoelectric ceramic transducer) element of the external cavity of the EC-QCL. As shown in Fig. 1, a 10% reflected laser beam is sent to a Fabry-Perot etalon for laser frequency calibration, and the 90% transmitted laser beam is directed into the multi-pass cell to perform long optical path absorption. The used modified-Herriot multi-pass cell (New Focus, Model 5612) was formed with two high reflectivity mirrors with a volume of 3.2 L. Laser light entered and exited the cell through a common hole equipped with a wedged entrance window at the front of the cell. In the present work, 90 passes were made between the mirrors (the mirror separation is 55 cm) resulting in a fixed effective optical path of 50 m. The exiting laser beam from the cell was focused into a thermoelectrically cooled infrared photovoltaic detector (PVI-4TE-10.6, VIGO System S.A.). A National Instruments data acquisition card (PCI 6251, NI Inc.), controlled using a LabVIEW program was applied for data sampling. The recorded data were transferred to a laptop for further data processing to retrieve N 2 O concentration.

Selection of a N 2 O absorption line for sensitive and selective trace gas monitoring

High spectral resolution is required in spectroscopic measurement for discrimination of the target gas absorption from the absorption of other interfering species. Careful selection of appropriate absorption line(s) well isolated from other interference lines was performed. Fig. 2 shows a simulation spectrum of the selected N 2 O absorption line (centered at 1261.0598 cm -1 with a line intensity of 9.677E-20 cm/molecule), based on the HITRAN database [12], The simulation was calculated using 300 ppbv N 2 O in a 50 m long absorption cell at 120 mbar. Meanwhile, potential interferences from 450 ppmv CO 2 and 1% H 2 O vapor were taken into account in the simulation. As can be seen in Fig. 3, this selected line, well isolated from spectral interferences of CO 2 and H 2 O, is a good tradeoff between the required sensitivity and selectivity for monitoring N 2 O by direct absorption spectroscopy in a 50-m long optical path at 120 mbar.

Frequency metrology and N 2 O absorption spectrum retrieval

The N 2 O absorption signal was recorded versus the data point number when scanning the EC-QCL frequency around 1261.0598 cm -1 using PZT scan mode. For the conversion of this absorption signal (a) to an absorption spectrum (d) (Fig. 3), interference fringes from a homemade Fabry-Perot etalon with a free spectral range (FSR) of 1 GHz (~ 0.0333 cm -1 ) were recorded (b) and used to determine the relationship between the data point number and the frequency in wave number (c). The absolute frequency was determined with the help of N 2 O absorption frequency provided by the HITRAN database [12].

N 2 O concentration retrieval

N 2 O concentration can be determined based on the Beer-Lambert law using known spectral parameters (such as absorption frequency, line intensity, etc.). In the present work, the N 2 O concentration was deduced from a calibration curve of concentration vs. integrated absorbance (absorbance integrated over the scanned spectral range [13]). For this purpose, N 2 O samples with different standard concentrations were produced using a high-precision gas dilutor (Model PPA 2000M, Calibrage Inc.).

A N 2 O cylinder with a standard concentration of 1000 ppmv (C initial ) with different flow rate (D 1 ) was mixed with N 2 gas at a fixed flow rate (D 2 ) in the gas dilutor. The concentration of the diluted N 2 O (C final ) was calculated using the following equations :

K C C initial final /  (3) 1 2 1 ) ( D D D K   ( 4
)
where K is the dilution factor, D The multi-pass cell was initially rinsed with pure nitrogen (N 2 ) before the N 2 O measurement. The N 2 O absorption spectra centered at 1261.0598 cm -1 of ambient air and of different concentrations produced by dilution were recorded at 120 mbar, as shown in Fig. 4 (a). The relationship between the integrated absorbance A I and the corresponding N 2 O concentration (Fig. 4 (b)) was obtained from a linear fit :

k A C I O N  2 (5)
where k = 7.7656E-4. Based on this calibration formula, the ambient N 2 O concentration was determined to be about 325±7 ppbv. The relative uncertainty of about 4% is mainly contributed by the uncertainties in the linear fit (Δk/k ˂ 2 %) and in the Voigt profile fitting (ΔA I /A I ˂ 2 %).

Measurement precision and limit of detection (LoD)

Analytical instrument stability is an important issue that affects the detection sensitivity and the measurement precision. In general, signal averaging is used to improve the detection sensitivity and the measurement precision. However, due to the instability of the instrument (such as changes in light intensity, laser wavelength shift and detector dark noise drift, etc.), any actual system is only stable for a limited time, i.e. an optimal averaging time should be determined via an Allan variance analysis [14].

In the present work, time series measurements of 1 ppmv N 2 O absorption spectra were carried out for the Allan variance analysis to determine the optimal averaging time. 9000 consecutive direct absorption spectra of N 2 O were experimentally recorded, with an acquisition time of 0.2 s for each spectrum. Fig. 5 plots an Allan deviation as a function of the averaging time [15] based on the time series measurements of N 2 O absorption spectra. The decaying slope (red dashed line) shows the efficient white noise reduction by signal averaging with a maximum averaging time (system stability time) of about 236 s, which is mainly limited by the temperature and current stability of the QCL controller. The corresponding measurement precision is 5.2 ppbv, leading to a relative uncertainty in measurement precision of 0.5%. After 236 s, the Allan deviation increases (blue dashed line), where the system instability plays a major role which surmounts the noise reduction by increasing averaging time.

Result analyses and conclusion

According to the chemical reaction mechanism shown in Eq. ( 2), combining the result shown in Fig. 9 with a given initial NO concentration (0.02% or 200 ppmv) in the catalytic reaction process, one can determine the conversion efficiency of NO to N 2 O using the concentration ratio of N 2 O to NO. Efficiencies of the catalytic conversion using Pt/SiO 2 catalyst are plotted in Fig. 10 in the temperature range of 50-500 ˚C. The conversion efficiencies of NO to N 2 (red) by reduction, to NO 2 (blue) by oxidation and to N 2 O (green) by reduction; as well as the conversion efficiency of CO to CO 2 (black) are shown in the figure. It can be seen that both N 2 (red data) and NO 2 (blue data) are the primary by-products, while N 2 O (green data, the data in curve are magnified 10 times) is a secondary product with a very small amount after 100% conversion of CO to CO 2 (black data) at 180 ˚C. At the temperature of max. N 2 O production, the reduction efficiencies of NO to N 2 (red data) and to N 2 O (green data) reach about 59% and 6%, respectively, and the oxidation efficiency of NO to NO 2 (blue data) is around 31%, accompanied with 100% oxidation efficiency of CO (black data) to CO 2 .

As shown in Fig. 10, at 250 ˚C, the reduction efficiency of NO to N 2 (red data) is 63%, nearly 4% to N 2 O (green data), and 30% oxidation efficiency of NO to NO 2 (blue data).

As can be seen, NO 2 (blue data) was produced after the full CO-CO 2 conversion (black data) through oxidation of NO by the residual O 2 in the exhaust gas flow, which reached 20% at 160 ˚C. The maximum favorable reduction efficiency of NO to N 2 (red data) was 63% at 250 ˚C. The optimal catalytic reaction conditions for zero N 2 O production was observed at a temperature higher than 340 ˚C where 47% of NO is converted to N 2 (red data) and 26% of NO converted to NO 2 (blue data) and still 27% residual NO in the exhaust flow gas. All NO conversion efficiencies at specific temperatures discussed above are summarized in Table 3.

Conclusions

We demonstrated the application of an 8 μm EC-QCL to real-time optical monitoring of N 2 O evolution in a catalytic reaction of NO-CO. Productions of N 2 O through catalytic reduction of NO by oxidizing CO over a Pt/SiO 2 catalyst were experimentally investigated under different temperatures, which allowed us to study the conversion efficiency of NO to N 2 O and to determine the optimal catalytic reaction temperature for zero N 2 O production.

Figure 1 2 Figure 2 4 Figure 3 6 Figure 4 6 Figure 5 7 Figure 6 9 Figure 7 11 Figure 8 12 Figure 9 13 Figure 10 15 Figure 11 20 Figure 12 21 Figure 13 22 Figure 14 22 Figure 1 . 1 40 Figure 1 . 2 41 Figure 1 . 3 41 Figure 1 . 4 42 Figure 1 . 5 43 Figure 1 . 6 44 ixFigure 1 . 7 44 Figure 1 . 8 45 Figure 1 . 9 48 Figure 1 . 10 49 Figure 1 . 11 49 Figure 1 . 12 50 Figure 1 . 13 51 Figure 1 . 52 Figure 1 . 15 53 Figure 1 . 16 60 Figure 1 . 17 61 Figure 1 . 18 62 Figure 1 . 19

 122436465769711812913101511201221132214221140124113411442154316441744184519481104911149112501135115211553116601176111862119 Figure 1 left: characteristic time scales for vertical transport; right: typical time scales for global horizontal transport in the troposphere……………....................................2 Figure 2 Schematic diagram of the nadir viewing geometry in BUV mode……...................4 Figure 3 Solar occultation viewing geometry…….................................................................6 Figure 4 Limb scattering viewing geometry with single scattering, surface reflection, and second order of scattering, respectively (the atmosphere's curvatu re is exaggerated) .............................................................................................................6 Figure 5 Limb emission viewing geometry…………….........................................................7 Figure 6 Principle of MAX-DOAS………………...…..........................................................9 Figure 7 Optical scheme of SAOZ instrument......................................................................11 Figure 8 Schematic of a FTS for retrieving vertical concentration profile of atmospheric trace gas………………...........................................................................................12 Figure 9 upper: map of the TCCON sites; lower: map of the NDACC sites…....................13 Figure 10 Schematic of a LHR for retrieving vertical concentration profile of atmospheric trace gas................................................................................................................15 Figure 11 Optical layout of the EC-QC-LHR developed by D. Weidmann et al..…….......20 Figure 12 Schematic of the mini-LHR developed by E. L. Wilson et al..............................21 Figure 13 Schematic diagram of the experimental setup of R. Alexander et al…...…........22 Figure 14 Schematic diagram of the experimental setup of a mid-IR LHR developed by J. Wang et al......................................................…............................................22 Figure 1.1 Basic concept of a typical LHR............................................................................40 Figure 1.2 left: geometric restriction of the antenna theory; right: solid angle Ω S vs. radiation wavelength .....…………....................................................................41 Figure 1.3 Geometry restriction of the solid angle Ω S and FoV in the antenna theory..............………………………….................................................….........41 Figure 1.4 Schematic diagram of a heterodyne receiver.……………...................................42 Figure 1.5 Schematic diagram of a LHR for photomixing of the sunlight beam and the LO beam….................................................................................................................43 Figure 1.6 Receiving bandwidth of double sidebands of a LHR receiver….........................44

Figure 1 . 64 Figure 1 . 21 67 Figure 2 . 1 75 Figure 2 . 2 Figure 2 . 3

 1641216721752223 Figure 1.20 (a) Calculated CH 4 absorption spectra at different altitudes in the infrared range of 1254.5-1255.5 cm -1 ; (b) Atmospheric transmission spectrum of CH 4 obtained by integrating spectra in (a); (c) Vertical concentration profile of atmospheric CH 4 at the location of TCCON-Paris station (WACCM model (Whole Atmosphere Community Climate Model))………...………………………......64 Figure 1.21 Flow chart of the data retrieval.………………………......................................67 Figure 2.1 Schematic diagram of a typical LHR system…………………...........................75 Figure 2.2 Schematic of sun tracker………………………...………...................................76 Figure 2.3 left: CSPHOT sun-photometer; right: sunlight collection optics (circled by green dotted line) installed on the CSPHOT sun-photometer, involved in NASA's near-IR-LHR setup……………………………………………...................................77

Figure 2 . 4

 24 Figure 2.4 Bruker A547N Sun tracker………………………………...................................77

Figure 2 . 5 78 Figure 2 . 6 80 xFigure 2 . 7 80 Figure 2 . 8 Figure 2 . 9 Figure 2 . 82 Figure 2 . 83 Figure 2 .

 25782680278028292822832 Figure 2.5 EKO sun-tracker (model STR-21G).....................................................................78 Figure 2.6 left: blackbody source (Oriel® Model 67030, Newport Inc.); right: major components of the 67030 Blackbody source........................................................80

Figure 2 . 85 Figure 2 . 87 Figure 2 . 88 Figure 2 . 16 Figure 2 . 17 92 Figure 2 . 18 93 Figure 2 . 19 94 Figure 2 . 20

 285287288216217922189321994220 Figure 2.13 left: PVI-4TE-10.6 VIGO detector; right: detector current responsivity and detectivity vs. wavelength..................................................................................85 Figure 2.14 left: RF amplifier (ZFL-500LN+); right: Noise Figure vs. frequency...............87 Figure 2.15 upper: Keysight 8472B schottky diode; lower: typical detector's square-law response (left) and diode V/I characteristics (right)...........................................88 Figure 2.16 Effective transfer function of a LIA. R is the resistor, C is the capacitor..……90 Figure 2.17 Simulation output spectra from the LP filter using different parameters (see Table 2.6). Condition of the Hitran simulation spectrum (input : black) : absorption line center: 1233.45 cm -1 , pressure: 250 mbar, concentration: 0.1, absorption cell: 13 cm…………………………………..……………..............92 Figure 2.18 Plot of the time constant vs. ΔT scan , associated with a linear fit………............93 Figure 2.19 Plot of V out (t) vs. V in (t) in point-by-point frequency tuning mode….…...........94Figure 2.20 Scheme of the LHR configurations involved in the present work….................95

Figure 2 . 95 Figure 2 . 22 98 Figure 2 . 23 98 Figure 2 . 24 100 Figure 2 . 25 101 Figure 2 . 26 101 Figure 2 . 27 101 Figure 2 . 28 102 Figure 2 . 29 103 Figure 2 .

 29522298223982241002251012261012271012281022291032 Figure 2.21 upper: schematic of a free-space telescope cage system for coupling sunlight; lower: photo of the developed telescope cage system.......................................95 Figure 2.22 Beam contraction layout (surf: surface of lens, f: focal length, D: lens diameter,

Figure 2 . 31 "Figure 2 . 32 106 Figure 3 . 1 111 Figure 3 . 2 112 Figure 3 . 3

 231232106311113211233 Figure 2.31 "STRConfig" Setting screen : GPS mode (upper) and manual mode (lower)…………………………..……………………………………………105 Figure 2.32 Measured sunlight intensities (blue curve) in comparison with a reference from a "Davis Vantage Pro2" weather station (black curve)…….….......................106 Figure 3.1 Experimental setup used for N 2 O monitoring of a chemical catalysis reaction of NO with CO........................................................................................................111 Figure 3.2 Simulation spectra of 300 ppbv N 2 O, 1% H 2 O, and 450 ppmv CO 2 absorptions in a multi-pass cell (L eff =50 m) at 120 mbar..........................................................112 Figure 3.3 Absorption signal of 5 ppmv N 2 O at 120 mbar (a) and its absorption spectrum (d), obtained using the relative wavenumber calibration curve (c) which allows one to convert "data point number" into "wavenumber" through the FSR of the used etalon (b).............................................................................................................113

Figure 3 . 4 115 xiiFigure 3 . 5 116 Figure 3 . 6 117 Figure 3 . 7 118 Figure 3 . 8 118 Figure 3 . 9 119 Figure 3 . 10

 341153511636117371183811839119310 Figure 3.4 (a) N 2 O absorption spectra at different concentrations at 120 mbar; (b) Plot of the integrated absorbance vs. concentration, associated with a linear fit. Error bars are one standard deviation of the integrated absorbance from Voigt profile fit.........................................................................................................................115

Figure 4 . 1

 41 Figure 4.1 upper: schematic of the developed LHR receiver; lower: picture of the developed 8 μm mid-IR LHR in the present work...............................................................124

Figure 4 . 2

 42 Figure 4.2 Beat note signal measured at the output of the LIA...........................................125

Figure 4 . 3

 43 Figure 4.3 Beat note amplitude vs. LO power.....................................................................126

Figure 4 . 4

 44 Figure 4.4 (a) Atmospheric absorption spectrum recorded with a Bruker IFS 125; (b) Simulation spectrum of multi-GHG using 0.5% H 2 O, 2 ppm CH 4 , 450 ppm CO 2 and 320 ppb N 2 O in the range of 1223-1263 cm -1 ..............................................127

Figure 4 . 5

 45 Figure 4.5 (a) Atmospheric absorption spectrum; (b) Simulation spectrum of multi-GHG using 0.5% H 2 O, 2 ppm CH 4 , 450 ppm CO 2 and 320 ppb N 2 O (black); Individually simulated absorption spectra of 0.5% H 2 O (blue), 2 ppm CH 4 (orange), 450 ppm CO 2 (in pink) and 320 ppb N 2 O (green) in the range of 1241.3-1242.5 cm -1 .............................................................................................128

Figure 4 . 6

 46 Figure 4.6 (a) Atmospheric absorption spectrum; (b) Simulation spectrum of multi-GHG using 0.5% H 2 O, 2 ppm CH 4 , 450 ppm CO 2 and 320 ppb N 2 O (black); Individual Simulation spectra of 0.5% H 2 O (blue), 2 ppm CH 4 (orange), 450 ppm CO 2 (pink) and 320 ppb N 2 O (green) in the range of 1261.2-1262.8 cm -1 ...........................128

Figure 4 . 7 130 xiiiFigure 4 . 8 131 Figure 4 . 9

 471304813149 Figure 4.7 upper: direct absorption used as spectrum reference (black) fitted with a Lorentz profile ( red); lower: heterodyne spectrum of CH 4 absorption near 8 µm (black) fitted with a Lorentz profile (red).......................................................................130

Figure 4 .

 4 Figure 4.10 BB-based heterodyne spectra of CH 4 absorption at a scanning speed υ sc of 0.1574 cm -1 /s (a scanning time ΔT scan of 342 ms) combined with different time constants, respectively......................................................................................133

Figure 4 .Figure 4 .

 44 Figure 4.11 BB-based heterodyne spectra of CH 4 absorption at a scanning speed υ sc of 0.3935 cm -1 /s (a scanning time ΔT scan of 137 ms) combined with different time constants, respectively......................................................................................134 Figure 4.12 left: external heliostat (sun-tracker) installed on the roof terrace; right: Bruker IFS 125HR located in the lower-level experimental room (TCCON-Paris station)..............................................................................................................136

Figure 4 . 137 Figure 4 . 14

 4137414 Figure 4.13 upper: schematic of a telescope system for free-space coupling of sunlight; lower: photo of the telescope system...............................................................137 Figure 4.14 Schematic of the LHR deployed for the field test on the QualAir platform at the UPMC..............................................................................................................138

Figure 4 .

 4 Figure 4.15 upper: sun-tracker installed on the roof terrace on the QualAir platform; lower: a free-space telescope coupling system used for sunlight coupling to the LHR in a field test at the UPMC...................................................................................138

Figure 4 .

 4 Figure 4.16 (a) Local oscillator signal; (b) Sunlight-coupled heterodyne signal; (c) Blackbody-coupled heterodyne signal.............................................................140

Figure 4 .

 4 Figure 4.17 (a) LHR CH 4 absorption signal (red) associated with a baseline of sunlight (blue) and BB-based LHR baseline (black) associated with a baseline of blackbody (pink); (b) Normalized LHR atmospheric CH 4 absorption signal (red) and LHR baseline (black); (c) Post-processed LHR atmospheric CH 4 transmission signal (blue) after normalization of the normalized LHR spectrum to the normalized BB baseline, both shown in (b)...........................................141

Figure 4 .Figure 4 . 19 142 Figure 5 . 1 146 Figure 5 . 2 146 Figure 5 . 3 147 Figure 5 . 4 150 Figure 5 . 5 151 Figure 5 . 6 152 Figure 5 . 7 153 Figure 5 . 8 154 Figure 5 . 9 Figure 5 .Figure 5 . 11 Figure 5 . 12 Figure 5 . 13 Figure 5 . 14 Figure 5 .Figure 5 . 16 Figure 5 .Figure 5 .

 44191425114652146531475415055151561525715358154595511512513514551655 Figure 4.18 (a) Recorded LHR signal (red) and baseline (black); (b) Normalized LHR signal (red) and baseline (black); (c) Normalized signal (blue) by dividing the

104 Table 3 . 1 114 Table 4 . 1 128 Table 4 . 2 130 Table 4 . 3 131 Table 4 . 4 132 Table 4 . 5 133 Table 4 . 6 Table 4 . 7 135 xviiTable 5 . 1 148 Table 5 . 2 Table 5 . 3 Table 5 . 4

 104311144112842130431314413245133464713551148525354 ............................................................................Relevant settings and the diluted concentration...................................................Selected CH 4 and N 2 O absorption lines...............................................................Used time constants at a given scanning speed of the LO frequency υ sc …….....Analysis of BB-based heterodyne spectra of CH 4 absorption at the scanning speed of the LO frequency (υ sc ) of 0.03148 cm -1 /s (the scanning time (ΔT scan ) of 1709 ms) with different time constants (τ)...........................................................................Analysis of BB-based heterodyne spectra of CH 4 absorption at the scanning speed of the LO frequency (υ sc ) of 0.0787 cm -1 /s (the scanning time (ΔT scan ) of 684 ms) with different time constants (τ)...........................................................................Analysis of BB-based heterodyne spectra of CH 4 absorption at the scanning speed of the LO frequency (υ sc ) of 0.1574 cm -1 /s (the scanning time (ΔT scan ) of 342 ms) with different time constants (τ)...........................................................................Analysis of BB-based heterodyne spectra of CH 4 absorption at the scanning speed of the LO frequency (υ sc ) of 0.3935 cm -1 /s (the scanning time (ΔT scan ) of 137 ms) with different time constants (τ)...........................................................................134 Analysis of BB-based heterodyne spectra of CH 4 absorption with optimal τ at given υ sc and ΔT scan ..............................................................................................Parameter setting on the Signal Analyzer............................................................Comparisons between theoretical Voigt line widths and measured Voigt line widths of LHR spectrum and direct spectrum.....................................................160 Noise density with different RF filter pass-bands................................................161 Analysis of BB-based heterodyne spectra (Fig. 5.13) of CH 4 absorption with the used time constants (τ) of 1 ms at different scanning speeds of the LO frequency ( sc ).......................................................................................................................163

Figure 1

 1 Figure 1 left: characteristic time scales for vertical transport; right: typical time scales for global horizontal transport in the troposphere [4].

Figure 2

 2 Figure 2 Schematic diagram of the nadir viewing geometry in BUV mode.

Figure 3

 3 Figure 3 Solar occultation viewing geometry. Note : the distances are not scaled. Solar radiation passes through space and arrives at the upper boundary of the Earth atmosphere. These solar radiations are attenuated by the atmospheric constituents. The blue, green and gray lines indicate the atmospheric absorption lengths at layer 1, 2

Figure 5

 5 Figure 5 Limb emission viewing geometry. The satellite instrument views toward the Earth's horizon. The point of the instruments' LOS closest to the Earth's surface is called tangent point [50].

)( 2 - 1 )

 21 Passive remote sensing based on ground-based platformsGround-based platforms incorporate some of the same viewing geometry concepts mentioned in the satellite platforms. Spectrometer on ground-based platforms is an instrument that infers vertical column density of trace gas by measuring the amount of sunlight reaching the Earth's surface, and from this deducing how much trace gas absorption takes place. Three types of spectrometers including MAX-DOAS (Multi-Axis Differential Optical Absorption Spectrometer), SAOZ (Système d'Analyse par Observation Zénithale), and FTS (Fourier Transform Spectrometer) are discussed below. Ground-based passive MAX-DOAS MAX-DOAS (Multiple Axis, i.e. elevation scanning with DOAS spectral analysis) is a widely used technique for remote sensing of vertical profiles of tropospheric trace gases[59].

Figure 6

 6 Figure 6 Principle of MAX-DOAS : Scattered sunlight is measured at different elevation angles α of the telescope to obtain vertical profiles of the target trace gases, where solar zenith angle (SZA) ϑ denotes the angle between the position of the Sun and the zenith direction.

Figure 8

 8 Figure 8 Schematic of a FTS for retrieving vertical concentration profiles of atmospheric trace gases (BS: beam splitter).

Figure 9

 9 Figure 9 upper: map of the TCCON sites [76]; lower: map of the NDACC sites [81].

Figure 10

 10 Photomixer LHR Figure 10 Schematic of a LHR for retrieving vertical concentration profiles of atmospheric trace gases.

  2011, D. Weidmann et al. of Rutherford Appleton Laboratory (RAL, UK) developed an EC-QC-LHR with a spectral tuning range of 118 cm -1 (a spectral region of 1120-1238 cm - 1 ) and a FoV of ~0.087˚. High-resolution (60 MHz or 0.002 cm -1 ) LHR spectra of solar radiation and the corresponding vertical profiles of H 2 O, O 3 , N 2 O, CH 4 , and CCl 2 F 2 have been measured and retrieved [146,147,151]. As shown in Fig. 11, solar radiation is captured with an external solar tracker and directed into the laboratory, and it is filtered with a narrowband filter and amplitude modulated with a chopper. It is then directed to a beam splitter and superimposed with the LO beam from an EC-QCL. The combined beams are imaged onto a high-speed (1 GHz) mercury cadmium telluride (MCT) photomixer to produce a heterodyne signal.

Figure 11

 11 Figure 11 Optical layout of the EC-QC-LHR developed by D. Weidmann et al [151]. M: mirror; BS: beam splitter; D1: solar intensity detector; D2: mid-IR detector; OAEM: off-axis elliptical mirror; OAPM: off-axis parabolic mirror; PM: photomixer.

Figure 12

 12 Figure 12 Schematic of the mini-LHR developed by E. L. Wilson et al [152].

Figure 13

 13 Figure 13 Schematic diagram of the experimental setup of R. Alexander et al. LO: local oscillator, SMOF: single-mode optical fiber; FC: fiber coupler; OA: optical attenuator; T: microtelescope; RC: reference gas cell; BD: balanced detector; AD: amplitude detector; ADC: analog-digital converter; PC: personal computer. fiber connectors are shown as green boxes.

Figure 14

 14 Figure 14 Schematic diagram of the experimental setup of a mid-IR LHR developed by J. Wang et al [154].

Figure 1 . 1

 11 Photomixer

Fig. 1 . 2 (

 12 Fig. 1.2 (left).

Figure 1 . 2 Figure 1 . 3

 1213 Figure 1.2 left: geometric restriction of the antenna theory; right: solid angle Ω S vs. radiation wavelength λ. (effective aperture of the mixer A T =0.25 mm 2 ).

Figure 1 . 5

 15 Figure 1.5 Schematic diagram of a LHR for photomixing of the sunlight beam and the LO beam.

  1.6). The detection diagram is shown in Fig. 1.7.

Figure 1 . 6

 16 Figure 1.6 Receiving bandwidth of double sidebands of a LHR receiver, assuming the RF filter has a

Figure 1 . 7

 17 Figure 1.7 Schematic diagram of a LHR for amplifying and filtering the RF signal.

Figure 1 . 8

 18 Figure 1.8 Schematic diagram of a LHR for power detection of the RF signal.

Figure 1 . 9

 19 Figure 1.9 Gaussian beam width w(z) as a function of the distance z along the beam. w 0 : beam waist; r: radial distance from the center axis of the beam; R(z): radius of curvature of the beam's wavefronts at z; z R : Rayleigh range; θ: full angle divergence.

Figure 1 . 10

 110 Figure 1.10 Coupling wavefronts of two Gaussian beams (R 1 , R 2 are the curvatures of the wavefronts of two Gaussian beams).

1 RFigure 1 . 11

 1111 Figure 1.11 Coupling wavefronts of a Gaussian beam and a plane beam (R 2 is the curvature of the wavefront of the plane beam with R 2 ).

dΘFigure 1 . 13

 113 Figure 1.13 Photomixing illuminated by the solar radiation and the LO light. Phase fronts of the both beams are normal to the propagation direction.

Figure 1 .

 1 Figure 1.14 left:  as a function of the mismatch angle Θ for several values d (at λ=8 µm); right: as a function of mismatch angle Θ for several values of λ (with d=0.5 mm).

Figure 1 . 15 1 . 4

 11514 Figure 1.15 Spatial distribution of the incident beams on the photomixer.

58 1. 4

 584

Figure 1 . 16

 116 Figure 1.16 Plot of SNR for an ideal LHR vs. wavelength, calculated with a quantum efficiency η of 0.5, a temperature of blackbody radiation T of 1273 K, a bandwidth of the instrument B of 485 MHz, an integration time τ of 1 s, and an overall optical coupling efficiency of the blackbody radiation κ of 0.4.

Fig. 1 .

 1 Fig.1.16 shows ideal SNR of a LHR as a function of wavelength with 1273 K blackbody radiation, 485 MHz spectral resolution, 0.5 quantum efficiency, 1 s integration time and 0.4

Figure 1 . 17

 117 Figure 1.17 Heterodyne radiometer sensitivity to thermal radiation (bandwidth of the LHR (B): 485 MHz; integration time (τ):1 ms; quantum efficiency (η): 0.5).

Figure 1 . 18

 118 Photomixer

Figure 1 . 19

 119 Figure 1.19 Quantitative comparison between SNR LHR and SNR FTS .

Figure 1 .

 1 Figure 1.20 (a) Calculated CH 4 absorption spectra at different altitudes in the infrared range of 1254.5-1255.5 cm -1 ; (b) Atmospheric transmission spectrum of CH 4 obtained by integrating spectra in (a); (c) Vertical concentration profile of atmospheric CH 4 at the location of TCCON-Paris station (WACCM model (Whole Atmosphere Community Climate Model) [39]). (Note : all Figures here are only used for schematic diagrams).

1. 8 . 1 . 1

 811 Atmospheric radiative transfer forward model In order to retrieve vertical concentration profiles of atmospheric trace gases, atmospheric radiative transfer equation (RTE) has to be applied. Because an exact analytic solution for RTE in most of the cases cannot been found under realistic atmospheric medium and multiple-scattering effects, a radiative transfer forward model has to be developed to get the analytic solution. The most known forward models are 6sSecond Simulation of the Satellite Signal in the Solar Spectrum (6S) [40], MODerate resolution TRANsmittance code (MODTRAN), and Line-By-Line Radiative Transfer Model (LBLRTM) based on Fast

Figure 1 . 21

 121 Figure 1.21 Flow chart of the data retrieval. VMRs : volume mixing ratios; LM : Levenberg-Marquardt [50].

Figure 2 . 2 ( 1 )Figure 2 . 3

 22123 Figure 2.2 Schematic of sun tracker.

( 2 )Figure 2 . 4

 224 Figure 2.4 Bruker A547N Sun tracker. M1, M2 : mirror 1 and mirror 2.

( 3 )Figure 2 . 5

 325 Figure 2.5 EKO sun-tracker (model STR-21G).

Figure 2 . 6

 26 Figure 2.6 left: blackbody source (Oriel® Model 67030, Newport Inc.); right: major components of the 67030 blackbody source.

Figure 2 . 7

 27 Figure 2.7 (a) Typical irradiance spectra of the used blackbody at different temperatures; (b) Emissivity of the blackbody at 1000 ˚C from a 0.5 inch (12.7 mm) aperture.

Figure 2 . 8

 28 Figure 2.8 left: emitter source IR-Si217; right: packaged emitter source with a CaF 2 window.

Fig. 2 .

 2 Fig. 2.9 shows calculated spectral radiances of the used two blackbody sources based on the Planck's law. As can be seen, two blackbodies have almost the same spectral radiance at 8 µm. IR-Si217 infrared emitter exhibits the unique advantage for field applications owing to its compact size and very low cost.

Figure 2 . 9

 29 Figure 2.9 Spectral radiances of an Oriel blackbody source (Model 67030, Newport Inc.) operating at 1000 ˚C with an emissivity of 1 (red curve) and an IR-Si217 infrared emitter operating at 1385 ˚C with an emissivity of 0.8 (black curve).

Figure 2 .

 2 Figure 2.10 left: CW Mode Hop-Free EC-QCL (Model CW-MHF 41000, Daylight Solution, Inc.); right: wide tuning of 1223 to 1263 cm -1 with output power of ~60 mW at 1223 cm -1 and more than 80 mW at ≥1247 cm -1 .

Figure 2 .

 2 Figure 2.11 upper: detectable molecules in the spectral coverage region of the EC-QCL used in the present work, based on the HITRAN database[6]; lower: absorption spectra of HONO[8] and N 2 O 5[7].

Figure 2 .

 2 Figure 2.12 left: PVMI-4TE-8 VIGO detector; right: detector current responsivity and detectivity vs.

Fig. 2 .

 2 Fig. 2.13 (right) shows its typical performance.

Figure 2 .

 2 Figure 2.13 left: PVI-4TE-10.6 VIGO detector; right: detector current responsivity and detectivity vs.wavelength.

  In the current RF receiver, 2 low-noise amplifiers (Model ZFL-500LN+, Mini-Circuits ® ), with a gain of 24 dB and a pass-band of 0.1-500 MHz each (Fig.2.14 left), are used for amplification of the RF beat signal. Fig.2.14 (right) shows the noise figure (NF) of the selected amplifiers, which characterizes the degradation in SNR by the amplifier and is expressed by : and SNR OUT are the SNR at the input and output of the amplifier, respectively.

Figure 2 .

 2 Figure 2.14 left: RF amplifier (ZFL-500LN+); right: Noise Figure vs. frequency.

  Dynamic reserve (the ratio by which input noise voltages may exceed the full-scale sensitivity value without causing overload) : 105 dB (high reserve),  85 dB (Normal), and 65 dB (high stability), respectively. Time constant τ (in [s]), related to the low-pass (LP) filter cut-off frequency in the LIA, is a very critical parameter for the use of LIA, which impacts on noise suppression and absorption line-shape. The cut-off frequency (f c ) of the LP filter is driven by the LIA time

Figure 2 . 16

 216 Figure 2.16 Effective transfer function of a LIA. R is the resistor; C is the capacitor.

Figure 2 . 18

 218 Figure 2.18 Plot of the time constant vs. ΔT scan , associated with a linear fit.

Figure 2 . 19

 219 Figure 2.19 Plot of V out (t) vs. V in (t) in point-by-point frequency tuning mode.

Figure 2 . 20

 220 Figure 2.20 Scheme of the LHR configurations involved in the present work.

Figure 2 .

 2 Figure 2.21 upper: schematic of a free-space telescope cage system for coupling sunlight; lower: photo of the developed telescope cage system. Lens 1 : f 1 = 150 mm, D 1 = 50 mm; Lens 2 : f 2 =75 mm, D 2 =25.4 mm.

Fig. 2 .

 2 Fig.2.21 (upper) shows that the sunlight (considered as plane beam) is collected and sizeinitialized by the mirror reflector to a beam size of 50 mm, then the collected sunlight is sizecontrolled by the adjustable diaphragm to a beam size of 25 mm as required. The sunlight is further shaped through a telescope consisted of two CaF 2 lenses for gathering sunlight power. Iris 2, located at the focal point of the two CaF 2 lenses, is used as a field stop to eliminate the stray light. The developed free-space telescope system based on a Thorlabs 60 mm cage assembly system is shown in Fig.2.21 (lower).

  diameter plano-convex lens with 150 mm focal length, (lens 1, #89-169, Edmund Inc.) and a 25.4 mm diameter bi-convex lens with 75 mm focal length (lens 2, LB5247, Thorlabs Inc.) are used to construct a 2× beam contraction Keplerian telescope. A 12.7 mm diameter planoconvex lens with 20 mm focal length (lens 3, LA5317, Thorlabs Inc.) and a 25.4 mm diameter plano-convex lens with 100 mm focal length (lens 4, LA5817, Thorlabs Inc.) are used to realize a 5× Kaplerian beam expander.

Table 2 . 8

 28 Lens data editor of the beam expander. indicates relative distance between two surfaces. All setting variables are radius, thickmess, glass and semi-diameter, respectively. The optimal distance between two lenses for the beam contraction is highlighted in a green frame.

Figure 2 . 24

 224 Figure 2.24 Optical layout of a free-space coupling mid-IR LHR (All size parameters are in [mm]).

  lens 5 are both smaller than the optical area (0.5 mm × 0.5 mm) and the FoV (35˚) of the VIGO photomixer, the size and the focusing angle 2θ of the emerging beams are studied as a function of the incident sunlight size. The results are shown in Figs. 2.25 and 2.26, respectively. The emerging beam size decreases as the sunlight size decreases, and its focusing angle decreases with the sunlight size. Meanwhile, the distance between two lenses of the sunlight beam contraction as a function of the sunlight size is built, as shown in Fig. 2.27. It would be practical to adjust the distance between two lenses, given the sunlight size.

Figure 2 . 25 4 Figure 2 . 26

 2254226 Figure 2.25 Emerging beam size after lens 5 as a function of the sunlight size.

8 Figure 2 . 27 Figure 2 . 28

 8227228 Figure 2.27 Distance needed between two lenses (f1=150 mm and f2=75 mm) for the beam contraction as a function of the sunlight size.

Figure 2 . 29 Figure 2 .

 2292 Photomixer

2 )Figure 2 . 32

 2232 Figure 2.32 Measured sunlight intensities (blue curve) in comparison with a reference from a "Davis Vantage Pro2" weather station (black curve). Note : conversion from the measured intensity (in [V]) to the radiation (in [W/m 2 ]) is given in Appendix 3.

3 . 1 .Figure 3 . 1 3 . 2 . 2 Figure 3 . 2

 313132232 Figure 3.1 Experimental setup used for N 2 O monitoring of a chemical catalysis reaction of NO with CO. BS: beam splitter; GC: gas chromatograph; MFC 1, 2, 3, 4, 5, 6: mass flow controllers; Th 1: thermocouple in the oven, Th 2: thermocouple in the blank, Th 3: thermocouple in the reactor, Th 4: thermocouple in the saturator; Prs: pressure sensor; VIGO: thermoelectrically cooled infrared photovoltaic detector; DAQ: data acquisition card.

Figure 3 . 3

 33 Figure 3.3 Absorption signal of 5 ppmv N 2 O at 120 mbar (a) and its absorption spectrum (d), obtained using the relative wavenumber calibration curve (c) which allows one to convert "data point number" into "wavenumber" through the FSR of the used etalon (b).

of N 2 O

 2 . The ambient N 2 O absorption spectra centered at 1261.0598 cm -1 and N 2 O at different concentrations produced by dilution were recorded at 120 mbar, as shown in Fig. 3.4 (a). The relationship between the integrated absorbance A I obtained from nonlinear least-square fitting of Voigt profile and the corresponding N 2 O concentration (Fig. 3.4 (b)) was obtained from a linear fit (r 2 =99.6) which allowed us to express N 2 O concentration from the measured A I through this calibration slope k :

Figure 3 . 4

 34 Figure 3.4 (a) N 2 O absorption spectra at different concentrations at 120 mbar; (b) Plot of the integrated absorbance vs. concentration, associated with a linear fit. Error bars are one standard deviation of the integrated absorbance from Voigt profile fit.

Figure 3 . 5

 35 Figure 3.5 Absorption spectrum of 6.13 ppmv N 2 O (black curve) at 120 mbar, accompanied with a Voigt profile fit (red curve).

Time series measurements of 1 ppmv N 2 O

 2 absorption spectra were carried out for the Allan variance analysis to determine the optimal averaging time. 9000 consecutive direct absorption spectra of N 2 O were experimentally recorded, with an acquisition time of 0.2 s per spectrum. Fig. 3.6 plots an Allan deviation as a function of the averaging time [8] based on the time series measurements of N 2 O absorption spectra. The decaying slope (red dashed line)

Figure 3 . 6

 36 Figure 3.6 Allan deviation plot.

Fig. 3 .

 3 Fig. 3.7 shows an experimental absorption spectrum of N 2 O (Av.=240 in 12 s) in air at a pressure of 120 mbar, which resulted in a N 2 O concentration of 325 ppbv. Based on the signal-to-noise ratio (SNR10) deduced from the residual of the Voigt profile fit to the experimental absorption spectrum of ambient N 2 O, a 1σ (SNR=1) limit of detection was determined to be 32.5 ppbv in 12 s.

Fig. 3 .

 3 Fig. 3.8 (left) shows the experimental setup of the studied catalytic reaction. Reactant gases composed of 20% CO 2 , 10% O 2 , 0.5% CO, 0.02% NO and He (eluent gas) with a total flow rate of 200 mL/min. The products of CO 2 and N 2 from the catalytic reduction of NO by oxidizing CO were analyzed by an on-line gas chromatography (TranceGC 1300 XXL, Global Analyzer Solutions G.A.S, Inc.), NO was analyzed with a NO analyzer (Xentra 4900C, Servomex Inc.), NO 2 was measured with the same NO analyzer after conversion of NO 2 to NO by a converter BÜNOx (Bühler Technologies Inc.), while N 2 O was monitored by the EC-QCL-based laser sensor as discussed above (Fig. 3.8 right).

Figure 3 . 8

 38 Figure 3.8 left: experiment of catalytic reaction of NO with CO to purify CO 2 in exhaust gas flow from oxyfuelcombustion; right: EC-QCL-based sensor of N 2 O.

1 )Figure 3 . 9

 139 Figure 3.9 Absorption spectrum of 6.13 ppmv N 2 O during a catalytic reaction of NO with CO over a Pt/SiO 2 catalyst at 190 ˚C at 120 mbar.

Fig. 3 .

 3 Fig. 3.10 shows time series measurement (with a step of 1˚C from 50 to 500 ˚C) of N 2 O concentrations produced during the NO-CO reaction over the Pt/SiO 2 catalyst. A max. concentration of ~6.1 ppmv N 2 O was observed at 190 ˚C.

Figure 3 . 10

 310 Figure 3.10 Time series measurement of N 2 O concentration during a NO-CO reaction over a Pt/SiO 2 catalyst vs. temperature.

catalysis process 123 Chapter 4 Figure 4 . 1

 123441 Photomixer

Figure 4 . 2

 42 Figure 4.2 Beat note signal measured at the output of the LIA.

(

  note : different experimental conditions from Section 4.2.1.1). The EC-QCL power intensities were monitored at the output of the photomixer and the beating levels were deduced from the difference of the LIA outputs with and without the injection of LO light. Beat signal amplitude versus LO signal level (in [mV]) is plotted in Fig. 4.3. As can be seen, the beat note increases linearly with the LO power, as predicted by Eq. (1.12) in Chapter 1.2.3. Heterodyning conversion efficiency can be deduced from the slope of the linear fit : P HET (in mV) ≈ 0.09 * P LO (in [V]), i.e. a heterodyning conversion efficiency of ~10 -4 .

Figure 4 . 3

 43 Figure 4.3 Beat note amplitude vs. LO power.

Fig. 4 .Figure 4 . 4 Figure 4 . 5 Figure 4 . 6

 4444546 Fig. 4.4 (a) shows an atmospheric absorption spectrum recorded with a high-resolution Fourier transform spectrometer (Bruker IFS 125HR) on the QualAir platform of the Université Pierre et Marie Curie (UPMC), accompanied with a HITRAN database-based [2] simulation spectrum of 5-km long absorption on the ground at atmospheric pressure. The following molecular species were taken into account : 0.5% H 2 O, 2 ppm CH 4 , 450 ppm CO 2 and 320 ppb N 2 O (Fig. 4.4 (b)).

  temperature of the BB : 1000 ˚C, -LO center frequency : 1233.25 cm -1 , -scanning frequency : 100 mHz, -scanning voltage and offset of a sine-wave signal : 3.0 V and 1.6 V, respectively, -electronic filter bandwidth : 6 MHz (pass-band : 27-33 MHz), -sensitivity and time constant of the LIA : 100 mV and 100 ms, respectively. Radiation from the blackbody was collected and collimated with OAPM 1. It was then focused and directed by OAPM 2 towards a 12.5-cm long single-pass cell filled with CH 4 mixture in air at atmospheric pressure. The beam emerging from the cell was amplitude modulated at 1 kHz using the chopper. The beam filtered by an optical filter was directed to a beam splitter on which it was superimposed with the LO beam from the EC-QCL. The combined beams were focused by OAPM 5 onto the VIGO photomixer. One part of the EC-QCL radiation separated by a beam splitter (CaF 2 window) was injected into a 12.5-cm single-pass cell filled with the CH 4 mixture in air at atmospheric pressure. The direct absorption spectrum of CH 4 in the single-pass cell was used to evaluate the laser heterodyne spectrum of CH 4 absorption. A PZT driven by a sine-wave signal was used to scan the LO (EC-QCL) frequency, direct CH 4 absorption spectrum of the LO in the single-pass cell (Fig. 4.7 upper) and its heterodyne absorption spectrum of the incident BB radiation (Fig. 4.7, lower) were recorded simultaneously. Heterodyne and direct CH 4 absorption spectra were both fitted to a Lorentz profile (Fig. 4.7 red) with a fixed center absorption frequency at 1233.45545 cm -1 , respectively. The FWHM (Full Width at Half Maximum) of the Lorentz line width of ~0.1065 cm -1 ) for the heterodyne CH 4 absorption spectrum (Fig. 4.7 lower) is well consistent with that of ~0.1068 cm -1 for the direct CH 4 absorption spectrum (Fig. 4.7 upper). The difference in absoption depth was resulted from strong background signal of LHR system. This work demonstrates the functionality of the PoC LHR.

  2). The results are shown in Figs. 4.8-4.11(black).

136 4. 3

 1363 Field measurement in Paris The developed PoC LHR was field tested on the QualAir platform of the UPMC, in collaboration with the « Laboratoire d'Études du Rayonnement et de la Matière en Astrophysique et Atmosphè res (LERMA) » of the UPMC in Paris. (Dr. Yao TE). The Paris' instrument is part of the TCCON (TCCON-Paris station). The TCCON is a network of ground-based Fourier transform spectrometers recording direct atmospheric absorption spectra in the infrared spectral region. From these spectra, accurate and precise column-averaged abundances of CO 2 , CH 4 , N 2 O, HF, CO, H 2 O, and HDO are retrieved (http://www.tccon.caltech.edu/). The QualAir platform Fourier transform spectrometer (Bruker's IFS 125HR) with a spectral resolution of 0.02 cm -1 is adapted for ground-based remote sensing of molecular species in the atmospheric column. Connected to a sun-tracker on the roof terrace (Fig. 4.12 left), the QualAir FTS (Fig. 4.12 right) operates in the solar absorption configuration and enables the detection of a large number of atmospheric pollutants.

Figure 4 .

 4 Figure 4.12 left: external heliostat (sun-tracker) installed on the roof terrace; right: Bruker IFS 125HR located in the lower-level experimental room (TCCON-Paris station).

Figure 4 .Figure 4 . 14 Figure 4 .

 44144 Figure 4.13 upper: schematic of a telescope system for free-space coupling of sunlight; lower: photo of the telescope system.

Figure 4 .

 4 Figure 4.16 (a) Local oscillator signal; (b) Sunlight-coupled heterodyne signal; (c) Blackbody-coupled heterodyne signal.

Figure 4 .

 4 Fig.4.17 (b). Fig.4.17 (c) shows the atmospheric CH 4 absorption signal after normalization.

  LO center frequency was tuned to a nearby non-absorbing frequency at 1231.45 cm -1 , the experimental process was repeated. The results are shown in Fig.4.18. In Fig.4.18 (a), the red curve shows the original heterodyne signal measured with sunlight, the black curve shows the original LHR baseline with blackbody radiation coupled into the LHR. In Fig.4.18 (b), the red and the black curves show their corresponding normalized heterodyne signal, respectively.The blue curve in Fig.4.18 (c) shows the result of normalization by dividing the normalized heterodyne signal by the normalized baseline. As can be seen, no absorption feature was observed, which confirms the absorption feature (blue) in Fig.4.17 resulting from atmospheric CH 4 absorption.

Figure 4 . 4 ( 1 Figure 4 . 19

 441419 Figure 4.18 (a) Recorded LHR signal (red) and baseline (black); (b) Normalized LHR signal (red) and baseline (black); (c) Normalized signal (blue) by dividing the red curve by the black one, both shown in (b).

Figure 5 . 1 Figure 5 . 2

 5152 Photomixer

Figure 5 . 3

 53 Figure 5.3 SNR measurement of the beat note at the output of the LIA. The mixed LO and BB power measured at the output of the photomixer were 3.66 V and 0.70 V, respectively. A filter with a pass-band of 27.5-270 MHz was used. A time constant of 1 s combined with LP filters (12 dB/oct) was used for the LIA.

5 . 4 , ( 1 ) 6 ) 7 )Fig. 5 . 5 Figure 5 . 5

 541675555 photomixer with both LO and BB radiation injections (Fig.5.4, (4) black curve) to that of the

Figure 5 . 6

 56 Figure 5.6 upper: noise density spectra from the RF output of the photomixer at different LO power-induced photocurrents measured with a signal analyzer; lower: zoom of the upper figure in the pass-band of 27.5-270 MHz.

5 . 7 , ( 2 ) 1 )

 5721 black square) was calculated by dividing the mean of all total noise amplitudes (including detection chain noise N Det and laser-induced noise N LIN ) measured in the pass-band of 27.5-270 MHz (i.e. the passband of the used RF filter) (Fig. 5.6 lower) by the square root of the RBW (100 kHz). Given the detection chain noise density of Hz nV red line) determined above (Eq. (5.7)), the laser-induced noise N LIN (Fig. 5.7, (3) blue triangle) was calculated by subtracting the detection chain noise N Det (Fig. 5.7, (1) red line) from the system total noise density N total (Fig. 5.7, (2) black square) based on Eq. (5.5).

Figure 5 . 7

 57 Figure 5.7 Plots of : (1) detection chain noise density N Det (red line), (2) measured system total noise density N total (black square), deduced from dividing the total noise amplitude measured at 150 MHz (Fig. 5.6 lower) by the square root of the RBW (100 kHz), and (3) the laser-induced noise N LIN (blue triangle) deduced by subtracting the detection chain noise N Det ((1) red line) from the total noise N total ((2) black square), vs. LO photocurrents.

Figure 5 . 9 Fig. 5 .

 595 Figure 5.9 Evolution of heterodyne signal (black square) and SNR (red square) as a function of LO photocurrent.

Figure 5 .

 5 Figure 5.10 left: background (red) and direct absorption signal of CH 4 at 260 mbar (black); direct absorption spectrum (blue) fitted with a Voigt profile (green); right: background (red) and heterodyne absorption signal of CH 4 at 260 mbar (black); heterodyne spectrum of CH 4 absorption (blue) fitted with a Voigt profile (green).

Figure 5 . 11

 511 Figure 5.11 Noise amplitude spectrum from the RF output of the photomixer in the 1kHz-500 MHz range.

Fig. 5 . 12

 512 Fig. 5.12 Heterodyne spectra of CH 4 extracted with different RF filter pass-bands.

Figure 5 . 13

 513 Figure 5.13 Heterodyne absorption spectra of CH 4 (red), fitted with Voigt profiles (blue).

Figure 5 . 14

 514 Photomixer

Figure 5 .

 5 Figure 5.15 LHR prototype in use for a field measurement test.

Figure 5 . 16

 516 Figure 5.16 Noise amplitude spectra of the RF output from the photomixer within the bandwidth of 1kHz-500 MHz.

Fig. 5 .

 5 Fig. 5.18 shows a comparison of our experimentally extracted LHR spectrum (black) with a FT-IR spectrum (red) measured using a high-resolution Bruker IFS 125HR Fourier transform spectrometer on the QualAir platform of the UPMC (48˚50′47″N/2˚21′21″E, 60 m above sea level), as well as with a spectrum from an atmospheric transmission model (blue).

  photodé tecteur utilisé comme photomixteur. L'amplitude du signal de battement ré sultant du photomixteur varie en fonction de la caracté ristique d'absorption des gaz traces atmosphé riques. En scannant la fré quence OL à travers cette caraté ristique, le spectre d'absorption atmosphé rique peut ê tre obtenu. Les profils de concentration verticale des gaz traces atmosphé riques cibles peuvent ê tre ré cupé ré s en se basant sur les spectres d'absorption mesuré s par RHL dans la colonne atmosphé rique à l'aide d'un algorithme de ré cupé ration approprié .

  photomixeur VIGO. Une partie du rayonnement EC-QCL sé paré e par un sé parateur de faisceau a é té injecté e dans une cellule à passage unique de 12,5 cm remplie du mé lange CH 4 dans l'air à la pression atmosphé rique. Le spectre d'absorption directe de CH 4 dans la cellule à passage unique a é té utilisé pour é valuer le spectre d'hé té rodè ne laser de l'absorption du CH 4 . Un PZT entraî né par un signal d'onde sinusoï que a é té utilisé pour numé riser la longueur d'onde OL (EC-QCL), le spectre d'absorption direct du CH 4 de la OL dans la cellule à une seule passe (Fig. 4.7 supé rieur) et son spectre d'absorption hé té rodiste du rayonnement BB incident (Fig. 4.7, infé rieur) ont é té enregistré s simultané ment. Les spectres d'absorption de l'hé té rodie et du CH 4 direct ont tous deux é té respectivement ajusté s sur un profil Lorentz (Fig. 4.7 rouge) avec une fré quence d'absorption centrale fixe à 1233,45545 cm -1 , respectivement. La largeur de la ligne Lorentz de 0,1065 cm -1 pour le spectre d'absorption de

)( 2 )

 2 photomixeur avec des injections de rayonnement OL et BB (Fig. 5.4, (4) courbe noire) à celle du photomixeur avec seulement injection OL (Fig. 5.4, (3) courbe verte), deux signaux s'étaient presque chevauchés, ce qui indique qu'il n'y a presque pas eu de contribution sonore supplé mentaire du rayonnement BB, c'est-à -dire que le N SIN , qui induit par le signal, peut ê tre né gligé à ce stade d'analyse. Par consé quent, la densité sonore totale N total (Éq. (5.2)) du systè me RHL devient Éq. (5.5). Comme on peut le voir dans la Fig. 5.4 (en haut), le bruit du systè me RHL (mesuré à la sortie RF du photomixeur) a é té principalement distribué dans la gamme de 1 kHz-100 MHz, qui est agrandi dans Fig. 5.4 plus bas. On voit que le bruit est principalement composé de 1/f et de bruits blancs. Dans la plage de basse fré quence, le bruit est dominé par 1/f, puis la distribution du bruit tend à ê tre plate. Par consé quent, la bande passante doit ê tre sé lectionné e dans la plage de fré quence sé minudre où 1/f est considé rablement ré duite. Afin d'é tudier les caracté ristiques du bruit blanc dans la plage de haute fré quence, le bruit de chaî ne de dé tection N Det a é té analysé à 150 MHz où le bruit est dominé par le bruit blanc.Compte tenu des lectures de l'analyseur de signaux à 150 MHz : 0,00709 mV pour l'amplitude sonore du bruit de fond de l'analyseur de signaux (Fig.5.4, (1) courbe bleue), et 0,02370 mV pour l'amplitude sonore (Fig.5.4, (2) courbe rouge) ré sultant de l'analyseur de signaux bruit de fond et le bruit de la chaî ne de dé tection, l'amplitude du bruit de la chaî ne de dé tection peut ê tre dé duite de l'Éq.(5.6). Il s'agissait du niveau de bruit de la chaî ne de dé tection inté gré e dans le set RBW de 100 kHz, la densité sonore correspondante de la chaî ne de dé tection N Det a é té ainsi calculé e pour ê tre Hz nV / 5 . 71 (c.f. Éq. (5.7)). En comparant les niveaux de signal avec l'injection OL (Fig. 5.4, (3) courbe verte) et sans injection OL (Fig. 5.4, (4) courbe noire), l'augmentation du niveau de bruit a é té observé e qui indique principalement une influence de l'injection OL, comprenant le bruit de tir induit par le laser et le bruit excessif de laser et les deux ré sultant de l'utilisation de L'EC-QCL OL.

( 2 . 1 )

 21 Bruit de tir par le laser induit (N LSN ) La tension V SN et le courant I SN du bruit de tir induit par le laser peuvent ê tre calculé s avec des Éqs. (5.8)-(5.10), respectivement, où R ti 6000 V/A est la transimpedance du photomixer, e = 1.602× 10 -19 C est la charge é lectrique, B = 5×10 8 Hz est la bande passante du photomixeur sur lequel le bruit est considé ré , I DC est le photocourant DC OL induit par la puissance laser OL dans le photomixer, V DC est la tension DC OL induite par la puissance laser OL surveillé e à la sortie du photomixeur et 10 6 repré sente la conversion de l'unité de V à µV.(2) L'efficacité globale du couplage optique de 0,40 pour le rayonnement du corps noir, basé e sur la transmission de chaque composant optique donné par le fabricant, serait surestimé e. L'efficacité globale mesuré e du couplage optique é tait d'environ 0,27, et cette diffé rence entre 0,27 et 0,40 po peut ê tre due à l'exposition à long terme de ces composants optiques à un environnement humide et salé au bord de la mer. Un facteur de correction supplé mentaire de  2 de 0,68 (0,27/0,40) a é té obtenu.

( a )

 a Impact de la bande de passe RF sur le spectre RHL Pour é tudier l'impact de la bande de passage du filtre RF sur le signal spectral RHL, les spectres d'absorption hé té rodine du CH 4 dans une cellule à passage unique ont é té extraits expé rimentalement et analysé s avec diffé rentes bandes de transmission de filtres RF. Les paramè tres expé rimentaux é taient les mê mes que ceux fixé s ci-dessus, à l'exception de :

Fig. 5 .

 5 11 montre un spectre d'amplitude sonore du signal RHL à partir de la sortie RF du photomixteur enregistré à l'aide d'un analyseur de signaux (avec un RBW de 100 kHz). Nous remarquons, il ya des forts bruits 1 / f dans la gamme de basse fré quence qui doit ê tre filtré .Les densité s de bruit dans les diffé rentes bandes de passage des filtres RF disponibles dans le pré sent travail ont é té estimé es en divisant le bruit inté gral sur chaque bande de passage par la bande passante et la racine carré e du RBW (100 kHz) (tableau 5.3). Comme le montre le tableau 5.3, la densité sonore du filtre RF avec une bande de passage de 27,5 à 270 MHz é tait la plus faible et la RSB correspondante é tait la plus é levé e en raison de sa bande passante filtraire plus large (au prix d'une ré solution spectrale plus faible).Des spectres d'absorption RHL CH 4 ont ensuite é té enregistré s avec ces cinq filtres RF disponibles, comme le montre la Fig.5.12. Les spectres d'absorption RHL CH 4 mesuré s par des filtres RF à col de bande AC (Fig.5.12 à gauche), qui peuvent filtrer considé rablement les bruits de basse fré quence, ont une RSB plus é levé e et une meilleure forme spectrale de ligne, tandis que les spectres mesuré s avec des filtres RF à faible passage à couplage DC (Fig.5.12 à droite) sont bruyants ré sultant d'un son é levé de 1/f. C'est montré que le niveau de bruit du spectre mesuré avec le filtre RF avec une bande de passage de 27,5-270 MHz (Fig.5.12 en noir) est infé rieur à celui mesuré avec une bande de passage de 27-33 MHz (Fig.5.12 en rouge). De plus, il n'y a pas de diffé rence é vidente dans les largeurs spectrales des lignes entre deux spectres d'absorption CH 4 RHL. La raison en est que la largeur thé orique de la ligne spectrale (FWHM) de l'absorption CH 4 autour de 1255,00 cm -1 à 280 mbar est de 0,034 cm -1 (1020 MHz qui est plus large que les bandes passantes de filtre RF doublé es (12 MHz et 485 MHz) et donc il n'y a pas d'effet é vident des largeurs de bande du filtre RF sur les largeurs de ligne mesuré es.En se basant sur cette analyse, le filtre RF avec une bande de passage de 27,5-270 MHz a é té sé lectionné pour le systè me RHL actuel.(b) RHL spectral line-shape vs vitesse de balayage de la fré quence OLComme nous l'avons vu dans les chapitres 2.1.6 et 4.2.2.3, afin d'obtenir un spectre d'hé té rothè ne de haute pré cision (avec un dé calage et une distorsion de la forme de la ligne minimisée), le temps ΔT scan de balayage de l'ensemble de la demi-largeur de la ligne d'absorption  HWHM (en [cm -1 ]), qui dé pend é galement de la vitesse de balayage de la fré quence OL  sc (en [cm -1 /s]), devrait ê tre adapté de maniè re approprié e à une constante temporelle de la LIA τ, telle que les spectres d'hé té rodè ne à base de BB à l'aide de diffé rentes vitesses de balayage avec une constante de temps LIA sé lectionné e de 1 ms ont é té effectué es. Dans cette é tude, les paramè tres expé rimentaux é taient les mê mes que ceux fixé s ci-dessus, à l'exception de :

  ) pression du mé lange CH 4 dans l'air dans la cellule à une seule passe : 280 mbar; Les spectres d'absorption RHL CH 4 enregistré s en scannant la fré quence OL à diffé rentes vitesses (voir le tableau 5.4) à l'aide de la mê me constante de temps LIA de 1 ms sont pré senté es à la Fig.5.13. Comme nous l'observons, la sélection de la vitesse de numérisation de la fré quence OL doit ê tre bien adapté e à la constante de temps LIA appliqué e. En comparant ces quatre spectres d'absorption hé té rodydine de CH 4 , RSB, é largissement de la largeur de ligne Δν b (FWHM), décalage de ligne et niveau de bruit (1σ) de ces spectres d'absorption hé té rodyne ont é té analysé s en fonction de l'ajustement du profil Voigt (Fig.5.13, bleu) et ré sumé s dans le tableau 5.4. Nous remarquons que la combinaison de 1 ms de la constant de temps et la vitesse de balayage 0,3935 cm -1 /s (avec un temps de numé risation de 36 ms), le spectre hé té rodiste a un niveau de bruit plus faible et un changement de ligne plus faible tout en gardant une ré solution spectrale é levé e (Fig.5.13 (b) et tableau 5.4 en gras).

Figure 2 Figure 3

 23 Figure 2 Calculated coupling efficiency curves of the first five HE1m modes in a 320-μm-core hollow-glass fiber.

14 Figure 4

 144 Figure 4 Calculated attenuation coefficients of the first four HE 1m modes in an Ag/AgI hollow-glass fiber.

Fig. 5

 5 Fig.5shows the coupling conditions necessary to achieve minimal loss through 1-m-long, 320-µm -core and 1000-μm-core hollow fibers. Maximum transmission occurs at a ƒ-number

20 Figure 5

 205 Figure 5Min-loss coupling conditions for 1-m-long, 320-μm-core and 1000-μm-core hollow fibers.

Figure 6

 6 Figure 6 Light coupling with a ratio of light spot size to fiber core size ω 0 /a. (a) ω 0 /a ˂ 0.64; (b) ω 0 /a = 0.64; (c) ω 0 /a  0.64.

14 Figure 7

 147 Figure 7 Calculated beam divergence of the first four HE 1m modes exciting a hollow fiber.

Figure 8

 8 Figure 8 Fiber-coupled LHR assembly.

Figure 9

 9 Figure 9 Dual lens collimating/focusing assembly

1 . 2 .

 12 Coupling sunlight : Opton-CP25MWLW250-SMA-DMHF (lens in Ge, AR coating (3-12 μm) with a focal length of 250 mm and 25 mm in diameter). Coupling laser : Opton-CP1MWLW50-SMA-DMHF (lens in Ge, AR coating (3-12 μm) with a focal length of 50 mm and 12.7 mm in diameter), mounted directly to the Daylight Solution laser head.3. Fiber-coupled beam mixing : OKSI Opton-2T1FB3201000MW-SMA-0.5m/0.5m (2 to 1 hollow core fiber bundle).

1

 1

  Solar emission spectrum is the distribution of the radiation energy associated with the given wavelengths. More than 99.9% of the energy is concentrated in the wavelength range from 0.2-10.0 µm, and the peak radiation is at 0.48 µm. The energy in the ultraviolet band (<0.40 μm), the visible light band (0.40-0.76 μm) and the infrared band (>0.76 μm) account for

Fig. 1

 1 Fig.1shows a solar irradiance spectrum in the range of 1223-1263 cm -1 computed through a Model by G. Wang[2], and there are no Fraunhofer lines in the range of 1241.4-1242.4 cm -1 (Fig.2 (a)). In the range of 1261.3-1262.5 cm -1 (Fig.2 (b)), there is a very weak Fraunhofer line which can be neglected compared with the atmospheric absorption lines for our research.

Figure 1 Figure 2

 12 Figure 1 Solar irradiance spectrum in the range of 1223-1263 cm -1 computed through a Model by G. Wang [2].

Fig. 1 .

 1 Fig. 1. Experimental setup used for N 2 O monitoring. BS : Beam-splitter; GC : Gas chromatograph; MFC 1, 2, 3, 4, 5, 6 : Mass Flow Controllers; Th 1 : Thermocouple oven, Th 2 : Thermocouple blank, Th 3 : Thermocouple reactor, Th 4 : Thermocouple saturator; Prs : Pressure sensor; VIGO : Thermoelectrically cooled infrared photovoltaic detector; DAQ : Data Acquisition card.

Fig. 2 .

 2 Fig. 2. Simulation of 300 ppbv N 2 O absorption spectrum in a multi-pass cell (L eff =50 m) at 120 mbar.

Fig. 3 .

 3 Fig. 3. Absorption signal of 5 ppmv N 2 O at 120 mbar (a); the corresponding absorption spectrum (d) obtained by using the relative wavenumber calibration curve (c) which allows one to convert "data point number" into "wave number" by means of the FRS of the used etalon (b).

5 Fig. 4 .

 54 Fig. 4. (a) N 2 O absorption spectra at different concentrations at 120 mbar; (b) Plot of the integrated absorbance vs. concentration, associated with a linear fit.

Fig. 5 .

 5 Fig. 5. Allan deviation plot.

Fig. 7 .

 7 Fig. 7. left: Experience of catalytic reduction of NO to purify CO 2 in exhaust gas flow from oxyfuel-combustion, right: EC-QCL-based Laser sensor.

3. 1 N 2 O

 12 evolution in catalytic reaction of NO with COThe catalytic reaction of NO with CO over the pre-treated Pt/SiO 2 catalyst in the temperature range of 50-500 ˚C was performed, N 2 O production was monitored and analyzed by the developed EC-QCL sensor.A N 2 O absorption spectrum recorded during the process of NO reaction with CO over a Pt/SiO 2 catalyst at 190 ˚C is shown in Fig.8. It was recorded at a pressure of 120 mbar in the multi-pass cell with 240 spectral averages in 12 s.

Fig. 8 .

 8 Fig. 8. Absorption spectrum of 6.13 ppmv N 2 O during a catalytic reaction of NO with CO over a Pt/SiO 2 catalyst at 190 ˚C @ 120 mbar.

Fig. 9

 9 Fig. 9 shows time series measurement (with a step of 1˚C from 50 to 500 ˚C) of N 2 O concentrations produced during the NO-CO reaction over the Pt/SiO 2 catalyst. A maximum concentration of ~ 6.1 ppmv N 2 O was observed at 190 ˚C.

Fig. 9 .

 9 Fig. 9. Concentration of N 2 O in a NO-CO reaction over a Pt/SiO 2 catalyst vs. temperature.

Fig. 10 .

 10 Fig. 10. Conversion efficiency of NO to N 2 (red), NO 2 (blue) and N 2 O (green, the values are magnified 20 times); and CO to CO 2 (black) over Pt/SiO 2 vs. temperature.

Table 1

 1 Comparisons among satellite, ground, and airplane/balloon platforms…..…......14

Table 2 . 1

 21 Specifications of three commercially available sun-trackers.................................79

Table 2 . 2

 22 Specifications of IR photomixers for LHR application………………….............86

Table 2 . 3

 23 Pass-bands of RF filters available for the present work……..……………….......87

Table 2 . 4

 24 Specifications of Keysight 8472B and Herotek DHM020BB schottky diodes.....89

Table 2 . 5

 25 Specifications of lock-in amplifier (Model 5110, AMETEK, Inc.)………….......89

Table 2 . 6

 26 Simulation of the effect of the LP filter on absoption line-shape with different ………………..………..………....................................................................…..91

Table 2 . 7

 27 Lens data editor of the beam contraction……………...........................................98

Table 2 . 8

 28 Lens data editor of the beam expander...................................................................99

Table 2 . 9

 29 The Lens editor....................................................................................................100

Table 2 .

 2 10 Specifications of the PIR fiber.

Table 5 . 5

 55 Comparisons between LHR and FTS...................................................................168

	xviii

Table 1

 1 Comparisons among satellite, ground, and airplane/balloon platforms.

	Platform	Advantage	Disadvantage
		1. Covering the entire earth or any	1. Complex instrumental characteristics and
	Satellite	designated area for a long time	physical processes
		2. Retrievals of tropospheric vertical	2. Data must be validated
		profiles	3. High overhead cost
			4. Low sensitivity at lower altitudes
	Ground	1. Accurate and continuous measurements
		near the ground
		2. Validation of satellite observations
	Airplane/	1. Large latitudinal/longitudinal transsects	1. Lower few hundred meters of the
	balloon	in a short time without cloud	atmosphere is difficult to measure
		interference	2. Discontinuous measurement due to limited
		2. Less affect from transport model errors	flight missions
		3. Valuable links between ground-based
		and satellite-based measurements

Chapter 1 Principle of Laser Heterodyne Radiometer Objective

	). Section 1.3 deals with the
	criteria on coupling efficiency of two light beams in a free-space coupling LHR. Instrument Laser heterodyne radiometer (LHR) is one of the most important instruments for the
	noise sources, system SNR and sensitivity are discussed in Section 1.4 to1.5. The method for measurement of vertical profiles of atmospheric trace gases. The principle of a LHR is
	extracting heterodyne signal is presented in Section 1.6. The SNR of the LHR is compared described in Section 1.1 to 1.2. Section 1.3 deals with the criteria on coupling efficiency of
	with that of the FT-IR instrument in Section 1.7. The principle of vertical profile retrieval two light beams in a free-space coupling LHR. Instrument noise sources, system SNR and
	from the LHR measured absorption spectrum in the atmospheric column is briefly stated in sensitivity are discussed in Section 1.4 to 1.5. The method for extracting heterodyne signal is
	Section 1.8. presented in Section 1.6. The SNR of the LHR is compared with that of the FT-IR instrument
	Chapter 2 is devoted to introduction and discussion on practical instrumental in Section 1.7. The principle of vertical profile retrieval from the measured absorption
	considerations and specifications of the devices involved in our mid-IR LHR system. Two spectrum in the atmospheric column is briefly presented in Section 1.8.
	systems for sunlight collection are presented, including (1) free-space telescope system, and
	(2) fiber coupling system. Principle of Laser Heterodyne Radiometer
	Chapter 3 evaluates the performance of the EC-QCL being used as the LO in our LHR In a LHR, the electromagnetic field of the sunlight E S (t) = A S0 (ω)cos(ωt) at frequency  is
	through N 2 O detection in a chemical catalysis process by direct absorption spectroscopy in a mixed in a photomixer with an electromagnetic field E L (t) = A L0 (ω L )cos(ω L t) at frequency  L
	multi-pass cell. The laser performance was evaluated in terms of laser emission line width, from a local oscillator (LO). A beat note at an intermediate frequency (IF, |- L |), produced
	single-mode wavelength tunability, stabilization of the LO source and wavelength-dependent from the photomixing, is amplified by a low-noise amplifier and filtered by a band-pass filter.
	baseline.
	Chapter 4 presents the development of a proof of concept (PoC) mid-IR LHR. The
	developed LHR was tested on the QualAir platform of the Université Pierre et Marie Curie
	(UPMC), in collaboration with Dr. Tao TE of the « Laboratoire d'Études du Rayonnement et
	de la Matiè re en Astrophysique et Atmosphè res (LERMA) ». Ground-based measurements of
	tropospheric CH 4 in the atmospheric column were performed.
	Chapter 5 describes the development of a fully transportable mid-IR LHR prototype. A
	mid-IR fiber was explored to couple the sunlight to the heterodyne receiver, which makes our
	LHR, equipped with an EKO sun-tracker, fully transportable. The developed LHR instrument
	was tested and validated via ground-based field measurements of tropospheric CH 4 and N 2 O
	in the atmospheric column on the roof terrace of the IRENE (Innovation Recherche en
	Environnement) platform in Dunkerque (51.05˚N/2.34˚E).
	Finally, the major achievements in this PhD work are summarized and some future
	directions for the ground-based LHR measurements of vertical concentration profiles of
	atmospheric trace gases are prospected.

Solar radiation LO Photomixer i IF (t) G Ampl. Band-pass filter i IF-B (t) P HET B/2 Square law Det.

	P		P		P		(1.11)
	HET		S

Table 2 . 1

 21 Specifications of three commercially available sun-trackers.

		Cimel CSPHOT	Bruker A547N	EKO STR-21G
	FoV	1.2˚	45˚	30˚
	Tracking accuracy	0.1˚	0.0167˚	0.01˚
	Portability	Yes	No	Yes
	Price	~ 25000 USD	~ 20000 USD	~ 14000 USD

2.1.2 IR blackbody sources

Blackbody sources with stable radiation are highly requested for the development and the performance characterization of LHR. In our experiments, an Oriel® blackbody source (Model 67030, Newport Inc.) and an IR blackbody emitter (Model IR-Si217, Hawkeye Technologies Inc.) are respectively used.

(1) Oriel® blackbody (Fig.

2

.6 left) is a highly uniform and temperature stabilized infrared radiation source, calibrated to a NIST (Natinal Institute of Standards and Technology, USA) standard. The major functional components of the blackbody are cavity, heater and dual thermocouples (Fig.

2

.6 right). A ceramic sealed heater coil uniformly heats a stainless 1.3, 0.64, and 0.32 mm in diameters, respectively.

Table 2 . 2

 22 Specifications of IR photomixers for LHR application.

	VIGO detector	PVI-4TE-10.6		PVMI-4TE-8
	Active Area	0.5*0.5 mm 2		1*1 mm 2
	Window	BaF2 (3 deg wedged)	BaF2 (wedged)
	Wavelength Range	3 to 12 µm		2 to 12 µm
	Transimpedance @ R LOAD = 50 Ω	6.0E+3 V/A		1.15E+4 V/A
	Detectivity ±20% @ 8 µm	5.0 E+09 cm	/W	8.3 E+09 cm	/W
	Current Responsivity ±20% @ 8 µm	4.2 A/W		0.226 A/W
	Voltage Responsivity @ 8 µm	2.52E+4 V/W		2.55E+3 V/W
	Output Voltage Noise Density	120 nV/		250 nV/
	Immersion Type / FOV	Hyperhemispherical / 35˚ Hyperhemispherical / 35˚
	Dynamic Resistance	150 Ω		1410 Ω
	Thermistor Resistance	320 kΩ		470 kΩ
	Reverse Bias Voltage	650 mV		0 V
	Stability of Temperature	0.01 K		0.01 K (estimated)

  , connected in cascade at the output of the photomixer, are applied to optimize the LHR performance. The filers available for the present LHR development are listed in Table2.3.

). Appropriate selection of their values can not only provide the requested spectral resolution, but also effectively remove noises resulting from the LO laser and electronic components. Various combinations of filters with different pass-bands

Table 2 . 3

 23 Pass-bands of RF filters available for the present work.

Table 2 . 4

 24 Specifications of Keysight 8472B and Herotek DHM020BB schottky diodes.

	Model	Frequency range	Frequency response	Low-level sensitivity*	Noise	Maximum input power	SWR
	Keysight 8472B	0-18 GHz	±0.2 dB	> 0.5 mV/µW	< 50 µV	200 mW	1.2
	DHM020BB	100 kHz-2 GHz	±0.3 dB	1.0 mV/µW	< 100 µV	200 mW	1.3
	* Note : Schottky diodes are designed to rectify very low levels of RF power to produce a DC output voltage
	proportional to the RF power. Therefore, the sensitivity of Schottky diodes is usually defined as low level
	sensitivity [9].

Table 2 .5 Specifications

 2

of lock-in amplifier (Model 5110, AMETEK, Inc.).

Table 2 . 6

 26 Simulation of the effect of the LP filter on absorption line-shape with different .

	Halfwidth Δ	] HWHM [cm -1	0.014 0.014 0.014 0.014 0.014 0.014 0.014 0.014 0.014 0.014
	Scanning range Δ	] scan [cm -1	1	1	1	1	1	1	1	1	1	1
	Scanning period T [s]		0.3	0.5	1	1.5	2	2.5	3	5	10	30
	Scanning speed 	sc [cm -1	/s]	3.33	2	1	0.67	0.5	0.4	0.33	0.2	0.1 0.033
	= Δ	scan /T
	Scanning time ΔT	scan [ms]	4.17 6

.95 13.9 20.85 27.8 34.75 41.7 69.5 139 417

  Simulation results for frequency scan in continuous mode are shown in Fig.2.17. Simulation output spectra from the LP filter using different parameters (see Table2.6). Condition of the Hitran simulation spectrum (input : black) : absorption line center: 1233.45 cm -1 , pressure: 250 mbar, concentration: 0.1, and length of the absorption cell: 13 cm.

			1.2									1.2
					Input 1 ms		 SC = 0.1 cm	-1 /s				Input 1 ms		 SC = 0.033 cm	-1 /s
	0.6 0.8 1.0 1.2 0.2 0.4 0.6 Output Output 1.0 0.8		Input 0.1 ms 0.3 ms 1 ms 3 ms 10 ms 30 ms 3 ms 10 ms 30 ms 100 ms		 = 0.3ms (Opt.) scan/ = 14  SC = 3.33 cm -1 /s scan= 4.17ms scan=139ms  = 1ms (Opt.) scan/ = 14		Output Output	0.6 0.8 1.0 1.2 0.2 0.4 0.6 1.0 0.8	Input 0.1 ms 0.3 ms 3 ms 10 ms 30 ms 1 ms 3 ms 10 ms 30 ms 100 ms 300 ms		 = 0.3ms (Opt.) scan/ = 23  SC = 2 cm scan=417ms -1 /s scan=6.95ms  = 3ms (Opt.) scan/ = 14
			0.4									0.4
			0.0									0.0
			0.2 1233.400	1233.425	1233.450	1233.475	1233.500	1233.525		0.2 1233.400	1233.425	1233.450	1233.475	1233.500	1233.525
						Wavenumber (cm -1 )								Wavenumber (cm -1 )
			0.0									0.0
	1233.400 Figure 2.17		1233.425	1233.450 Wavenumber (cm 1233.475 -1 )	1233.500	1233.525		1233.400	1233.425		1233.450 Wavenumber (cm 1233.475 -1 )	1233.500	1233.525
		1.2									1.2
		1.0		Input 0.1 ms 0.3 ms 1 ms		 SC = 1 cm scan= 13.9ms -1 /s			1.0	Input 0.1 ms 0.3 ms 1 ms		-1 /s scan=20.85ms  SC = 0.67 cm
	Output	0.6 0.8		3 ms 10 ms 30 ms 100ms						Output	0.6 0.8	3 ms 10 ms 30 ms		 = 1ms (Opt.) scan/ = 21
		0.4									0.4
		0.2									0.2
		0.0									0.0
			1233.400		1233.425	1233.450	1233.475	1233.500	1233.525		1233.400	1233.425		1233.450	1233.475	1233.500	1233.525
						Wavenumber (cm -1 )								Wavenumber (cm -1 )
			1.2									1.2
			0.8 1.0		Input 0.1 ms 0.3 ms 3 ms 10 ms 30 ms 1 ms		 SC = 0.5 cm  = 3ms (Opt.) -1 /s scan/ = 9 scan=27.8ms			0.8 1.0	Input 0.3 ms 30 ms 10 ms 3 ms 1 ms		 SC = 0.4 cm scan/ = 12 -1 /s  = 3ms (Opt.) scan=34.75ms
	Output		0.6								Output	0.6
			0.4									0.4
			0.2				0.1	0.1	0.1	0.1 0.2	0.1	0.3	0.3	0.3	1	1
			1233.400 0.0	 1233.425  [ms]	0.3 1233.475 1 Wavenumber (cm 1233.450 -1 )	0.3 1233.500 1	0.3 1233.525 1	0.3 0.0 1233.400 1	0.3 1233.425 1	1 3	1 3 Wavenumber (cm 1233.450 1233.475 -1 )	1 3	1233.500	3 10	1233.525	3 10
			1.2									1.2
			0.8 1.0		Input 0.3 ms 1 ms 10 ms 30 ms 3 ms		3 10  = 3ms (Opt.) 3 10 scan/ = 14  SC = 0.33 cm -1 /s scan=41.7ms	3 10	3 10 0.8 1.0	3 10 30 ms 10 ms 3 ms Input 0.3 ms 1 ms	10 30	10 30	10 30 scan/ = 23 30 100  = 3ms (Opt.)  SC = 0.2 cm -1 /s scan= 69.5ms	30 100
	Output	0.6				30	30		30	30 0.6 Output	30	-	-	-	-	300
			0.4									0.4
							-	-	100	-	-	-	-	-	-	-
			0.2									0.2
			0.0									0.0
			1233.400	1233.425	1233.450	1233.475	1233.500	1233.525		1233.400	1233.425		1233.450	1233.475	1233.500	1233.525
						Wavenumber (cm -1 )								Wavenumber (cm -1 )
															92

 = 1ms (Opt.) scan/ = 14

100 Table 2 . 9

 10029 The Lens editor.

		Object Type	Comment	Material	X position	Y position	Z position	Tilt About X
						(Vertical)	(Horizontal)	(in degree)
	1	Source Ellipse	LASER		0.000000	120.000000 380.000000 180.000000
	2	Standard Lens	Lens 3 : LA5317	CAF2	0.000000	120.000000 320.000000 180.000000
	3	Standard Lens	Lens 4 : LA5817	CAF2	0.000000	120.000000 175.926504 180.000000
	4	Standard Lens Mirror 1 : PF10-03-M01	MIRROR	0.000000	120.000000 130.000000	45.000000
	5	Standard Lens Mirror 2 : PF10-03-M01	MIRROR	0.000000	60.000000	130.000000 135.000000
	6	Standard Lens Mirror 3 : PF10-03-M01	MIRROR	0.000000	60.000000	340.000000	0.000000
	7	Source Ellipse	Sunlight		0.000000	0.000000	0.000000	0.000000
	8	Standard Lens	Lens 1 : #89-169	CAF2	0.000000	0.000000	20.000000	0.000000
	9	Standard Lens	Lens 2 : LB5247	CAF2	0.000000	0.000000	302.200000	0.000000
	10 Standard Lens	Splitter. POB	CAF2	3 0.000000	0.000000	340.000000 135.000000
	11 Standard Lens 12 Detector Rect	Lens 5 : LA5370 VIGO	CAF2	0.000000	0.000000 Wavelength (cm -1 ) 360.000000 0.000000 0.000000 412.300000 0.000000

Table 2 .

 2 10 Specifications of the PIR fiber.

	Fiber Specification
	Core diameter [µm ]	860 ± 20
	Minimum bend radius [mm]	150
	Transmission Range [µm ]	3 -18
	Core material	AgCl 0.25 Br 0.75
	Cladding material	AgCl 0.50 Br 0.50
	Core refractive index	2.15
	Effective NA	0.30 ± 0.03
	Operating temperature [˚C]	-50 < T < 140
	Maximum transmitted Power [W]	40 (CW)
	Length [m]	1.5 ± 0.05

Table 3 . 1

 31 Relevant settings and the diluted concentration.

	D 1 [ml/min]	K	C initial [ppmv]	C final [ppbv]
	0.50	4173.0	1000	239.64
	1.06	1968.9	1000	507.89
	2.06	1013.6	1000	986.56
	3.06	682.7	1000	1464.77
	4.20	497.7	1000	2009.38
	5.16	405.3	1000	2467.53
	7.06	296.5	1000	3373.05
	10.55	198.7	1000	5032.08

Table 4 . 1

 41 Selected CH 4 and N 2 O absorption lines.

	Mol.	HITRAN		FTS*
		Wavenumber (cm -1 ) Line intensity (cm/molecule) Wavenumber (cm -1 )
	CH 4	1241.8632	6.590E-21	1241.8626
	CH 4	1241.9489	6.596E-21	1241.9474
	CH 4	1261.6450	1.834E-20	1261.6370
	N 2 O	1261.9871	1.044E-19	1261.9854
	CH 4	1262.2249	2.748E-20	1262.2321

* FTS frequencies were obtained from the atmospheric absorption spectrum recorded with a FTS (Bruker IFS 125HR) on the QualAir platform of the UPMC (TCCON-Paris station).

Table 4 . 2

 42 Used time constants at a given scanning speed of the LO frequency  sc . (Note : the spectral half width ν HWHM of the used CH 4 line around 1233.46 cm -1 is 0.0538 cm -1[2] at ambient pressure.)

	Scanning frequency (mHz)	20	50	100	250
	Scanning period T (s)	25	10	5	2
	Scanning range Δ scan (cm -1 )	0.787	0.787	0.787	0.787
	halfwidth ν HWHM (cm -1 )	0.0538	0.0538	0.0538	0.0538
	Scanning speed  sc (cm -1 /s)	0.03148	0.0787	0.1574	0.3935
	= Δ scan /T
	Scanning time ΔT scan (ms) = ν HWHM /  sc	1709	684	342	137
		100	30	10	1
	 (ms)	300	100	30	10
		1000	300	100	30
		-	1000	300	-

Figure 4.8 BB-based heterodyne spectra of CH 4 absorption at a scanning speed  sc of 0.03148 cm -1 /s (a scanning time ΔT scan of 1709 ms) combined with different time constants, respectively.

Table 4 .3 Analysis

 4

	 sc (cm -1 /s)	ΔT scan (ms)	 (ms)	SNR	Δν b (cm -1 )	Absorption depth	δν (cm -1 )	Fit residual (1σ)
			100	5	0.0545	0.0126	0.0032	0.0026
	0.03148	1709	300	8	0.0656	0.0114	0.0095	0.0015
			1000	8	0.0711	0.0062	0.0325	0.0008

of BB-based heterodyne spectra of CH 4 absorption at the scanning speed of the LO frequency ( sc ) of 0.03148 cm -1 /s (the scanning time (ΔT scan ) of 1709 ms) with different time constants (τ) (Fig. 4.8) (1 σ : Standard deviation).

)

Figure 4.9 BB-based heterodyne spectra of CH 4 absorption at a scanning speed  sc of 0.0787 cm -1 /s (a scanning time ΔT scan of 684 ms) combined with different time constants, respectively.

Table 4 .4 Analysis

 4

	 sc (cm -1 /s)	ΔT scan (ms)	 (ms)	SNR	Δν b (cm -1 )	Absorption depth	δν (cm -1 )	Fit residual (1σ)
			30	5	0.0548	0.01258	0.0031	0.00230
	0.0787	684	100	6	0.0640	0.01244	0.0081	0.00210
			300	6	0.0722	0.01154	0.0243	0.00180
			1000	6	0.1222	0.00570	0.0821	0.00089

of BB-based heterodyne spectra of CH 4 absorption at the scanning speed of the LO frequency ( sc ) of 0.0787 cm -1 /s (the scanning time (ΔT scan ) of 684 ms) with different time constants (τ) (Fig. 4.9) (1 σ : Standard deviation).

)

Figure 4.10 BB-based heterodyne spectra of CH 4 absorption at a scanning speed  sc of 0.1574 cm -1 /s (a scanning time ΔT scan of 342 ms) combined with different time constants, respectively.

Table 4 .5 Analysis

 4

	 sc (cm -1 /s)	ΔT scan (ms)	 (ms)	SNR	Δν b (cm -1 )	Absorption depth	δν (cm -1 )	Fit residual (1σ)
			10	5	0.0550	0.01251	0.0016	0.00230
	0.1574	342	30	6	0.0627	0.01204	0.0048	0.00209
			100	7	0.0672	0.01101	0.0181	0.00156
			300	7	0.0812	0.00824	0.0490	0.00115

of BB-based heterodyne spectra of CH 4 absorption at the scanning speed of the LO frequency ( sc ) of 0.1574 cm -1 /s (the scanning time (ΔT scan ) of 342 ms) with different time constants (τ) (Fig. 4.10) (1 σ : Standard deviation).

)

Figure 4.11 BB-based heterodyne spectra of CH 4 absorption at a scanning speed  sc of 0.3935 cm -1 /s (a scanning time ΔT scan of 137 ms) combined with different time constants, respectively.

Table 4 .6 Analysis

 4 sc ) and scanning times (ΔT scan ) were obtained for the current work, as shown in Table4.3-4.6 in bold and Fig.4.8-4.11 in red.

	 sc (cm -1 /s)	ΔT scan (ms)	 (ms)	SNR	Δν b (cm -1 )	Absorption depth	δν (cm -1 )	Fit residual (1σ)
			1	7	0.0541	0.01261	0.0004	0.00174
	0.3935	137	10	9	0.0599	0.01181	0.0041	0.00129
			30	8	0.0733	0.00736	0.0120	0.00096
	Based on the analysis of the heterodyne absorption spectra shown in Figs. 4.8-4.11

of BB-based heterodyne spectra of CH 4 absorption at the scanning speed of the LO frequency ( sc ) of 0.3935 cm -1 /s (the scanning time (ΔT scan ) of 137 ms) with different time constants (τ) (Fig. 4.11) (1 σ : Standard deviation). (black), SNR, line width broadening (Δν b ), absorption depth, line shift (δν) and noise level (1σ) of these spectra were analyzed from the Lorentz profile fits (Figs. 4.8-4.11 red and blue) and summarized in Table 4.3-4.6, the optimal time constants (τ) at given scanning speeds of LO frequency (

Table 4 .

 4 7, the combination of the scanning speed of the LO frequency of 0.3935 cm -1 /s (the scanning time of 137 ms) and the LIA time constant of 1 ms has a relatively low noise level, highest absorption depth, no significant shift in absorption center frequency and no distortion of absorption line shape (Table4.7 in bold).

Table 4 . 7

 47 Analysis of BB-based heterodyne spectra of CH 4 absorption with optimal at given  sc and ΔT scan .

	 sc (cm -1 /s)	ΔT scan (ms)	 (ms)	SNR	Δν b (cm -1 )	Absorption depth	δν (cm -1 )	Fit residual (1σ)
	0.03148	1709	300	8	0.0656	0.01143	0.0095	0.00148
	0.0787	684	100	6	0.0640	0.01244	0.0081	0.00210
	0.1574	342	100	7	0.0672	0.01101	0.0181	0.00156
	0.3935	137	1	7	0.0541	0.01261	0.0004	0.00174

Table 5 . 1

 51 Parameter setting on the Signal Analyzer.

	RBW	VBW	Frequency scan range	Average count
	100 kHz	51 Hz	1 kHz-500 MHz	1

Table 5 . 2

 52 Comparisons between theoretical Voigt linewidths and measured Voigt linewidths of the LHR and the direct absorption spectra.

		LHR	Direct
	Theoretical Voigt linewidth (cm -1 )	0.0314	0.0228
	Measured Voigt linewidth (cm -1 )	0.0457	0.0239

Table 5 .

 5 2 shows comparisons of theoretical Voigt linewidths to the measured Voigt linewidths of the LHR and the direct absorption spectra. It is seen that the measured Voigt linewidth of the direct absorption spectrum was comparable to the theoretical value, while the measured Voigt linewidth of LHR spectrum was obviously wider than the theoretical value.

Table 5 . 3

 53 Noise density with different RF filter pass-bands.

	Pass-band (MHz)			DC-270	DC-520	DC-720	27-33	27.5-270
	Noise density (	V / 	Hz	)	0.396	0.239	0.239	0.180	0.149

Table 5 . 4

 54 Analysis of BB-based heterodyne spectra (Fig. 5.13) of CH 4 absorption with the used time constants (τ) of 1 ms at different scanning speeds of the LO frequency ( sc ). (Note : the halfwidth of the used CH 4 line

	 HWHM at 280 mbaris 0.014 cm -1 [6].)
	 (ms)	 sc (cm -1 /s)	ΔT scan (ms)	SNR	Δν b (cm -1 )	Absorption depth	δν (cm -1 )	Fit residual (1σ)
		0.1574	89	13	0.038	0.1142	1.6E-4	0.0091
	1	0.3935	36	24	0.042	0.1037	4.0E-4	0.0043
		0.7870	18	30	0.048	0.0975	8.2E-4	0.0032
		1.1799	12	43	0.079	0.0909	1.2E-3	0.0021
	1 σ : Standard Deviation (SD)

Table 5 . 5

 55 Comparisons between LHR and FTS

		Spectral resolution	FoV	Operation temperature Instrument size / weight
	LHR	0.003 cm -1	~0.4 mrad	Room temperature	~0.6 × 1.5 m 2 / ~30 kg
	FTS	0.02 cm -1	~2.39 mrad	Liquid nitrogen-cooled detector	~2 × 4 m 2 / ~700 kg
	Conclusion
	In this chapter, a full transportable LHR prototype involving a mid-IR fiber to collect sunlight
	through an EKO sun-tracker was developed. Evaluation and optimization of the developed
	LHR prototype with the help of a stable high temperature blackbody radiation to simulate the
	sunlight was performed. The developed LHR instrument was then tested and validated via
	ground-based field measurements of tropospheric CH 4 and N 2 O in the atmospheric column
	on the roof of the IRENE platform of the ULCO in Dunkerque (51.05˚N/2.34˚E). The
	extracted spectrum by the LHR was in a good agreement with the FT-IR spectrum measured
	using a Bruker IFS 125HR FTS and with an atmospheric transmission modelling spectrum,

Évaluation de la performance de l'oscillateur local utilisé

  Afin de tester notre appareil et de caracté riser ses performances, un recepteur RHL mi-IR a é té mis au point comme Preuve de Concept (PdC). Il a é té validé sur la plate-forme QualAir de l'Université Pierre et Marie Curie (UPMC) associé à un héliostat de la station TCCON-Paris. Ainsi, le spectre d'absorption du CH 4 pré sent dans la colonne atmosphé rique a é té extrait du rayonnement solaire à l'aide de notre ré cepteur RHL. Il est en bon accord avec le spectre mesuré par la station TCCON-Paris. Aprè s cette validation d'essai sur le terrain, un instrument LHR mi-IR (~8 µm) entiè rement transportable a é té dé veloppé . Une fibre IR nouvellement disponible dans le commerce est exploité e pour coupler la lumiè re du soleil au ré cepteur RHL, é quipé d'un EKO sun-tracker, ce qui rend le RHL mid-IR trè s transportable et stable. Le prototype RHL dé veloppé est dé ployé sur le toit de la plate-forme IRENE de l'Université du Littoral Côte d'Opale (ULCO) à Dunkerque pour la té lé dé tection sur le terrain de CH 4 et N 2 O dans la colonne atmosphé rique. Le spectre LHR de CH 4 et N 2 O dans la colonne atmosphé rique est en bon accord avec le spectre FT-IR de CH 4 et N 2 O et la modé lisation de la transmission atmosphé rique. L'instrument LHR mi-IR entiè rement transportable mis au point dans le cadre de cette thèse possède un fort potentiel d'utilisation dans la mesure des profils verticaux de concentration d'espèces clés atmosphérique. Il peut potentiellement être positionné sur des engins spatiaux, sur des plates-formes aé roporté es ou au sol. Herriot modifié e. La fré quence EC-QCL est numé risé e sur une ligne d'absorption N 2 O approprié e pour dé terminer son absorption inté gré e dé pendante de la concentration en adaptant le spectre d'absorption expé rimental à un modè le de profil Voigt. Le ré glage de fré quence fine de l'EC-QCL est ré alisé en appliquant un signal de 50 Hz sinusoï d-ondes (avec une amplitude de 3,0 V PP et un dé calage de 1,6 V DC ) à partir d'un gé né rateur de fonction à l'é lé ment PZT de la cavité externe de l'EC-QCL. Comme le montre la Fig. 3.1 (à gauche), 10 % de faisceau laser ré flé chi est envoyé à un etalon Fabry-Perot pour l'é talonnage de la fré quence laser, et 90 % du faisceau laser transmis est dirigé vers la cellule multi-pass pour sonder l'absorption de long chemin optique de N 2 O. La cellule multi-pass modifié e de 3,2 L utilisé e est formé e de deux miroirs de ré flectivité é levé s (sé paré s par 55 cm). La lumiè re laser entre et sort de la cellule multi-pass à travers un trou commun é quipé d'une fenê tre d'accouplement coincé e à l'avant de la cellule. Dans le pré sent travail, 90 parcours ont é té faites entre les miroirs, ce qui a donné une longueur optique efficace de 50 m. Le faisceau laser sortant de la cellule multi-pass est concentré dans un dé tecteur thermoé lectrique de photovoltaï que infrarouge refroidi. Une carte d'acquisition de donné es de National Instruments, contrôlé e par un programme LabVIEW, est utilisé e pour l'é chantillonnage et l'acquisition de donné es. Les donné es enregistré es sont numé risé es et transfé ré es sur un ordinateur portable pour un traitement ulté rieur des donné es afin de ré cupé rer la concentration N 2 O.

	Dans un premier temps, la performance d'un EC-QCL qui sera utilisé comme OL dans notre
	systè me RHL mid-IR, en termes de largeur de ligne d'é mission laser, de ré glage de longueur
	d'onde en mode unique, de stabilisation de la source OL et de ligne de base dé pendante de la
	longueur d'onde, a é té é valué e par la surveillance en temps ré el de N 2 O produit dans un
	processus de catalyse chimique. Ce travail a é té ré alisé en collaboration avec l'UCEIV de
	l'ULCO. (Note : Dans cette partie, pour les figures, les tableaux et les formules, veuillez vous
	ré fé rer au Chapitre 3.)
	i.1. Surveillance N 2 O par spectroscopie optique d'absorption de longue trajectoire
	La configuration expé rimentale est montré e dans la Fig. 3.1. Une onde continue EC-QCL, est
	utilisé e comme OL dans notre expé rience mi-RHL, est couplé e à une cellule multi-pass
	hermanti-

i.

i.

2. Évaluation de la largeur de la ligne laser

	La largeur de la ligne de l'é mission EC-QCL utilisé e comme OL joue un rôle clé dans la
	ré solution spectrale du RHL. Ce paramè tre a é té é valué dans le travail actuel en utilisant la
	mé thode spectroscopique.
	Une largeur de ligne de laser (FWHM) de 9.2 MHz a é té dé duite expé rimentalement qui
	correspond à une puissance de ré solution de laser d'environ 10 7 . Ce ré sultat dé montre que
	l'EC-QCL est trè s approprié pour une utilisation comme OL dans le systè me RHL en cours de
	dé veloppement et il pourrait assurer l'exigence de ré solution spectrale é levé e (la largeur de la
	ligne laser-bande de filtre é lectronique classique allant de 10 MHz à quelques dizaines de
	MHz).
	i.3.

Pré cision de mesure et LoD La

  stabilité d'un instrument d'analyse est un paramè tre important qui affecte la sensibilité de dé tection et la pré cision de mesure. La moyenne des signaux est gé né ralement utilisé e pour amé liorer la sensibilité à la dé tection et la pré cision de la mesure. Cependant, en raison de l'instabilité de l'instrument (tels que les changements dans l'intensité lumineuse, les dé calages de longueur d'onde laser et les dé rives sonores sombres de dé tecteur, les dé rives de tempé rature, les franges mobiles, les changements dans les spectres de fond, etc.), n'importe quel systè me ré el n'est stable que pour un temps limité , donc qu'un temps moyen optimal devrait ê tre pré cisé par une analyse de variance Allan afin de dé terminer le maximum. moyenne, c-à -d., la meilleure pré cision de mesure. Mesures de la sé rie chronologique de spectre d'absorption 1 ppmv N 2 O ont é té effectué es pour l'analyse de variance d'Allan afin de dé terminer le temps moyen optimal. 9000 spectres consé cutifs d'absorption directe de N 2 O ont é té enregistré s expé rimentalement, avec un temps d'acquisition de 0,2 s par spectre. La Fig. 3.6 pré sente une dé viation d'Allan en fonction du temps moyen basé sur les mesures de la sé rie chronologique des spectres d'absorption N 2 O. La pente en dé composition (ligne pointillé e rouge) montre la ré duction efficace du bruit blanc en signalant en moyenne dans un dé lai moyen maximal (temps de stabilité du systè me) d'environ 236 s, ce qui est principalement limité par la tempé rature et la stabilité actuelle du contrôleur QCL. La pré cision de mesure correspondante est de 5,2 ppbv, ce qui conduit à une incertitude relative dans la pré cision de mesure de 0,5%. Aprè s 236 s, l'é cart Allan augmente (ligne pointillé e bleue), c-à -d., les instabilité s du systè me instrumental contrebalancent né anmoins la ré duction de bruit donné e par la moyenne de temps. sans interruption avec une ligne de base lisse. En fait, dans un instrument RHL, la ligne de base spectrale est principalement dé terminé e par la variation de puissance du laser (OL) lors de la numé risation de la longueur d'onde laser par le biais de la caracté ristique d'absorption molé culaire cible. Il est donc fortement souhaitable d'avoir une ligne de base spectrale induite par la puissance laser aussi lisse que possible afin d'obtenir une ré cupé ration de haute qualité du spectre RHL atmosphé rique. Le ré cepteur RHL dé veloppé a é té testé sur la plate-forme QualAir de l'UPMC avec l'aide de l'hé liostat de la station TCCON-Paris. Le spectre d'absorption RHL de CH 4 dans la colonne atmosphé rique a é té extrait du rayonnement solaire à l'aide du ré cepteur RHL au sol dé veloppé et en bon conformité avec le spectre mesuré par la station TCCON-Paris. (Note : Dans cette partie, pour les figures, les tableaux et les formules, veuillez vous ré fé rer au Le RHL PdC dé veloppé est sché matiquement pré senté dans la Fig. 4.1. Un ré cepteur RHL typique comprend un systè me de collecte de lumiè re du soleil associé à un traceur solaire, un oscillateur local, un photomixeur, un ré cepteur RF, un module de dé modulation et de modulation du signal, ainsi qu'un module de mé trologie de fré quence (dans notre cas, l'absorption directe de la molé cule cible dans une cellule de ré fé rence à passage unique de 12,5 cm de long a é té utilisé e). Pour caracté riser et optimiser les performances du ré cepteur PdC RHL dé veloppé , une source stable de corps noir a é té utilisé e comme lumiè re du soleil. intensité et la polarisation ajusté e à l'aide d'un polariseur IR à large bande. Les faisceaux combiné s sont concentré s par OAPM5 sur un photomixeur VIGO. Le signal de la note de battement à |- L | dans le domaine RF, gé né ré à partir du photomixeur, entre dans le ré cepteur RF par un filtre de 27-33 MHz passe-bande suivi par des amplificateurs à faible bruit à 2 é tapes avec un gain de 24 dB chacun. Aprè s cela, le signal de battement amplifié est relié à une diode Schottky de loi carré e pour la mesure de puissance du signal RF qui est proportionnelle au carré de l'amplitude de signal de battement d'entré e. Le signal de sortie du dé tecteur de droit carré est dé modu. Une carte d'acquisition de donné es de National Instruments est utilisé e pour numé riser le signal de sortie de la LIA via un programme LabVIEW. Les donné es sont ensuite transfé ré es sur un ordinateur portable pour un traitement

	Il est important de noter que ce max. du temps de stabilisation de 236 s prouve é galement que le temps de stabilité de l'EC-QCL utilisé est au moins aussi bon que 236 s, ce qui est trè s approprié pour l'acquisition de spectres RHL (~ minute par spectre). i.4. Conclusion La performance d'un EC-QCL, qui sera utilisé comme OL dans le systè me RHL, a é té é valué e en termes de largeur de ligne d'é mission laser, de ré glage de longueur d'onde en mode unique, de stabilisation de la source OL et de ligne de base dé pendante de la longueur d'onde. En se basant sur l'analyse des spectres d'absorption N 2 O mesuré s, la largeur de la ligne d'é mission EC-QCL de 9,2 MHz a é té dé duite. Un temps de fonctionnement stable de la OL aussi bon que 236 s a é té estimé à l'aide de l'analyse de variance d'Allan, il est adé quat pour la mesure RHL du spectre d'absorption molé culaire. L'EC-QCL est en ré glage continu Deuxiè mement, afin de tester notre conception d'un instrument RHL à mid-IR entiè rement transportable et de caracté riser ses performances, un ré cepteur RHL de mid-IR PdC impliquant un systè me de té lescope spatial libre pour le couplage de la lumiè re du soleil a é té mode-hop ii. Dé veloppement d'une preuve de concept mid-IR RHL dé veloppé . Chapitre 4.) ii.1. Un RHL PdC fonctionnant à 8 µm Des mesures d'hé té rodyne des spectres d'absorption de CH 4 ont é té exé cuté es dans une cellule de 12,5 cm à passage unique en laboratoire. Le rayonnement d'un corps noir est collecté et collimaté avec le miroir parabolique hors axe (OAPM) 1 et OAPM2. Le faisceau BB est filtré par un filtre optique (en Ge). La modulation d'amplitude du faisceau BB injecté est faite à 1 kHz à l'aide d'un couperet situé au point focal ré el de OAPM2. Il est ensuite dirigé vers un sé parateur de faisceau. Le faisceau BB sera superposé avec le faisceau OL de l'EC-QCL qui est é largi par deux OAPM, contrôlé par l'ulté rieur. ii.2.

Spectre d'hé té rodie laser de l'absorption de CH 4 à 8 µm

  Afin de valider les performances spectroscopiques du ré cepteur RHL dé veloppé , le spectre d'hé té rodè ne laser et le spectre d'absorption directe de CH 4 à 8 µm ont é té simultané ment mesuré s et comparé s. Dans ce travail, le spectre d'hé té rodè ne laser de l'absorption de CH 4 à 1233.46 cm -1 a é té enregistré avec la fré quence de balayage de 100 mHz et une LIA constante de temps de 100 ms.

3. Vitesse de balayage de fré quence par rapport à la constante de temps de la LIA La

  constante de temps (τ) de la LIA est un paramè tre trè s critique qui a un impact sur la suppression du bruit et la forme de la ligne d'absorption du spectre RHL mesuré . Une constante de temps τ plus longue peut ré duire considé rablement le bruit, mais elle entraî ne é galement un dé placement du centre spectral de ligne et dé forme la forme de ligne. Afin de minimiser ces effets indé sirables, le temps  scan de numé risation de la demi-largeur ν HWHM de la ligne d'absorption doit ê tre au moins é gal à 14 fois de la constante temporelle de la LIA (c.f. Chapitre 2.1.6).Une é tude expé rimentale sur les spectres d'hé té rodè ne à base de BB à l'aide de diffé rentes combinaisons de  et de  sc a é té effectué e. Les spectres d'hé té rodie de CH 4 ont é té enregistré s à l'aide de quatre combinaisons de diffé rents et de  sc (tableau 4.2). Les ré sultats sont pré senté s dans Figs. 4.8-4.11 (noir). Sur la base de l'analyse des spectres d'absorption hé té rodine montré s dans Figs. 4.8-4.11 (noir), SNR, é largissement de la largeur de la ligne Comme nous le constatons, la sé lection de la constante de temps LIA doit ê tre bien adapté e à la vitesse de numé risation de la fré quence OL ainsi que le temps de numé risation.Lorsque la constante de temps est trop petite, le bruit augmentera. Tandis que qaund elle est , plus longue (que la constante optimale), la constante de temps se traduirait par une ré duction de la profondeur d'absorption, dans le dé calage de la fré quence du centre d'absorption et dans la distorsion de la forme de la ligne d'absorption.En comparant au-dessus de quatre combinaisons optimales pour la dé tection de l'hé té rodie, ré sumé es dans le tableau 4.7, la combinaison de la vitesse de balayage de la fré quence OL de 0,3935 cm -1 /s (le temps de balayage de 137 ms) et de la constante de temps LIA de 1 ms a un niveau de bruit relativement faible, une profondeur d'absorption la plus é levé e, aucun changement significatif de la fré quence du centre d'absorption et aucune distorsion de la forme de la ligne d'absorption (tableau 4.7 en gras).En principe, la relation entre le temps de numé risation (ΔT scan ) doit ê tre é gale ou supérieure à 14 fois la constante de temps de la LIA (τ) (c.f. Chapitre 2.1.6).

	Selon ΔT scan et τ dans le tableau 4.7, la combinaison du temps de balayage de 137 ms et
	de la constante de temps de 1 ms s'accorde bien Éq. (4.
	2) qui peut ré duire efficacement le bruit sans causer de changement é vident et de
	distorsion de la forme de la ligne, et est compatible avec notre l'analyse spectrale comme
	discuté ci-dessus. Cette combinaison a donc é té sé lectionné e pour nos autres mesures RHL.
	ii.4.
	(Δν b ), profondeur d'absorption, décalage de ligne (δν) et niveau de bruit (1σ) de ces spectres
	ont é té analysé s à partir des ajustements de profil Lorentz (Figs. 4.8-4.11 rouge et bleu) et
	ré sumé es dans le tableau 4.3-4.6, les constantes de temps optimales (τ) à des vitesses de
	balayage donné es de la fré quence OL (υ sc ) et des temps de numé risation (ΔT scan ) ont é té
	obtenues pour les travaux en cours, comme le montre le tableau 4.3-4.6 en gras et Fig.4.8-
	4.11 en rouge.

Mesure de terrain à Paris Le

  PdC RHL dé veloppé a é té testé sur le terrain sur la plate-forme QualAir de l'UPMC, en collaboration avec le LERMA de l'UPMC à Paris (Dr. Yao TE). L'instrument parisien fait partie du TCCON (gare De Paris). Le TCCON est un ré seau de spectromè tres fourier Transform au sol enregistrant des spectres d'absorption atmosphé rique directe dans la ré gion spectrale infrarouge. À partir de ces spectres, des abondances pré cises et cohé rentes de CO 2 , CH 4 , N 2 O, HF, CO, H 2 O et HDO sont ré cupé ré es

	(http://www.tccon.caltech.edu/). La plate-forme QualAir Fourier transforme le spectromè tre
	(Bruker's IFS 125HR) avec une ré solution spectrale de 0,02 cm -1 adapté e à la té lé dé tection au
	sol des espè ces molé culaires dans la colonne atmosphé rique. Connecté à un traceur solaire
	sur la terrasse sur le toit (Fig. 4.12 à gauche), le QualAir FTS (Fig. 4.12 à droite) fonctionne
	dans la configuration d'absorption solaire et permet de dé tecter un grand nombre de polluants
	atmosphé riques.
	ii.4.1.

RHL impliquant un systè me de té lescope pour le couplage de l'espace libre de la lumiè re du soleil

  Afin de coupler la lumiè re du soleil, recueillie par l'hé liostat sur la plate-forme QualAir, à notre RHL, un systè me d'assemblage de cages Thorlabs de 60 mm a é té utilisé pour un systè me de té lescope de couplage en espace libre. Le systè me d'assemblage de cage utilisant quatre tiges rigides en acier sur lesquelles les composants optiques peuvent ê tre monté s le long d'un axe optique commun, fournit un moyen commode pour construction des systè mes opto-mé caniques stables avec une ligne é tablie de blocs de construction de pré cisionmachines conç us pour une grande flexibilité et un alignement pré cis.Le systè me de cage utilisé pour l'accouplement de la lumiè re du soleil se compose d'un miroir monté dans un cube rotatif pour reflé ter la lumiè re du soleil de l'hé liostat à notre RHL, un diaphragme a é té utilisé pour contrôler la taille du faisceau de lumière du soleil, et deux lentilles (en CaF 2 , f1 = 150 mm et f2 = 75 mm) ont é té utilisé s pour 2 × contraction de faisceau, comme le montre la Fig. 4.13. La configuration expé rimentale dé ployé e sur la plate-forme QualAir est pré senté e par sché ma dans Figs. 4.14 et 4.15. Le rayonnement solaire est capté par un hé liostat externe installé sur la terrasse du toit et dirigé vers le laboratoire de bas niveau. La lumiè re du soleil est d'abord refleté e, collimaté et faç onné e par le systè me de cage. Ce dernier est filtré par un filtre optique (pour enlever les rayons UV et les rayonnements visibles et limiter la bande passante du rayonnement incident dans la ré gion infrarouge) et l'amplitude modulé e avec un couperet à 1 kHz. Il est ensuite dirigé vers un sé parateur de faisceau sur lequel il est superposé avec le faisceau OL de l'EC-QCL. La taille du faisceau laser OL est d'abord augmenté e par OAPM3-OAPM4, avec une intensité controllable et une polarisation ajusté e à l'aide d'un polariseur IR à large bande. Les faisceaux combiné s sont concentré s avec OAPM5 sur le mixer VIGO. La puissance OL ré flé chie par un sé parateur de faisceau (fenê tre CaF 2 )est utilisé e pour la mé trologie de fré quence, par l'absorption directe de CH 4 dans une cellule de passage unique à la pression atmosphé rique, ou par un etalon fait maison de 12,5 cm de long dans Ge pour enregistrer des franges etalon pour une fré quence relative é talonnage.

ii.4.2. Pré liminaires des essais sur le terrain du RHL PdC dé veloppé

  Les trois spectres sont tracé s dans la Fig. 4.19. Bien qu'en raison de la ligne de base structuré e ré sultant du OL, le spectre RHL atmosphé rique du CH 4 (Fig. 4.19 (b)) doit ê tre extrait d'une ligne de base basé e sur BB, la forme spectrale globale de ligne est compatible avec le spectre atmosphé rique correspondant de FTS (Fig. 4.19 (a)) et la modé lisation de la transmission atmosphé rique du spectre CH 4 (Fig. 4.19 (c)). Des spectres d'hé té rodè ne bb-basé s de CH 4 dans une seule cellule à ~8 µm ont é té employé s pour la caracté risation du RHL dé veloppé . Le RHL dé veloppé a ensuite é té dé ployé pour des essais sur le terrain sur la plate-forme QualAir à l'UPMC. La mesure au sol du CH 4 troposphé rique dans la colonne atmosphé rique a é té obtenue. Bien qu'il ait subit à la ligne de base structuré e ré sultant du dysfonctionnement du OL EC-QCL utilisé , le spectre RHL extrait de CH 4 a é té confirmé par la mesure de non-absorption RHL d'à proximité et par une comparaison avec le spectre FTR mesuré par un Bruker IFS 125HR FTS et avec un spectre de modé lisation de la transmission atmosphé rique. Dans les travaux suivants, de grands efforts ont é té consacré s pour rendre le RHL mid-IR transportable et compact pour la mesure in situ, et de dé placer la longueur d'onde OL à une autre ligne molé culaire pour é viter la ligne de base structuré e au laser autant que possible.

	Le signal d'absorption atmosphé rique du CH 4 a é té extrait sur le champ à l'aide du RHL dé veloppé . Dans cette é tude, les paramè tres du ré cepteur RHL ont é té fixé s comme suit : OL (EC-QCL) a é té numé risé à l'aide du mode de balayage PZT autour de 1242,00 cm -1 avec une fré quence de balayage de 250 mHz. La tension de balayage est de 3,0 V avec un dé calage de 1,6 V. Bande passante de filtre é lectronique et LIA constante de temps sont 6 MHz et 1 ms, respectivement. Le spectre RHL atmosphé rique extrait expé rimentalement de CH 4 a é té comparé à un spectre d'un Bruker IFS 125HR FTS à haute ré solution et à un modè le de transmission Un RHL de mid-IR de PdC a é té dé veloppé et sa performance a é té é valué e et optimisé e à l'aide d'un corps noir d'IR à haute tempé rature utilisé comme lumiè re du soleil avec l'intensité stable. iii. Dé veloppement d'un prototype RHL moyen-IR transportable Enfin, sur la base du ré cepteur RHL au sol dé veloppé , un prototype complet de RHL mid-IR transportable a é té dé veloppé . Nous avons exploré une fibre mid-IR pour coupler la lumiè re du soleil au ré cepteur hé té rodin, ce qui rend notre RHL, é quipé d'un EKO sun-tracker, entiè rement transportable. L'instrument RHL dé veloppé a é té testé et validé au moyen de mesures au sol sur le terrain du CH 4 et du N 2 O troposphé riques dans la colonne atmosphé rique sur la terrasse du toit de la plate-forme IRENE à Dunkerque (51.05°N/2.34°E). (Note : Dans cette partie, pour les figures, les tableaux et les formules, veuillez vous ré fé rer au Chapitre 5.) atmosphé rique. ii.5. Conclusion iii.1.

Prototype RHL impliquant une fibre mid-IR pour coupler le rayonnement du corps noir iii.1.1. Description instrumentale

  Le rayonnement du corps noir est collecté et collimaté avec une lentille CaF 2 , puis couplé à une fibre polycrystalline de 860 μm-noyau à travers une deuxiè me lentille CaF 2 . Le rayonnement du corps noir é mergeant de la fibre est ensuite collimaté et filtré à l'aide d'une lens3 dans Germanium avec revê tement AR pour 3-12 μm ré gion. L'amplitude du faisceau BB est amplitude modulé e à 1 kHz à l'aide d'un couperet mé canique et est ensuite dirigé vers un sé parateur de faisceaux. Le faisceau BB est superposé avec le faisceau OL de l'EC-QCL. La lumiè re OL est é tendue de taille par un facteur de 3 à deux OAPM, avec une intensité controllable et une polarisation ajusté e à l'aide d'un polariseur IR à large bande. Les faisceaux combiné s BB et OL sont ensuite concentré s par un OAPM6 (f6 à 38,1 mm) sur un photomixeur VIGO. Le signal de note de battement RF du photomixer introduit le mê me ré cepteur RF impliqué dans le PdC mid-IR RHL (c.f. Chapitre 4) à l'exception du filtre RF ayant une bande de passage de 27,5-270 MHz au lieu de 27-33 MHz. la LIA à une fré quence OL (1242,3 cm -1 ou 3.73×10 13 Hz), un RSB limité par le bruit de tir d'environ 1430 a é té obtenu. Le RSB thé orique limité par le bruit de tir est 3,4 plus é levé que le RSB mesuré à un photocourant de 610 µA, où un facteur de 0,29 dans le RSB thé orique est observé . Le facteur de 0,29 (=419/1430) peut provenir de la performance

	inattendue du RHL dé veloppé .
	A noter que dans la description de l'expé rience suivante, la puissance OL et BB sera
	exprimé e en photocourant (en [µA]).
	Les photocourants induits par l'é nergie OL et BB é taient respectivement de 610 et 117 µA .
	D'aprè s la mesure (Fig. 5.3) d'une amplitude de note de battement de 150,18 µV et d'un
	niveau de bruit (1 σ) de 0.36 µV dans la note de battement, un RSB de ~419 a é té dé duit.
	Le RSB thé orique limité au bruit de tir du RHL peut ê tre exprimé par l'é quation. (5.1), où
	l'efficacité globale de couplage optique κ est d'environ 0,396. L'efficacité hé té rodydine η het du
	photomixage du faisceau de lumiè re du soleil et du faisceau OL est considé ré e comme 1 dans

Afin de tester et de caracté riser les performances de la fibre mid-IR nouvellement disponible dans le commerce utilisé pour l'application RHL, une configuration RHL utilisant le couplage de fibres de rayonnement du corps noir a é té ré alisé e (Figs 5.1 et 5.2). iii.1.2. Caracté risation des performances du prototype RHL iii.1.2.1. RSB du signal de battement Afin de caracté riser la performance RHL à l'aide d'un systè me de couplage de fibres pour la collecte de la lumiè re du soleil, l'enquê te en termes de RSB du signal RHL a é té effectué e à l'aide d'une source de corps noir calibré . Dans cette é tude, la tempé rature du corps noir a é té fixé e à 1000 o C. Des mesures de sé rie de temps du signal RF du LIA avec et sans injection de rayonnement de OL ont é té effectué es. Les puissances efficaces de OL et de BB ont é té mesuré s à la sortie du photomixer et affiché s sur l'oscilloscope (en [V]). Ces puissances de lumiè re sont exprimé s dans ce travail en termes de photocourant, en [µA], induit par la puissance lumineuse incidente, qui est obtenue en divisant la puissance de lumiè re en [V] par la transimpedance photomixeur de 6000 V/A. le cas idéal (c.f. Chapitre 1.3), l'efficacité quantique η du photomixteur fourni par le fabricant à cette longueur d'onde est de 0,5. Dans ces conditions, avec une bande passante double RHL de 485 MHz (pour une bande de passage RF de 27,5-270 MHz) et une constante de temps de 1 s de iii.1.

2.2. Sources de bruit dans le systè me RHL Afin

  de comprendre la diffé rence entre les RSB idé aux mesuré s et calculé s, les bruits dans diverses parties du systè me RHL ont é té é tudié s à l'aide d'un analyseur de signaux. Dans cette é tude, les paramè tres de l'analyseur de signaux ont é té fixé s comme le montre le tableau 5.1.

	Dans cette é tude, la densité sonore totale N total (	nV /	Hz	) du systè me RHL peut ê tre

exprimé e par Éqs. (5.2)-(5.4) (c.f. Chapitre 1.4), où N Det , N LIN et N SIN sont respectivement : le bruit de la chaî ne de dé tection, le bruit induit par laser et le bruit induit par le signal. Le bruit induit par laser inclut le bruit de tir induit par laser N LSN et le bruit excessif de laser N LEN , respectivement. Tandis que le bruit induit par le signal inclut le bruit de tir induit par le signal N SSN et le bruit excessif de signal N SEN .

  1,14 à gauche). Un facteur de correction supplé mentaire de  3 de 0,72 (0,8×0,9) a é té atteint. D'aprè s l'analyse ci-dessus, un facteur de correction total , exp pour le RSB thé orique, a ré sulté des raisons ci-dessus, est de  1 × 2 × 3 = 0.30 qui est comparable au facteur de 0,29. bruit de la chaî ne de dé tection et l'homogé né ité de la ré ponse du dé tecteur affecteront les performances.Par consé quent, la puissance OL doit ê tre ajusté e avec pré cision afin de ré duire considé rablement le bruit sur le signal hé té rodè ne pour atteindre une RSB é levé e sans aucune saturation de l'appareil.En se basant sur l'analyse ci-dessus, les performances spectroscopiques du systè me RHL seront é valué es dans la section suivante sous le photocourant OL optimal.La capacité de la fibre optique mid-IR utilisé e pour coupler la source à large bande (BB ou lumiè re du soleil) a é té é valué e dans cette section. Pour cette raison, la mê me source de corps noir utilisé e dans le chapitre 4 a é té couplé e à une cellule d'absorption directe à travers la fibre optique. Les paramè tres communs ont é té fixé s comme suit :

	iii.1.2.5. Performance spectroscopique
	P HET		S P		L P	,
	avant d'atteindre un point de roulement à un photocourant OL de 610 µA. Le RSB augmente
	avec la puissance OL et atteint un maximum lorsque OL photocurrent est é gal à ~610 µA trop.
	Au-dessus de 610 µA, le signal hé té rodyne est devenu plus petit et le bruit sur le signal
	hé té rodè ne a rapidement augmenté (c.f. Figs. 5.7 et 5.8), c'est-à -dire que le RSB a
	considé rablement diminué . Les donné es montrent que le RSB maximum du RHL peut ê tre
	obtenu avec un photocourant OL optimal. Le photocourant OL optimal dé pend fortement de

iii.1.2.4. Signal hé té rodè ne et RSB du Photocurrent RHL vs OL En se basant sur l'é tude ré alisé e sur les bruits en fonction du photocourant induit par la puissance OL, nous é tudions maintenant le signal hé té rodè ne et le RSB correspondant comme fonction du photocourant OL. La puissance OL a é té modifié e en ajustant un polariseur devant la sortie OL, à la fois le signal moyen d'hé té rodie et son é cart standard ont é té mesuré s à partir de desquels, le RSB correspondant a é té dé rivé . Les ré sultats sont pré senté s à la Fig. 5.9.

Fig. 5.9 montre clairement que l'amplitude du signal hé té rodiste augmente presque liné airement à faible OL photocurrent (carré noir), ce qui est compatible avec la technologie et des caracté ristiques du dé tecteur (utilisé comme photomixeur). Pour chaque type de dé tecteur, le photocourant OL optimal doit ê tre dé terminé parce que les effets de saturation, le

Prototype RHL impliquant une fibre mid-IR pour coupler le rayonnement solaire iii.2.1. Description instrumentale

  La collecte de la lumiè re du soleil dans la colonne atmosphé rique dans une fibre mid-IR est ré alisé e par une lentille associé e à un filtre optique dans Germanium. L'optique de collecte est installé e sur la monture d'instrument du sun-tracker. Le filtre Ge en face de la fibre est utilisé pour proté ger le terminal d'entré e de fibres contre les dé gats causé s par l'exposition directe à l'ultraviolet intense et la partie visible de la lumiè re du soleil, et pour limiter la bande passante optique du rayonnement incident et de laisser seulement la transmission du rayonnement solaire à des longueurs d'onde supé rieures à 7 µm.La lumiè re du soleil é mergente de la fibre est collimaté avec une lens4 et injecté e dans l'espace libre. L'amplitude de la lumière du soleil est ensuite modulée à une vitesse d'environ 1 kHz et dirigé e vers un sé parateur de faisceau. Le faisceau solaire de 12,5 mm de diamè tre est superposé au sé parateur de faisceau avec un faisceau OL de 7,5 mm de l'EC-QCL à l'avance de taille é largie par deux OAPM, en ajustant son intensité à l'aide d'un polariseur IR.

	5,1,2.2) II. Cependant, le bruit (1σ : 0,0091) était le plus élevé et le RSB (~12) était le plus faible (tableau 5.4). Un compromis doit ê tre fait. Par consé quent, à la constante de temps LIA de 1 ms, la vitesse de balayage de la fré quence OL de  cm -1 /s (le temps de numé risation de 36 ms), avec laquelle le bruit (1σ : 0,0043) é tait relativement faible, le RNS du systè me (~24) é tait relativement é levé, le dé calage de ligne (~0,0004 cm -1 ) é tait relativement faible et la ré solution spectrale ré alisable (largeur spectrale de la ligne spectrale de ~0,042 cm -1 ) é tait relativement é levé e, elle a donc é té sé lectionné e pour la mesure du prototype RHL. iii.2. Les faisceaux combiné s concentré s par un OAPM2 sont injecté s dans le photomixteur VIGO pour la dé tection de l'hé té rodie.

Le prototype RHL dé veloppé utilisant une fibre polycrystalline mid-IR pour coupler la lumiè re du soleil au ré cepteur RHL est sché matiquement montré dans les Fig.

5

.14 et Fig. 5.15. Le prototype RHL utilise un EKO sun-tracker pour suivre en temps ré el le mouvement 193 du Soleil. Une partie du faisceau OL (puissance OL transmise par le sé parateur de faisceau) est dirigé e soit vers une cellule de passage unique de 12,5 cm remplie d'un mé lange CH 4 dans l'air pour une dé termination de fré quence absolue, soit vers un Ge-etalon fait maison de 12,5 cm (FSR à 0,0333 cm -1 ) pour une calibration de fré quence relative lorsque la fré quence OL est ré glé e. iii.2.

2. Mesure de l'hé té rodie du spectre d'absorption atmosphé rique CH 4 et N 2 O

  Lors de la vé rification du bruit du systè me au port de sortie RF du photomixteur avec l'analyseur de signaux, il a é té constaté que le bruit du systè me a é té augmenté dans les 110 MHz, et est devenu particuliè rement important autour de 100 MHz, comme le montre la Fig.

	Le prototype RHL dé veloppé a é té dé ployé sur le toit de la plate-forme ULCO-IRENE à
	Dunkerque (51.05°N/2.34°E) pour la té lé dé tection au sol des gaz traces dans la colonne
	atmosphé rique.
	5.16.
	Par consé quent, la bande de filtre RF pré cé demment optimisé e de 27,5-270 MHz n'é tait
	plus adapté e, un nouveau filtre RF avec une bande de passage de 225-270 MHz a é té

sé lectionné pour é liminer cet excè s de bruit. Les paramè tres opé rationnels du RHL ont é té fixé s comme suit :

Table 1

 1 Values of µ 1m for the first five HE 1m modes.

	µ 11 2.40482555769577
	µ 12 5.52007811028631
	µ 13 8.65372791291101
	µ 14 11.7915344390142
	µ 15 14.9309177084877

Table 1 .

 1 Mass-to-charge (m/z) ratio of the mass fragments of the main exhaust gases from oxyfuel-combustion.

	Fragment		m/z (in [Kg/C])
	N 2 O	44	30	28	16
	NO	30	15	16
	NO 2	30	46	16
	CO	28	16
	CO 2	44	28	16

Table 2 .

 2 2 is fixed at a constant rate of 2086 ml/min. Different N 2 O concentrations were produced at 0.24, 0.51, 0.99, 1.46, 2.01, 2.48, 3.37 and 5.03 ppmv for the calibration in the present work. The relevant settings and the obtained final concentrations are presented in Table 2. Relevant settings and the diluted concentration.

	D 1 [ml/min]	K	C initial [ppmv]	C final [ppmv]
	0.50	4173.0	1000	0.24
	1.06	1968.9	1000	0.51
	2.06	1013.6	1000	0.99
	3.06	682.7	1000	1.46
	4.20	497.7	1000	2.01
	5.16	405.3	1000	2.48
	7.06	296.5	1000	3.37
	10.55	198.7	1000	5.03

Table 3 .

 3 Conversion efficiency of NO to N 2 , N 2 O and NO 2 vs. temperature.

	Temperature		NO conversion efficiency
	(˚C)	NO → N 2	NO → N 2 O	NO → NO 2	NO
	190	59%	6%	31%	4%
	250	63%	4%	30%	3%
	340	47%	0%	26%	27%

Acknowledgements

Here in is the last phase of writing this thesis. In fact, it is not the easiest part, but certainly the closest to my heart. Indeed, all of this work would not have been possible without the support of some very special people. This work was realized at the Laboratoire de Physico-Chimie de l' Atmosphè re (LPAC) at the Université du Littoral Côte d'Opale (ULCO). First, I would like to express my heartfelt appreciation to Mr. Weidong CHEN, my thesis 204 4. Collimating/focusing : OKSI Opton-CLF2MWLW5025-SMA-T/M (lens in Ge, AR coating (3-12 μm) with a focal length of 25.4 mm and 12.7 mm in diameter).

For this configuration, during the field realization, the problem is that the 2 to 1 fiber cannot be bent on the sun-tracker, and due to the limitation of the sun-tracker, it is not practical to install a coaxial telescope as shown in Fig. 1. Therefore, it is not possible to follow the Sun's movement to collect the solar radiation.

Acknowledgements

The authors thank the financial supports from the CaPPA project (ANR-10-LABX005) and the CPER-CLIMIBIO program. S. F. thanks the Labex CaPPA program and the "Pôle Métropolitain de la Côte d'Opale" (PMCO) for the PhD fellowship.

Acknowledgments The authors thank the financial supports from the CaPPA project (ANR-10-LABX005) and the CPER CLIMIBIO program. S. F. thanks the program Labex CaPPA and the "Pôle Métropolitain de la Côte d'Opale" (PMCO) for the PhD fellowship support.

LBSD is widely used for continuous-wave or pulsed power detection and frequency response test of microwave components. This diode detector does not require a DC bias, making it very easy for use. It also offers very good ruggedness and burnout protection, easy for integration with other circuit elements to minimize stray reactance and optimize broadband performance. In the square-law region (Fig. 2.15 lower, left), the diode detector typically operates within 0.5 dB of square-law from the tangential signal sensitivity level up to -18 dBm. Fig. 2.15 lower (right) shows the characteristic transmission curves of a typical Schottky diode detector and a LBSD. As can be seen, the LBSD has a higher voltage transmission coefficient, i.e. higher sensitivity. LBSD provides also improved broadband flatness and smaller standing wave ratio (SWR) over point-contact Schottky diode.

Two commercially available LBSDs (low-barrier Schottky diode Keysight 8472B and zero-bias Schottky diode Herotek DHM020BB) are compared and their specifications are summarized in Table 2.4. The Keysight 8472B exhibits better performance, in terms of broader frequency range, smaller frequency response, smaller SWR (i.e. smaller uncertainty of power measurement) and smaller noise, except from its smaller low-level sensitivity.

(2) Design optimization using Zemax Because of using stock lenses, the only variable involved in Zemax lens data editors for the design is the distance between two lenses, i.e. the value of the thickness of surface 3 as shown in Tables 2.7 and2 information on latitude, longitude, date and time. One is "GPS mode", which can automatically achieve such geographical location and time information through a built-in GPS sensor. The other is "manual mode", in which such information should be set manually via a specific software "STRconfig", as shown in Fig. 2.31. In the context of climate change mitigation, reuse of carbon dioxide (CO 2 ) represents a great interest for applications in chemical industry and power generation. For this purpose, CO 2 must be purified. Combustion processes lead to high amounts of CO 2 but still with impurities and also accompanied by toxic gases (mainly NO and CO). A catalytic reduction process of NO (to N 2 ) while oxidizing CO into CO 2 is a promising method to purify the CO 2 in combustion processes. However, nitrous oxide (N 2 O), having a global warming potential of 300 times greater than CO 2 , may be a by-product from this process. It is therefore necessary to optimize the chemical reaction conditions to minimize N 2 O production.

Introduction

The characteristics of a laser source used as a LO largely determine the performance of a LHR instrument. The laser source should primarily fulfill the following requirements : narrow laser emission line width (for high spectral resolution and hence high spatial resolution in LHR measurements), single-mode emission and mode-hop free wavelength tunability (high precision spectroscopic measurement), as well as a wavelength-dependent baseline as smooth as possible (for high quality spectral normalization). Performance of the external-cavity quantum cascade laser (EC-QCL) being used as a LO was evaluated via the concentration measurement of trace gas N 2 O produced during a chemical catalysis process of carbon dioxide (CO 2 ) purification. CO 2 is responsible for 55-60% of anthropogenic radiative forcing on global warming. To reduce CO 2 injected into the atmosphere, reuse of CO 2 is a promising and alternative solution,

LHR prototype involving a mid-IR fiber to couple blackbody radiation

Instrumental description

In order to test and characterize the performance of the newly commercially available mid-IR fiber used for LHR application, a LHR setup using fiber coupling of blackbody radiation was realized (Figs 5.1 and 5.2).

Radiation from the blackbody (Model 67030, Newport Inc.) is collected and collimated with a CaF 2 lens (f1 = 40 mm, dia. = 25.4 mm) and then coupled to an 860-μm-core polycrystalline fiber through a second CaF 2 lens (f2 = 20 mm, dia. = 12.7 mm). The blackbody radiation emerging from the fiber is then collimated and filtered using a lens3 (f3 = 50 mm, dia. = 12.7 mm) in Germanium with AR coating for 3-12 μm region in order to filter out radiation out of the spectral region of interest to minimize shot noise resulting from the BB source [1]). The BB beam is amplitude modulated at 1 kHz using a mechanical chopper (Model MC2000B, Thorlabs, Inc.) and is then directed to a 5% (R) -95% (T) beam splitter (BS, in CaF 2 ). The BB beam is superimposed with the LO beam from the EC-QCL.

The LO light is size-expanded by a factor of 3 through two OAPMs (OAPM4: f4 = 12. Therefore, the total noise density N total (Eq. (5.2)) of the LHR system becomes :

As can be seen in Fig. 5.4 upper, the LHR system noise (measured at the RF output of the photomixer) was mainly distributed in the range of 1 kHz-100 MHz, which is enlarged in Fig.

lower.

It is seen that the noise is mainly composed of 1/f and white noises. In the low frequency range, the noise is dominated by 1/f, and then the noise distribution tends to be flat.

Therefore, the pass-band should be selected in the higher frequency range where 1/f is significantly reduced. In order to study the characteristics of white noise in the high frequency range, the detection chain noise N Det was analyzed at 150 MHz where the noise is dominated by white noise.

Given the readings from the signal analyzer at 150 MHz : 0.00709 mV for the noise amplitude of the signal analyzer's background noise (Fig. (2.2) Laser excess noise (N LEN )

The laser excess noise N LEN (Fig. 5.8, (5) green star) can then be calculated (Eq. ( 5.3)) by subtracting the laser-induced shot noise N LSN (Fig. 5.8, (4) black circle), determined using Eq.

(5.11), from the laser-induced noise N LIN (Fig. 5.8, (3) blue triangle). As can be seen from Fig. 5.8, at LO photocurrents I DC < 450 µA the detection chain noise N Det ((1) red line) is larger than the laser-induced shot noise N LSN ((4) black circle), only in the range of 450 µA < I DC < 656 µA the laser excess noise N LEN ((5) green star) and the detection chain noise N Det ((1) red line) are both smaller than the laser-induced shot noise N LSN ((4) black circle), and the LHR system operates in shot-noise dominated regime (with shot-noise limited high sensitivity performance). The higher LO photocurrent limit could not be verified, because the saturation of detector preamplifier for optical powers above 733 µA was observed.

I.2 Theoretical SNR vs. measured SNR

Based on the above analysis of the system noises, compared to the measured SNR (~419)

with the theoretical SNR (~1430), the factor of 0.29 (=419/1430) is analyzed as follows :

(1) At a LO power-induced photocurrent of 610 µA, at which SNR=419 was determined, the laser excess noise N LEN (Fig. 5.8, (5) green star) and the detection chain noise N Det (Fig. knowledge of additional atmospheric parameters, like solar angle, atmospheric temperature, atmospheric pressure, composition of the atmosphere, and refractive index [12].

Summary and perspectives

LHR is advantageous in terms of high spectral resolution, high sensitivity and high vertical resolution in conjunction with a compact instrumental size deployable for field remote sensing of vertical concentration profiles of key trace gases in the atmospheric column. This field measurement validates that the developed fully transportable mid-IR LHR instrument could be used for ground-based measurements of key trace gases in the atmospheric column. In addition, it also has high potential for applications on spacecraft or on airborne platform.

Compared to other currently existed LHR instruments, the developed LHR is advantageous due to the following two characteristics :

(1) fully transportable in the mid-IR : a mid-IR polycrystalline fiber with high flexibility and high transmission at 8 µm was firstly applied to couple the sunlight to the LHR receiver which makes LHR system fully transportable.

(2) very compact in the mid-IR : a commercially available and mature EC-QCL from Daylight Inc. was firstly used as the LO. It operates at room temperature and has high output optical power and narrow emission line width.

Ground-based measurement of vertical concentration profiles of trace gases with high spectral resolution, high sensitivity and high vertical resolution is a key challenge in atmospheric science and climate change research. For the developments on going, the following considerations are taken into account :

(1) In order to well match the theoretical atmospheric absorption spectrum, LHR baseline and LHR background signal should be subtracted, and variation in solar power should be corrected.

(2) The tracking accuracy of the sun-tracker is 0.01˚ which may result in a minor oscillation that can be seen in the LHR baseline when scanning the LO frequency. To calibrate this oscillation, a beam splitter in combination with a mid-IR photodetector should be introduced as a reference channel performing simultaneous monitoring of the solar radiation. This channel is sensitive to the accuracy of the sun-tracker as well as drops in the signal due to cloud covering.

(3) To satisfy the demands for the measurements of vertical concentration profiles of the key atmospheric trace gases, it is quite necessary to make a profound research about the retrieval algorithm in collaboration with Moscow Institute of Physics and Technology (MIPT) who has well developed a retrieval algorithm.

(4) Unlike the near-IR, in the mid-IR, there is no commercially available fiber collimating optics, coupling sunlight into the mid-IR fiber with a spatially separated optics is thus a big challenge which needs a very professional and precise alignment. Furthermore following the movement of the Sun, the fiber should be long enough and also can be bended, which increases the power loss. Therefore all integrated fiber coupling system having a potential to highly increase the heterodyne efficiency is a good choice for compensating for above losses (c.f. Appendix 1).

(

Appendix Appendix 1 All fiber-coupled LHR

A compact mid-IR laser heterodyne radiometer involving an all fiber-coupled optical system in principle could significantly improve photomixing efficiency, system stability and flexibility (Fig. 1). Sunlight is coupled to a polycrystalline fiber via a lens associated with a Ge-filter to block the solar radiation with wavelength short than the near-IR. The outgoing beam from the fiber is coupled to a 320-μm-core single-mode fiber by a collimator. This incoming sunlight is amplitude modulated at a rate of about 1 kHz. Light from the EC-QCL laser (LO) is also coupled to a 320-μm-core single-mode fiber. These two fiber-coupled light beams are superimposed in a larger 1000-μm-core multi-mode fiber and injected into the VIGO photomixer via free-space coupling. Before the design of such all fiber-coupled optical transmission system, the beam coupling loss due to the fiber modes is studied.

(1) Fiber coupling efficiency to the HE 1m modes

When a Gaussian beam is on-axis focused into a hollow fiber, only the HE 1m modes are excited. The spatial profiles of the HE 1m modes in a fiber can be approximated by the zeroorder Bessel function, that is :

Appendix 2 Optimization using Zemax

In computer-aided sequential lens design, rays are traced from one surface to the next in the order in which they are listed. To do this, ZEMAX uses a spreadsheet format called the Lens Data Editor (LDE).

Upon opening ZEMAX, a blank LDE will appear within the main ZEMAX window. The LDE is the primary spreadsheet where the majority of the lens data is entered. Some of the main entries include the following :

-Surf : Type : the type of surface (Standard, Even Asphere, Diffraction Grating, etc), -Comment : an optional field for typing in surface specific comments, -Radius : surface radius of curvature (the inverse of curvature) in lens units, -Thickness : the thickness in lens units separating the vertex of the current surface to the vertex of the following surface, -Glass : the material type (glass, air, etc.) which separates the current surface and the next surface listed in the LDE, -Semi-Diameter : the half-size of the surface in lens units.

The Lens Data Editor Each row within the LDE represents a single surface. In sequential ZEMAX, each optical system begins at the object (OBJ) and ends at the image (IMA). In addition to the object and image planes, one of the surfaces must be defined as the aperture stop (STO).

Data can be entered into the LDE by typing in the required values in the highlighted cell.

The cursor keys or the mouse may move the highlighted bar to whichever column is desired.

Once the system settings have been defined, information specific to each surface can be entered into the Lens Data Editor. To reiterate, each row in the LDE represents a single surface. Therefore, two surfaces separated by glass comprise a single element. So, for the purposes of the beam contraction, a total of 7 surfaces are needed :

1. Surface (OBJ) : the location where rays are launched is infinity (Thickness);

Appendix 3 Conversion from the measured intensity (in [V]) to the radiation (in [W/m 2 ])

In order to convert the measured intensity (in [V]) to the radiation (in [W/m 2 ]), the following conversion process has been executed :

The relationship between the outputs of the detector and the lock-in amplifier

Labview reading from the output of the lock-in amplifier : V lab = 0.27456 V;

Oscilloscope reading from the Vigo detector : V det = 920 mV;

The relationship between the detector output V lab and lock-in amplifier output V det :

The relationship between the intensity and power

The response characteristics of the Vigo detector from the datasheet :

(1) The voltage responsivity (acc. ± 20% at 10.6 µm) : R = 2.7E + 4 V/W;

(2) The active area : S = 0.5 mm × 0.5 mm.

The relationship between the intensity (in [V]) and the power (in [W]) : In the present work on monitoring a chemical reaction, a measurement precision of 10.8 ppbv (corresponding to a relative precision uncertainty of 1.1%) in 12 s was used to real-time track N 2 O production. Fig. 6 shows an experimental absorption spectrum of N 2 O in air at a pressure of 120 mbar with 240 averaged spectra in 12 s, the concentration retrieved was 325 ppbv. Based on the signal-to-noise ratio (SNR = 10.1) deduced from the Voigt profile fit to an experimental absorption spectrum of N 2 O in air and the fit residual, a 1σ (SNR = 1) limit of detection was determined to be 32.3 ppbv in 12 s.

Results and discussions

Before performing the catalytic reaction of NO with CO, a Pt/SiO 2 catalyst was pretreated in a flow of He with a flow rate of 40 mL/min at 200 ˚C for 1.5 hours. The catalyst was sieved in order to retain particles of a diameter between 0.315 and 0.500 mm which aims to select particles with the same diameter because the diameter of the catalyst has an influence on the catalytic activity. It was then diluted to a constant volume by SiC (not active in CO 2 purification from 50 to 500 ˚C). CO 2 purification was then carried out by catalytic reduction of NO by CO in a fixed-bed flow reactor containing 150 mg Pt/SiO 2 catalyst at ambient pressure. All above experiments were carried out at a GHSV (Gas Hour Space Velocity : the ratio between the volumetric flow rate and the volume of the catalyst) of 2.24 10 4 h -1 .

In a typical catalytic reaction process (Fig. 7 left), the flow of the reactant gases was composed of 20% CO 2 , 10% O 2 , 0.5% CO, 0.02% NO and He (eluent gas) with a total flow rate of 200 mL/min. The products of CO 2 and N 2 from the catalytic reduction of NO by oxidizing CO were analyzed by an on-line gas chromatography (TranceGC 1300 XXL, Global Analyzer Solutions G.A.S., Inc.), NO was analyzed with a NO analyzer (Xentra 4900C, Servomex Inc.), NO 2 was measured with the same NO analyzer after conversion of NO 2 to NO by a converter BÜNOx (Bühler Technologies Inc.), while N 2 O was monitored by the EC-QCL-based Laser sensor (Fig. 7 right). carbon dioxide (CO 2 ) [3,4], methane (CH 4 ) [2,4], nitrous oxide (N 2 O) [2] and water vapor (H 2 O) [2], is extremely important for our understanding of regional air quality and global climate change trends.

In this context, a portable mid-infrared laser heterodyne radiometer (mid-IR LHR) has been developed [5] in the present work which aims at ground-based remote measurements of trace gases in the atmospheric column.

The solar radiation undergoing absorption by multi-species in the atmosphere was coupled into an optical fiber through a telescope that was installed on a sun tracker following the Sun's movement. An external cavity quantum cascade laser (EC-QCL) tunable from 1223 to 1263 cm -1 was used as local oscillator (LO) to mix the Sun light in a fast photodetector to generate a beat note at radio frequency (RF). Scanning the LO frequency across absorption lines allows one to recover the absorption feature of the target molecular trace gases from the total absorption of the solar radiation in the atmospheric column.

A field test has been performed on the roof of the laboratory in Dunkerque (51.05°N/2.34°E). The preliminary result of heterodyne measurement of tropospheric CH 4 and N 2 O in the atmospheric column will be presented and discussed.