Nelkin -Ghatak

Voigt

Yes Hard Yes

Keywords: Lamb dip, saturation, CRDS, water

Doppler-free saturated-absorption Lamb dips were measured at sub-Pa pressures on rovibrational lines of H2 16 O near 7180 cm -1 , using optical feedback frequency stabilized cavity ring-down spectroscopy. The saturation of the considered lines is so high that at the early stage of the ring down, the cavity loss rate remains unaffected by the absorption. By referencing the laser source to an optical frequency comb, transition frequencies are determined down to 100 Hz precision and kHz accuracy. The developed setup allows resolving highly K-type blended doublets separated by about 10 MHz (to be compared to a HWHM Doppler width on the order of 300 MHz). The comparison to the most recent spectroscopic databases is discussed. The determined K-type splittings are found to be very well predicted by the most recent variational calculations.

Abstract

High-precision molecular absorption spectroscopy has become a widely used tool in physics and metrology. More recently, such techniques have gained some favor in the earth sciences and industrial monitoring, mostly for their compactness and robustness. The determination of isotopic ratios of different isotopic systems is nowadays possible with commercially available laser spectrometers. However, in particular for CO 2 , the full potential of such techniques for highest precision measurements has yet to be exploited. In this thesis, we present a new spectrometer based on optical feedback frequency locking of a fibered distributed feedback laser (DFB) to a highly stable V-shaped reference cell. In such way, we obtain a near infra-red source reaching sub-kHz frequency resolution with a drift of 30 Hz/s. This ultra-narrow, ultra-stable laser source was then combined with a high-stability, high-finesse ring-down cell, using a robust dither lock scheme. We demonstrated a single-spectrum sensitivity of 1.2 x 10 -12 cm -1 , obtained in 30 seconds, and reported, for a narrow scan, a record-setting minimum detection level 3.8 x 10 -14 cm -1 , after less than 10 hours of measurement. We applied this instrument to the measurement of isotopic ratios in CO 2 and demonstrated the feasibility of direct measurements of ∆ 17 O in CO 2 . ∆ 17 O is a super-ratio which requires precise measurements of three isotopologues, offering information over the hydrological environment of the past, if measured from carbonate rocks. The instrument yielded a precision of 10 ppm in a record-setting measurement time of 10 minutes, demonstrating that laser spectrometers now perform on the same level as state-of-the-art isotopic ratio mass spectrometers currently used in geoscientific studies. We also demonstrated the first laser based measurements of the ratio 16 O 13 C 18 O/ 13 C 16 O 2 ("clumped isotopes"), demonstrating a precision of 20 ppm with a strong potential to go further. The instrument shows the potential to measure all geoscientifically relevant isotopologue ratios in CO 2 in one single measurement. Furthermore, we applied the instrument to Doppler-free saturated absorption spectroscopy. We determined the transition frequencies of the 3001200001 band of 16 O 13 C 16 O in natural abundance with kHz accuracy by referencing the laser source to a GPS-referenced optical frequency comb. Using combination differences, we were able to redetermine the B,D and H constant of the upper and lower state, providing evidence for differences between our experimental data and literature. Moreover, we investigated the S(2) transition of D 2 . The zero-pressure transition frequency was determined with a record-setting precision of 32 kHz, meaning an accuracy of 0.17 ppb. The impact of line profile choices on the retrieval of line specific parameters has been investigated. The instrumentation which was built during this thesis fulfills two major tasks: First, we have proven the capability of measuring ∆ 17 O in CO 2 with outstanding precision in record time. Moreover, we demonstrated a successful proof of concept for clumped isotope measurements. While a thorough investigation of memory ef-fects and external reproducibility has yet to be done, it shows the great potential of this technique for use in the geosciences. Secondly, the instrument is a valuable tool for spectroscopy, exhibiting extremely high sensitivity and thus allowing the very precise determination of line-shape parameters and the validation of the most advanced line profiles. Moreover, combreferencing allows for precise and accurate determination of transition frequencies and pressure induced shifts.

Chapter 1 Introduction

To date, most isotopologue abundance ratios are readily measured by isotope ratio mass spectrometers (IRMS). However, limitations with regard to isobaric interferences do not allow for a direct determination of the triple-oxygen system in CO 2 . This is because the isotopologue of interest, 16 O 12 C 17 O, is masked by the much more abundant 16 O 13 C 16 O. Several approaches to overcome this have been made over the time [1,2,3,4,5,6]. All of these methods rely on transferal of the Oxygen atom to another molecule. While these methods produce reliable results and have been used in extensive studies (e.g. [4]), they are costly and time intensive. A promising alternative to IRMS is molecular absorption spectroscopy. This technique features an extremely high selectivity and is not affected by molecular mass interferences. In the last decade, new spectrometers based on molecular absorption spectroscopy have arrived on the market. The main advantage of these instruments is seen in their compactness and robustness, making them particularly favorable for (industrial) monitoring applications (e.g. [7,8,9]) and field applications (e.g. [10,11]). To date, one may argue, the biggest impact of such instruments in the scientific community is found in the field of water isotopologues [12,13,14], where they outperform conventional mass spectrometers in terms of measurement frequency, sample preparation requirements and their capability for field deployment. Several systems are commercially available, covering a broad range of applications in the field of isotope geochemistry. Let us consider some of the most prominent ones. Picarro Inc. (USA), uses cavity ring down spectroscopy (CRDS) in their laser spectrometers. Their systems are measuring a variety of species, most notably CO 2 (δ 13 C) with an attainable precision of down to 10 ppm (e.g. [15,16]) and H 2 O (δ 18 O, δD, δ 17 O and 17 O-excess), with a precision on the order of tens of ppm (e.g. [17]), other systems are offered for isotopic analysis of CH 4 and N 2 O, O 2 . Other commercial instruments rely on off-axis integrated cavity output spectroscopy, such as the Los Gatos (USA) analyzers, available for CO 2 (e.g. [18]) and H 2 O (e.g. [19]). The Los Gatos CCIA-48 CO 2 analyzer allows measurements of δ 13 C, δ 18 O and δ 17 O, with a specified precision (100 seconds) of 70, 70 and 200 ppm. Thermo Fisher Scientific (USA) offers a multi-pass direct absorption laser spectrometer for CO 2 (e.g. [7]) as does Aerodyne Research (USA) (e.g. [20]). Aerodyne Research as well offers an instrument for non-traditional isotope ratios, stating a precision of 2. 3 for the clumped isotope 16 O 13 C 18 O and 0.35 for 16 O 12 C 17 O, insufficient for the analysis of subtle changes as obtained in the carbonate rock record. While the potential of laser based techniques for robust, low-cost, table-top instrumentation is now a widely accepted fact, the full potential for high-precision measurements, in particular for CO 2 , has yet to be fully realized. The present thesis is the result of a cooperation between the Laboratoire des Sciences du Climat et de l'Environnement (LSCE), an institute for environmental sciences, and the Laboratoire Interdisciplinaire de Physique (LIPhy), where the group Lasers, Molécules et Environnement (LAME), has an extensive experience in the development of spectroscopic instrumentation. Inspired by the constantly increasing performance levels of laser based instrumentation for isotope geochemistry, the prime target of this thesis was the development of a new laser spectrometer for the analysis of 17 O anomalies in CO 2 derived from carbonates. We built on previous work by Burkart et al. [21], who constructed an extremely sensitive and stable optical feedback frequency stabilized cavity ring down spectrometer (OFFS-CRDS) for absorption line metrology. This thesis has a very strong experimental part, during which a new instrument for molecular absorption spectroscopy in the near infrared was built. The instrument can be seen as a variation of OFFS-CRDS, which has been adapted for the needs of isotope ratio measurements. A significant part of the thesis work was concerned with the design of custom-made electronics, serving the special requirements of the setup. During this process, an eight-channel, autonomous, temperature PID system has been designed to precisely stabilize the ring-down cavity, while minimizing system failures. Furthermore, we designed a control unit for a nested Mach-Zehndermodulator (MZM), in an attempt to further automatize and stabilize the system. The experiment is controlled by software which has been written and subsequently optimized during this thesis, so that the instrument is highly automatized and requires very little user input for routine operation. Chapter 1 of this manuscript aims at providing a comprehensive introduction which highlights the current analytical state of the art in isotope geochemistry of CO 2 , points out the main problems and specifies how molecular absorption spectroscopy can be a powerful alternative to IRMS. We give a summary of the fundamentals of molecular absorption spectroscopy, starting with molecular transitions and the various effects that contribute to their shape in an absorption spectrum. We show that the choice of the right line profile is of utmost importance for spectroscopic analysis. Subsequently, we give an overview of methodological approaches to quantify molecular absorption, covering the most important techniques from direct absorption methods, over multi-pass systems to optical resonators, which today provide the highest sensitivity. We finish Chapter 1 with an overview over the current state of the art in high-sensitivity absorption line metrology in the near-infrared. In chapter 2, we give detailed insight in the technical aspects of the current setup. A comprehensive insight into the fundamentals of optical feedback locking is followed by a detailed description of our reference cell. Furthermore, we describe our temperature stabilization system, which, as we will show, is of considerable importance for isotopic ratio determination. We describe the referencing of our setup to an optical frequency comb (OFC), which allows us to determine transition frequencies around 1.6 µm with parts-per-trillion accuracy. Current limitations of our reference cell are discussed together with a description of a new, third generation reference cell, which was set up in collaboration with Mathieu Casado who works on the Combiniso project of Dr. Amaelle Landais. We then continue with a description of our frequency detuning system based on a nested MZM, which allows us to arbitrarily place spectral points within a range of 1-20 GHz. After this, we offer a detailed characterization of our ring-down cavity. An in-depth description of the home-made Chapter 1 electronics for a very robust and tight dither-lock is followed by a detailed description of the two different vacuum/inlet systems that have been in use in this thesis. Subsequently, we give an overview over the setup as a whole, reference side and measurement side combined. In this light, we discuss the different software workflows we have developed. The descriptive part concludes with an example of spectral averaging, where we demonstrate that, for a narrow spectral interval of 2.5 MHz, we reached a record-breaking baseline noise of 3.8 x 10 -14 cm -1 after less than 10 hours of averaging. It should be noted, that the averaging process was terminated after 10 hours with no indication of a deviation from white-noise averaging behavior. The descriptive part is followed by a comprehensive overview of possible error sources in CRDS. Subsequently, we give a detailed description of the fitting routine we used for the treatment of absorption spectra. This is followed by the publication, "Direct, Precise Measurements of Isotopologue Abundance Ratios in CO 2 Using Molecular Absorption Spectroscopy: Application to ∆ 17 O". The letter gives a comprehensive summary of the technological development together with results on the determination of ∆ 17 O. We show that the instrument developed in this thesis is capable of measuring 17 O anomalies directly in pure CO 2 with a precision of 10 ppm within 10 minutes of measurement time. This is, to our best knowledge, the fastest method for the determination of this isotopic anomaly. Chapter 2 is concluded by a description of a Python-script we wrote. This script interfaces with the spectroscopic database Hitran [23] using the Python library HAPI [24] and aims at identifying the best absorption lines for any isotopologue of interest. The quality of an absorption line is determined based on a series of criteria. Furthermore, the script is able to determine optimal regions for the measurement of many isotopologues in one single MZM scan of 19 GHz. Chapter 3 includes several applications conducted during the thesis work. The first which we discuss concerns the measurement of the S(2) transition of D 2 . We carried out an extensive line-profile study on this transition, using several line profiles. We evaluated the degree to which those models are able to capture the line shape of the transition as a function of pressure. It is highlighted, that only advanced models including speed-dependence and Dicke-Narrowing, such as the Hartmann-Tran-Profile (HTP) [25] are capable to correctly capture the shape at pressures exceeding 25 mbar and provide trustworthy line parameters. Furthermore, we employed our instrument to the Doppler-free absorption spectroscopy measurement of a set of 14 transitions of the 3001200001 band of 13 CO 2 in natural abundance near 6250 cm -1 . The transition frequencies have been determined with kHz accuracy. We used combination differences to determine rotational constants of both, the higher and the lower level with very high precision, showing differences with literature. We are now planning on extending the study to higher rotational numbers. Finally, our Python-script was able to identify absorption lines of the rare "clumped" isotopologue 16 O 13 C 18 O near 6707 cm -1 . Preliminary tests showed the feasibility to measure clumped isotopes with the current setup, marked by a performance level of 20 ppm in about one hour of measurement time for the ratio 16 O 13 C 18 O/ 16 O 13 C 16 O at 10 mbar experimental pressure. Another 16 O 13 C 18 O absorption line with the potential to improve on the previous result by a factor of almost two has been identified. However, due to limitations with the currently used laser diode cooling system we could not yet address it. Finally, we end this thesis with a conclusion and an outlook towards future prospects of this instrument.

Chapter 1 1.1. STABLE ISOTOPES

Stable Isotopes

Atoms are built from neutrons, protons and electrons. The number of protons defines the element, the sum of protons and neutrons gives the weight but it is the number of neutrons which defines the isotope of a given element. For example, about 99 % of Earth's carbon has 6 neutrons and 6 protons, hence an atomic weight of 12.

To reflect the atomic weight, we refer to this isotope as 12 C. However, roughly 1 % has 7 neutrons and 6 protons, referred to as 13 C. If an isotope is not radioactive, that is, it does not decay into other species, we refer to it as a stable isotope. Molecules of the same elemental combination but different isotopic compositions are referred to as "isotopologues", whereas molecules of the same isotopic composition but differing in the position of isotopic substitution are referred to as "isotopomers". For precise definitions we refer to the IUPAC "Gold Book" guidelines [26]. For example, CO 2 may exist in its most common form 16 isotopologues in the geosciences are marked in bold. Throughout the thesis we will refer to the different isotopologues using the Air Force Geophysics Laboratory (AFGL) shorthand notation [23]. This notation abbreviates one isotopologue to, in case of CO 2 , a series of three numbers. For instance, the isotopologue 16 O 12 C 16 O is abbreviated to 626.

The "traditional" isotopologue abundance ratios in CO 2 , 628/626 (δ 18 O) and 636/626 (δ 13 C), involve only the three most abundant isotopologues. Increase in measurement precision has widened the range of measurable species, and thus two additional isotopologues have fallen in the field of interest, the singly substituted 627 and the doubly substituted, "clumped" 638. The aim of this thesis is the development of a new measurement technique for unconventional isotopic ratios in carbon dioxide. The following sections will give an overview over the development of the field of stable isotope geochemistry and discuss the state of the art of current measurement techniques. Chapter 1 1.1. STABLE ISOTOPES

A Short History of Stable Isotope Geochemistry

The analysis of stable isotopes dates to the early 20th century. In 1913, Thomson suggested for the first time the existence of two stable isotopes of neon, marking the first measurement of stable isotopes [27]. Those early measurements relied on photographic rather than the electronic methods in use nowadays to measure the ion current in the mass spectrometer (see figure 1.1). Pioneers like Dempster and Bainbridge [27,28,29] pushed the field forward in those early years. The possibility of isotopic fractionation due to physical-chemical processes has been first proposed by Briscoe and Robinson in 1925 for the boron system [30].

Figure 1.1: First measurement of two stable isotopes of Neon, using the Thomson apparatus in 1913 [27].

The graphs shows the imprint of ion beams on a photographic plate, distinct white lines mark different m/z.

The field experienced a significant advancement in the 1930's and 1940's, when Alfred Nier published his work on mass spectrometry. In 1939, he first determined variations in carbonate isotopes [32]. One year later, he demonstrated the first sector field mass spectrometer, designed for routine measurements of isotopic abundances [31], thus being commonly seen as the founder of modern mass spectrometry. The sector field mass spectrometer is until today the most commonly used mass spectrometer. The predominant difference with its predecessors is the electronic rather than photographic measurement of ion beams. In 1947, he proposed a new, updated version of his initial mass spectrometer [33] making use of improved vacuum technology, effectively making this technology suitable for a wider scientific public [34].

Evidently, the field of stable isotope geochemistry has always been strongly tied to technological developments, either by lowering the barriers towards routine measurements, or by increasing the precision or sensitivity to resolve subtle isotopic effects. The first geoscientific application of stable isotope geochemistry has been demonstrated by Wickman in 1941 [35], who estimated the total amount of coal and bitumen on earth from its isotopic composition. Today, however, the birth of stable isotope geochemistry is mostly linked to Urey's classic 1946 lecture that later has been published in form of the paper "The thermodynamic properties of isotopic substances". In this, Urey did not only suggest the possibility of isotopic fractionations based on thermodynamic calculations but also already noted their potential use in the geosciences. This paper lead to one discovery that continues to be of significance: The temperature dependence of the isotopic fractionation of oxygen between water and marine shells [37,38,39], thus introducing the δ 18 O paleo-temperature proxy. In the years after this, the general trend in stable isotope geochemistry has been one of diversification towards a broader span of elements, such as hydrogen, carbon, nitrogen, sulfur, and others. A deeper understanding of those systems and recent advances in measurement precision allowed a "revisiting" of isotopic systems, and lead, for example, to the development of the field of clumped isotopes [40], which studies the deviation from a stochastic distribution of heavy, rare multiply-substituted isotopologues, leading to the development of interesting proxies such as the 13 C - 18 O-bonds in carbonates as studied in the Chapter 1 1.1. STABLE ISOTOPES ∆47 paleo thermometer.

Notation

Before we will discuss isotopic fractionation processes, let us consider some of the notations used in the stable isotope geochemistry community. By convention, isotopologue abundance ratios are expressed as the ratio of the rare isotopologue to the most abundant isotopologue: R x = abundance of rare isotopologue abundance of abundant isotopologue (1.1) Variations in the ratios of stable isotopologues are typically in the range of parts per thousands and are thus commonly reported as deviations from the same ratio in some standard material in using the δ-notation. In section 1.2, we will show that the main reason for relative notations in isotope geochemistry is the fact that the precision and accuracy of the measurement of relative differences is significantly higher than the accuracy on absolute isotopic ratio measurements. A wide range of standards has been established over time, such as VSMOW (Vienna Standard Mean Ocean Water), in case of δ 18 O, or VPDB (Vienna Pee Dee Belemnite), in case of δ 13 C. For practicability and due to the finite amount of international standards, most labs use working standards for day to day measurement routine. Working standards are referenced to international standards, and are used as a bridge for referencing samples to international standards. Equation 1.2 shows the computation of the δ-notation at the example of δ 17 O.

δ 17 O =    17 O 16 O sample 17 O 16 O ref erence -1    × 1000 ( ) (1.2)
Another important notation used in the field of stable isotopes is the ∆-notation, expressing deviations from an assumed mathematical relation in a three isotope system. For example, ∆ 17 O is defined as:

∆ 17 O = ln(δ 17 O + 1) -λ R × (δ 18 O + 1) (1.3)
where λ R defines on the specific system being studied, such as CO 2 [41,42,43] or H 2 O [44,45]. In this case, the ∆-notation is used to quantify a deviation from a mass-dependent fractionation law.

Isotopic Fractionation

The field of stable isotope geochemistry aims to understand subtle deviations from expected patterns of isotopic or isotopologue fractionation in nature. The fractionation between two phases A and B is typically denoted in form of the fractionation factor α, which is equal to the ratio of the abundance ratios of two isotopologues s1 and s2 in the two phases:

α A/B = (s1/s2) A (s1/s2) B (1.4)
In nature, there are two main drivers behind isotopic fractionation.

equilibrium fractionation

STABLE ISOTOPES kinetic fractionation

Equilibrium fractionation is an effect of differences in rotational, vibrational or translational movements of molecules. The by far biggest impact can be attributed to vibrational movements and the associated energy levels. Vibrational motions inside a molecule lead to changes in the relative distance of its constituents. With the distance between the atoms changing, the potential energy of the molecule is changed in turn. The bonding strength of a molecule is therefore directly linked to its vibrational energy. Hence, molecules comprised of heavier isotopes will be more stable than their light counterpart. One can write equilibrium exchange functions as

aA s1 + bB s2 = aA s2 + bB s1 (1.5)
Where the subscripts s1 and s2 indicate that species A or B incorporate the light or heavy isotopes s1 or s2, respectively. The equilibrium constant for this reaction can be expressed as

K eq = (A s2 /A s1 ) a (B s2 /B s1 ) b (1.6)
Where the terms in parentheses may refer to the molar ratios of the species. Because equilibrium fractionation fundamentally is a quantum mechanical effect, it should be written in terms of the partition functions Q of the corresponding species. Or, more precisely, as the ratios of the partition function of the isotopologic species in A and B.

k eq = (Q A s2 /Q A s1 ) a (Q B s2 /Q B s1 ) b (1.7)
The partition function for a given isotopologue is defined as:

Q = i (g i exp(-E i /kT )) (1.8)
Where E i refers to an individual energy level, g i to the corresponding statistical weight, k to the Boltzmann constant and T to the temperature. The summation is thus over all energy levels, combining all vibrational, rotational and translational energies [46]. There are three principal rules for equilibrium fractionation. Schauble (2004) [47], characterized them as:

1. Equilibrium fractionation is inversely proportional to temperature, roughly by 1/T Equilibrium effects related to temperature are the basis for some of the most important paleo-thermometers, e.g. the δ 18 O proxy. If the fractionation factor associated with temperature changes is big enough, one can use measurements of isotopologue ratios to reconstruct paleo temperatures. However, this assumes that the fractionation between two phases is entirely governed by equilibrium fractionation.

Chapter 1

MEASUREMENT PRINCIPLES

The main interfering process in the beautiful world of equilibrium fractionations is kinetic fractionation, which describes processes that are unidirectional and typically fast, caused by evaporation, diffusion, dissociation or biologic mediation. Biologically mediated processes usually prefer molecules with a lower dissociation energy and thus higher reactivity. The kinetic energy of a molecule in an ideal gas is given by E = 1 2 mv 2 , clearly illustrating its mass dependence. Diffusion processes, for example, therefore discriminate for light isotopologues, as does evaporation. Kinetic fractionation, hence, tends to be opposed to equilibrium processes, preferring lighter isotopologues over heavier. From what we have seen up to now, most isotope fractionation effects in nature seem to be mass-dependent. For instance, the depletion of δ 16 O relative to δ 18 O should be roughly twice as big as the depletion of δ 17 O relative to δ 18 O. While this assumption holds for a wide range of natural processes, recent advances in measurement precision resolved deviations from mass-dependent fractionation laws in a variety of natural systems. First deviations from those patterns have been observed in meteorites [START_REF] Black | Trapped neon in meteorites-II[END_REF][START_REF] Robert N Clayton | A component of primitive nuclear composition in carbonaceous meteorites[END_REF][START_REF] Gary | Presolar diamond, SiC, and graphite in primitive chondrites: Abundances as a function of meteorite class and petrologic type[END_REF], which experience processes far from thermodynamic equilibrium. Later, a variety of systems has been analyzed, e.g. the bio-geochemistry of sulfur (e.g. Farquhar et al., 2003 [51]), or, as analyzed in this study, the δ 17 O/δ 18 O system in CO 2 [4,[START_REF] Benjamin | Triple oxygen isotopes in biogenic and sedimentary carbonates[END_REF]. 17 O anomalies are thought to be linked to a variety of processes and have been proposed to be used as a proxy for terrestrial gross carbon fluxes [START_REF] Ka Boering | Observations of the anomalous oxygen isotopic composition of carbon dioxide in the lower stratosphere and the flux of the anomaly to the troposphere[END_REF]5], deep stratospheric intrusions [START_REF] Liang | Oxygen anomaly in near surface carbon dioxide reveals deep stratospheric intrusion[END_REF] and, if derived from carbonates, for paleohydrological processes. Such deviations are typically plotted in a three-isotopologue plot and denoted in ∆-notation, as mentioned in the previous section. In this particular case, several slightly differing versions of the ∆-notation exist. We refer the reader to [START_REF] Ss Assonov | Reporting small ∆17O values: existing definitions and concepts[END_REF] [START_REF] Ss Assonov | Reporting small ∆17O values: existing definitions and concepts[END_REF] for a detailed overview over the different versions. In the following, we will describe the analytical techniques used for the analysis of subtle isotopologue effects.

Measurement Principles

Sample Preparation

Since we cannot directly measure carbonates, we rely on converting them to CO 2 . This is done by acid digestion of the carbonate by phosphoric acid [START_REF] Morden | On the isotopic chemistry of carbonates and a paleotemperature scale[END_REF]:

CaCO 3 + H 3 P O 4 CaHP O 4 + CO 2 + H 2 O (1.9)
The process maintains the original bonding, however, there is the possibility of fractionation. This is a topic under active debate in the clumped isotope society (e.g. [START_REF] Guo | Isotopic fractionations associated with phosphoric acid digestion of carbonate minerals: insights from first-principles theoretical modeling and clumped isotope measurements[END_REF][START_REF] Müller | Clumped isotope fractionation during phosphoric acid digestion of carbonates at 70°C[END_REF][START_REF] Fernandez | Are acid digestion styles responsible for differences in clumped isotope calibrations?[END_REF]). An instrument achieving excellent precision will most likely finally be limited by the sample preparation process.

Isotope Ratio Mass Spectrometry

Currently, the most widely used method for the determination of isotopologue abundance ratios is IRMS. As mentioned earlier, the modern mass spectrometer is largely based on the work of Alfred Nier in the 1930's and 1940's. Most modern mass spectrometers still adhere to the same principles. In the following we will give an Chapter 1 1.2. MEASUREMENT PRINCIPLES overview over principles of mass spectrometry, current trends and limitations.

A modern IRMS comprises of five principal components:

(1) Inlet system

(2) Ion source A schematic of a gas-source IRMS system can be seen in Figure 1.2. A gaseous sample is introduced into a mass spectrometer via an inlet system. Two main inlet systems are in use nowadays, continuous-flow systems and dual-inlet systems. Currently, the best performances are achieved by dual-inlet systems. Several factors influence the quality of an IRMS. The inlet system is important for clean introduction of the sample into the mass spectrometer. Current inlet systems are mostly made of stainless steel (piping, body) and gold (gaskets). The central part of the inlet systems is the change-over-valve (see Figure 1.2), allowing quick changes from sample to reference gas. Both, sample and reference, are always either directed towards the ion source, or towards a vacuum waste pump in order to never interrupt the flow. Capillaries between change-over-valve and gas reservoir are used to exclude effusion related fractionation processes when the gas flows into the ion source. Repeated switching between sample and reference measurements ensure measurements with high precision and accuracy.

After leaving the inlet system, molecules are bombarded with electrons to create ions. The electrons are emitted by heated filaments, typically made from tungsten or rhenium and accelerated to electrostatic potentials of up to 150 eV before they Chapter 1

MEASUREMENT PRINCIPLES

enter the ionization chamber. The sensitivity of a mass spectrometer directly depends on the efficiency of this ionization process, which is typically in the order of one ion per 1000 to 2000 molecules [START_REF] Brand | Mass spectrometer hardware for analyzing stable isotope ratios[END_REF]. This dependency becomes clear if one considers that the counting of ions follows the laws of Poisson statistics [START_REF] De Matthews | Isotope-ratio-monitoring gas chromatographymass spectrometry[END_REF][START_REF] Merritt | Factors controlling precision and accuracy in isotope-ratio-monitoring mass spectrometry[END_REF].

The precision is therefore given by:

σ = 1 √ N (1.10)
where N is the number of ions. The fundamental limit of IRMS sensitivity is therefore given by the ionization efficiency. The ion source is the origin of several non-linearities. For example, the emission-rate of the filament must remain stable in order to guarantee constant ionization rates.

Slow or incomplete extraction of ions from the source can lead to the appearance of protonated species due to ion-molecule interactions [START_REF] Brand | Mass spectrometer hardware for analyzing stable isotope ratios[END_REF], causing further deviations from linear behavior. The ions are subsequently uniformly accelerated by an electric field. The kinetic energy of the ions is then given as:

1 2 mv 2 = zV (1.11)
where m is the mass, v is the velocity, V is the electrostatic potential and z is the charge of the ion. Focusing optics further focus the ion beam on its way into the flight tube, where they are exposed to an orthogonally oriented magnetic field. The magnetic field bends the beams based on their mass/charge ratio with a bending radius r:

r = m/z × 2V B 2 (1.12)
where B is the magnetic flux density. Therefore, for a fixed m/z the bending depends on the magnetic field strength and the accelerating voltage. Faraday cups are placed according to the calculated ion beam curvature. Most modern mass spectrometers use electron multipliers in their detection systems. In such, the accelerated ion hits a plate, causing the emission of secondary ions. Typically, several plates are cascaded, drastically increasing the gain of the system to the 10 6 region. The induced current is then measured and can be related to the corresponding mass/charge ratio. Secondary-electron multipliers exhibit mass discrimination effects, due to differences in the kinetic energy of impacting ions [START_REF] Ml Alexandrov | Discrimination effects in inorganic ion-cluster detection by secondary-electron multiplier in mass spectrometry experiments[END_REF]. Most high-end IRMS systems use Faraday cups instead. The Faraday cup is placed in the way of one ion beam. When an ion hits the cup it is neutralized and its charge is transferred to the cup. Discharging the cup, allows measuring the induced current and thus determine the corresponding number of ions. Since this method is just depending on transferred charge, it does not exhibit mass discrimination effects.

State of the Art

Most high-precision isotope ratio measurements are currently carried out on IRMS systems. From classical proxies like δ 18 O to challenging applications such as clumpedisotope-palaeothermometry, IRMS is the current standard to compare to. However, one main limitation of the technique remains. Being a technology based on the detection of mass differences, a predisposition for isobaric interferences is Chapter 1 2016)). The CO 2 isotopologues 636 and 627 exhibit a mass difference of 8.6 x 10 -4 g × mol -1 . The minimum required mass resolving power (m/∆m) is thus 52,000. Currently, one therefore resorts to chemical pretreatment to evade isobaric interferences. In the case of 627/626 (δ 17 O), several approaches to avoid the 636 mass interference by chemical pretreatment have been reported in recent years. Such methods include conversion to molecular oxygen by fluorination [1], exchange with cerium or copper oxide [2,6,3], or equilibration with water [4,5] or molecular oxygen [2]. While all those methods work and have their own, specific benefits and drawbacks, they all come at a significant cost in terms of time and resources. In the following we will describe an alternative to IRMS systems: molecular absorption spectroscopy.

Molecular Absorption Spectroscopy

The main alternative to IRMS is molecular absorption spectroscopy. Based on the interaction of light and matter, it has a distinctively different foundation than IRMS, and thus comes with different advantages and disadvantages. Starting with the principles of light-matter interaction and finishing with the fundamentals of spectroscopic tools, the following sections will explore the foundations for the instrument developed during this thesis.

Energy Levels

Molecular absorption spectroscopy is based on exciting molecules from one energy level to another. In the following, we will discuss the principles of molecular energy levels.

A linear molecule, such as CO 2 can rotate around its y and z axis, where the y axis is along the paper plane and the z axis out of the paper plane. Effects of rotation around the x axis can be neglected in absence of bending vibration. The molecule can therefore be approximated by a rigid rotor model with two rotational degrees of freedom [START_REF] Ingolf | Atoms, molecules and optical physics[END_REF]. The rotational energy levels F(J) can then be computed as

F (J) = BJ(J + 1), (1.14)
where J is the total angular momentum quantum number and B is the rotational constant, defined as

B = h 2 8π 2 I b . (1.15)
where I b is the associated inertia and h is the Planck-constant. However, rotational motion creates centrifugal forces, thus pulling the atoms of the molecule apart. To account for those centrifugal distortions, the rigid-rotor model is not sufficient. The effects of centrifugal distortion can be modeled as:

F (J) = BJ(J + 1) -DJ 2 (J + 1) 2 + HJ 3 (J + 1) 3 (1.16) Chapter 1 1.2. MEASUREMENT PRINCIPLES
where D is the quartic centrifugal distortion constant and H is the sextic centrifugal distortion constants, both a measure of bond stiffness, and v is the vibrational quantum number. This effect is of more importance for higher rotational energies and consequently higher rotation rates. Molecular vibrations refer to intramolecular movements. If one imagines a linear molecule as a set of spheres connected by springs, one would expect number of modes = 3N -5 = 3 × 3 -5 = 4 (1.17) vibrational degrees of freedom, where N is the number of atoms. In the case of CO 2 the 4 degrees of freedom are associated with distinct vibrational modes. For CO 2 , there is the symmetric stretch mode, Q 1 , where the two oxygen atoms both move towards or away from the center with the same rate, while the carbon remains still. There are two indistinguishable bending modes Q 2 , where the atoms move orthogonal to the paper plane and Q 3 where the carbon atom counters and reinforces the movement of both oxygen atoms. Finally, there is an asymmetric stretching mode. The associated eigenfrequencies ω are given by Hertel and Schulz as follows [START_REF] Ingolf | Atoms, molecules and optical physics[END_REF]. The given masses m A and m B as well as the given coordinates q i are assigned in Figure 1.3.

For the symmetric stretch:

ω 1 = k/m B (1.18)
where k is the spring constant. For the asymmetric stretch, the eigenfrequency is:

ω 3 = q 1 -2 m B /m A q 2 + q 3 2 + 4m B /m A . (1.19)
To a first order, the vibrational modes can be approximated by a simple harmonic oscillator. The associated energy then is

E(v) = (v + 1/2)hν, (1.20)
Where v is the vibrational quantum number and ν is the vibrational frequency. If one expresses the same function in cm -1 instead of Joules

E(v) = (v + 1/2)ω e (1.21)
where ω e is the harmonic vibrational frequency or energy expressed in wavenumbers. This approximation holds well close to the bottom of the potential well, where the potential resembles a harmonic oscillator quite well. However, accounting for non-harmonic potentials in real molecules requires to write it in form of a series expansion: From the equation above one can deduce that the effect of non-harmonic components is a narrowing of the spacing between energy levels towards higher vibrational 20 Chapter 1

E(v) = (v + 1/2)ω e -(v + 1/2)
1.2. MEASUREMENT PRINCIPLES wavenumbers until at some point the difference will approach 0, marking the dissociation energy of the molecule. Note, that the zero-point-energy (ZPE), can be estimated by substituting ν with 0. Under thermal conditions, the population distribution within the different modes is given by the Boltzmann distribution

p i = e -E i /kT M J=1 e -E j /kT (1.23)
With p i being the probability of the state i, E i the energy of the state i, k the Boltzmann constant, T the temperature and M the number of all available states of the system. The denominator is equal to the partition function Q, which is the sum of the probabilities of all accessible states:

Q = M i=1 e -E i /kT (1.24)
Accounting for rotational degeneracy yields:

Q = M i=1 Ω(E i )e -BhcJ(J+1)/kT (1.25)
where h is the Planck constant and Ω(E i ) is the degeneracy factor. This illustrates the thermal sensitivity of molecular absorption spectroscopy, since the population probability of a given mode is inherently linked to the thermal environment of the gas.

Line Profiles

Molecular absorption spectroscopy fundamentally builds on the accurate determination of the shape of an absorption line. This shape is a convolution of line shapes associated with different local effects, the most important of which being: natural line broadening pressure/collisional broadening Doppler broadening

Natural Line Broadening

From the energy-time uncertainty relation:

∆E∆t ≥ h/2 (1.26)
follows, that a state with a finite lifetime will exhibit a certain uncertainty on the energy determination, leading to a natural broadening which expresses itself in a Lorentzian profile. We refer to this as the natural line width.

Collisional Broadening

However, the natural line broadening by spontaneous emission is hidden by other, significantly stronger effects, the most important of which being pressure broadening. Molecules in a gas phase collide with a frequency Ω st of approximately

Ω st = N σv (1.27) Chapter 1 1.2. MEASUREMENT PRINCIPLES
Where, σ is the collision cross section. This collision frequency, hence, is directly proportional to the particle density N, which is linked to the pressure as

N = p m A v 2 /3 (1.28)
, where v is the velocity and clearly showing the proportionality to pressure p. This collisional or pressure broadening expresses itself in a Lorentzian line profile [START_REF] Tennyson | Recommended isolated-line profile for representing high-resolution spectroscopic transitions (IUPAC Technical Report)[END_REF]:

F L (ν -ν 0 ) = 1 π Γ (ν -ν 0 -∆) 2 + Γ 2 (1.29)
where Γ is the pressure broadened half-width at half maximum and ∆ is the pressure induced line-shift. Those effects are due to a shortening of the optical life time of the molecular states by collisions.

Doppler (thermal) broadening

The second important contribution to the line shape is Doppler-broadening. An observer (e.g. a molecule) moving towards or away from a frequency emitter (e.g. the laser source) will be subjected to a higher or lower frequency. This effect is called the Doppler-Effect. Under experimental conditions, the predominant cause for this is thermally induced motion of molecules. Following the Maxwell-Boltzmann distribution, every molecule will thus absorb at a shifted frequency f D ,

f D = f 0 (1 + v c ) (1.30)
The associated line profile has a Gaussian shape and is given as [START_REF] Tennyson | Recommended isolated-line profile for representing high-resolution spectroscopic transitions (IUPAC Technical Report)[END_REF]:

F D (ν -ν 0 ) = ln(2) π 1 Γ D exp(-ln(2)( ν -ν 0 Γ D ) 2 ) (1.31)
where, for a temperature T and a mass m the Doppler half-width Γ D is

Γ D = 2ln(2)kT mc 2 ν 0 (1.32)
where k is the Boltzmann constant and c the speed of light. In practice, all of the described processes influence a given absorption line. It's shape is therefore a convolution of the Doppler-associated Gaussian shape, and the pressure induced Lorentzian shape (with a very small contribution of natural line broadening). This convolution is expressed in the Voigt-Profile (VP) [START_REF] Hartmann | Collisional effects on molecular spectra: laboratory experiments and models, consequences for applications[END_REF]:

I V (x, y) = 1 √ π × Re[w(x, y)] (1.33)
where w(x, y) is the complex probability function given by: turn, however, this is not the case for low pressure measurements. With increasing instrumental resolution, it became clear that additional effects contribute to spectral line shapes and that in order to accurately fit an absorption line, new, more complex models were needed. We list several important models in table 1.2, with the corresponding parameters. In the following, we will explain some of the physical effects used in different models. We refer the reader to the table 1.2 for the parameter abbreviations used hereafter.

w(x, y) = i π +∞ -∞ e t 2 x -t + iy dt (1.34)

Dicke-Narrowing

One of the most obvious effects to be accounted for is known as Dicke-narrowing, named after Dicke [START_REF] Rh Dicke | The effect of collisions upon the Doppler width of spectral lines[END_REF]. Dicke-narrowing describes collision induced changes to the spectral line shape. If a molecule has a mean-free path which is significantly shorter than the wavelength of the probing laser, several collisions with other molecules may occur during absorption. These collisions change the velocity of the molecule or its direction. Therefore, several Doppler states will be probed, resulting in a profile which is narrower than a normal Doppler profile. There are several line profiles that address this effect. Two main approaches to this exist, an example or the first of which is the NGP, which was first proposed by Nelkin and Ghatak in 1964 [START_REF] Nelkin | Simple binary collision model for Van Hove's G s (r, t)[END_REF] and subsequently completed by Rautian and Sobel'man to include pressure broadening [START_REF] Sergei | The effect of collisions on the Doppler broadening of spectral lines[END_REF]. This model considers only "hard" collisions, which means that it assumes a complete loss of the velocity memory of the molecule after a collision. This means that a complete thermalization of the velocity distribution after collision is assumed, rendering it independent from the initial velocity. The frequency of velocity changing collisions ν V C is considered to be speed-independent [START_REF] Hartmann | Collisional effects on molecular spectra: laboratory experiments and models, consequences for applications[END_REF]. Another approach to implement Dicke-narrowing is the so-called "soft"-collision approach. In such, many collisions are needed to generate a significant change in the molecules velocity. One Chapter 1

Table 1.2: Overview of important line-profiles. Compilation taken from [START_REF] Tennyson | Recommended isolated-line profile for representing high-resolution spectroscopic transitions (IUPAC Technical Report)[END_REF] example for such models is the GP [START_REF] Galatry | Simultaneous effect of Doppler and foreign gas broadening on spectral lines[END_REF].

Speed Dependence

A second class of line-profiles considers a speed-dependence of the relaxation rates, which lead to the creation of the SDVP by Berman [START_REF] Paul R Berman | Speed-dependent collisional width and shift parameters in spectral profiles[END_REF]. This model reduces to a conventional VP in absence of speed-dependent effects (e.g. at very low pressures). It introduced several new parameters, Γ 0 and ∆ 0 , the collisional width and shift averaged over all velocity classes and Γ 2 and ∆ 2 , which characterize the dependence on the speed of the active molecule.

Higher-Order Models

A third class of line profiles can be considered as higher-order profiles. Such profiles combine some of the physical aspects caught by lower-order profiles. One of these models is the SDNGP, which adds speed-dependence to the NGP. The most advanced model used in this thesis is the HTP model, which combines the principles of hard-collisions with speed-dependence and an additional correlation parameter η. This profile has been recommended by IUPAC as the profile to be used for highresolution spectroscopy [START_REF] Tennyson | Recommended isolated-line profile for representing high-resolution spectroscopic transitions (IUPAC Technical Report)[END_REF]. This profile is universal, in that it reduces to one of the several lower order models, if certain parameters are set to 0. For instance, if the correlation parameter and the frequency of velocity changes are set to 0, the model will default to a qSDVP (meaning a SDVP using a quadratic approximation of speed-dependence) [START_REF] Ngo | An isolated line-shape model to go beyond the Voigt profile in spectroscopic databases and radiative transfer codes[END_REF].

The exact definition of similarly acting parameters is somewhat fluctuating in literature according to computation methods or the type of approximation used. Therefore, we will state the definitions used in this thesis in the following. For Dickenarrowing we fit a parameter ζ:

ζ = ν H V C /∆ω D (1.35)
where ∆ω D is the 1/e Doppler half with. In the qSDVP and the qSDNGP we use the following definition

Γ(v) -i∆(v) = (Γ 0 -i∆ 0 ) + (Γ 2 -i∆ 2 ) v ṽ 2 - 3 2 (1.36)
For the HTP, the speed dependent velocity changing frequency υVC is dependent on a correlation parameter η

υV C = υ V C -η{Γ(v) -i∆(v)} (1.37) 1.2. MEASUREMENT PRINCIPLES
where υ VC refers to the frequency of velocity changing collisions assuming no correlation between velocity and rotational-state changes [START_REF] Ngo | An isolated line-shape model to go beyond the Voigt profile in spectroscopic databases and radiative transfer codes[END_REF].

A last note must be made on computational issues. Advanced models, such as the GP or the SDVP require significant computational power. Thus, some efforts have been done towards finding efficient ways of computing. In this thesis, we use the rotational approximation for the complex probability function as proposed by Humlìček [START_REF] Humlìček | An efficient method for evaluation of the complex probability function: the Voigt function and its derivatives[END_REF] in all profiles that include a Voigt component, to significantly reduce computation times. Also in all speed-dependent models we use a quadratic approximation rather than the hypergeometric version, indicated by a "q" in front of the profile abbreviation.

The choice of the line profile directly impacts the retrieved line center frequency and the retrieved line surface (see section 3.1). A correct determination of the line surface is necessary to correctly determine partial pressure, therefore great care has to be taken in the choice of line profiles. Hereafter, we will explore the most important methods used to quantify molecular absorption.

Direct Absorption Techniques

The fundamental basis of spectroscopic methods is the attenuation of light when passing through a medium of absorbing species. This attenuation is described by the Lambert-Beer-Law:

I(exp) = I 0 e -αL = I 0 e -σN L (1. 38
)
where I is the transmitted intensity, α the particle absorption coefficient, N the molecule density and L the path length. Equation 1.38 shows that the sensitivity of an absorption spectrometer is dependent on two technical constraints, the path length through the sample and the stability of the light source. The most direct implementation of the Lambert-Beer-law is direct laser absorption spectroscopy (DLAS). In DLAS one compares the light intensity after passage through an absorbing medium I out to the the incident light intensity I 0 . The absorption coefficient can then be determined as

α = - 1 L ln( I out I 0 ) (1.39)
Frequency scanning the laser while recording the absorption coefficient allows the construction of an optical spectrum, a plot of the absorption coefficient over the laser frequency. The sensitivity of a DLAS experiment scales with length and absorption strength. The simplicity of the setup, however, implies restrictions and disadvantages. DLAS compares very small variations in power, often close to unity. It is therefore highly sensitive towards small fluctuations of the laser power and electronic noise, imposing limitations on the measurement potential. There are several options to partly overcome those limitations. For instance, recording several spectra allows to average retrieved absorption coefficients and thus decrease the measurement noise by 1 √

(n)

. Simultaneous measurement of I 0 and I out allow to cancel out coherent laser noise. A third option consists in prolonging the path way, a possibility addressed by multi-pass systems. Such systems use mirrors to redirect the laser beam in a cell to create a series of reflective passes hence prolonging the optical path way and increasing the instrumental sensitivity. The most common types of multi-pass cells in use are White and Herriot cells. A Herriot-cell consists of two opposing spherical mirrors with an entry hole in one or both, as shown in figure 1.5 [START_REF] Donald | Folded optical delay lines[END_REF]. The beam Chapter 1

1.2. MEASUREMENT PRINCIPLES Figure 1.5: A classical Herriot cell with a circular reflection path [START_REF] Inc | cell[END_REF] follows a circular pattern on the mirror and exits after a given number of passes through a hole machined in one of the mirrors. This type of cell can reach up to 50 m optical path length [START_REF] Das | Very long optical path-length from a compact multi-pass cell[END_REF]. The slightly more complex White cell is built out of three spherical concave mirrors [START_REF] John U White | Long optical paths of large aperture[END_REF], allowing for an optical path length of up to hundreds of meters (e.g. Doussin, Dominique, and Patrick, 1999). Both, multipass and direct absorption techniques are mostly used in the mid-infrared region to probe fundamental vibrational transitions, exhibiting the strongest absorbance, up to a 1000 times stronger than the transitions addressed in this work.

As we have seen, direct absorption and multi-pass schemes are limited to a few 100 meters of optical path length and still suffer from laser fluctuations and fluctuations due to optical fringes.

Cavity Enhanced Absorption Techniques

Further increasing the sensitivity requires the use of optical resonators. The simplest optical resonator consists of two partly transmissive, concave mirrors facing each other with a distance of L, called a Fabry-Perot Interferometer [START_REF] Fabry | Sur les franges des lames minces argentées et leur application à la mesure de petites épaisseurs d'air[END_REF]. A laser beam entering through one of the two would be reflected on itself many times as a function of the mirrors reflectivity R. Due to constructive and destructive interference, such resonator has a discrete set of resonant frequencies, appearing at integer multiples of the incident lights frequency, as illustrated in figure 1.6. We will refer to those resonant frequencies as cavity modes [START_REF] Demtröder | Laser spectroscopy: basic concepts and instrumentation[END_REF]. The spacing of the cavity modes, that is, the Free Spectral Range (FSR) can be derived as a function of L, R and the refraction index n 0 . For a linear, non-confocal cavity:

F SR = c 2n 0 L (1.40)
where c is the speed of light. For a V-shaped cavity, with three mirrors and two arms of length L the FSR is

F SR V = c 4n 0 L (1.41)
One may further argue that the width of a resonant mode must be a function of the reflectivity, since more passes increase destructive interference at non-resonant frequencies leading to stronger suppression outside resonance. This quality parameter Different reflectivities are given. The width of the mode is a function of the mirror reflectivity R. The transmission is periodic, separated by the FSR. Graphic from [START_REF] Berden | Cavity ring-down spectroscopy: techniques and applications[END_REF] is described as the finesse F :

F = π √ R 1 -R (1.42)
The resolution of an optical resonator is determined by the extinction of nonresonant frequencies, that is, the width of resonant modes. The cavity mode width ∆ν can be calculated as ∆ν = F SR/F (1.43)

Note, that the maximal resolution attainable experimentally is therefore limited by the reflectivity of the mirrors but also by the line width of a coupled laser, being a fundamental driver of coupling efficiency. Should the laser source be significantly wider than the cavity mode width, only very little of the total available light will be coupled into the cavity. The use of optical resonators therefore necessitates the use of mode matching optics. Light will only be coupled into a cavity, when the laser is in resonance, or "matched", with a cavity mode. Typically, the lowest order TEM 00 mode is chosen for excitation. This can be controlled by steering mirrors and a focusing lens. In order to optimize the coupling efficiency, typically lenses are used to match the spatial characteristics of the TEM 00 mode. In modern spectroscopy, there are several measurement principles that are based on optical resonators. The most common ones are cavity enhanced absorption spectroscopy (CEAS) and CRDS, which are based on a version of the schematic shown in figure 1.7.

MEASUREMENT PRINCIPLES

CEAS uses, as the name implies, optical resonators, or cavities, to enhance absorption effects. The fundamental methodology is thus identical to DLAS or Multi-pass systems, in that CEAS measures I I 0 . The transmission T of a cavity mirror is given by T = 1-A-R, where R is the reflectivity, and A is the sum of cavity mirror losses by scattering, absorption and diffraction in the mirror coating. The steady state transmission of a cavity is then given as [START_REF] Barbara | An historical overview of cavity-enhanced methods[END_REF]

I = C P I 0 T 2(1 -R) , (1.44)
where I 0 is the laser intensity and C P is the coupling efficiency in the cavity mode. Following equation 1.38 the absorption signal is I 0 ×αL. Therefore, if we place a sample in the cavity, [START_REF] Barbara | An historical overview of cavity-enhanced methods[END_REF] ∆I

I = (1 -e αL ) × R/(1 -R) 1 + (R/(1 -R))(1 -e αL )
.

(1.45)

Note, that this technique is sensitive to changes in the mirror parameters, cavity length changes and laser intensity fluctuations. A change in cell length, for example, would change the cavity FSR and consequently cause strong fluctuations in cavity transmission. It should be mentioned, that the fundamental limit in terms of cell size, and thus sample size, are the geometric properties of the cavity mode. The lower limit of sample size is thus determined by practical considerations regarding the cavity alignment, fundamentally limited by cavity and mirror fabrication.

The first implementations of a technology of this kind have been done in the and Anderson proposed another option to generate a quasi-continuous transmission pattern, by aligning the optical resonator in a strictly off-axis scheme. In such a scheme, the beam is not reflected on itself but is guided in a way very similar to multi-pass cells until it is finally reflected on itself again. The longer this re-entrant condition, that is the more passes the laser does before being reflected on itself again, the smaller the FSR of the cavity, rendering the transmission of the cavity less frequency dependent. In principle, every stable optical resonator can be aligned in an off-axis pattern. This condition is defined as

0 < (1 -L/R 1 )(1 -L/R 2 ) < 1, (1.46)
where R 1 and R 2 are the mirror radii of curvature [START_REF] Paul | Ultrasensitive absorption spectroscopy with a high-finesse optical cavity and off-axis alignment[END_REF]. The re-entrant condition can be deduced from the per-pass-rotation of the laser reflection on the mirror, (σ,

cosσ = 1 -L/R, (1.47)
assuming R 1 = R 2 [START_REF] Paul | Ultrasensitive absorption spectroscopy with a high-finesse optical cavity and off-axis alignment[END_REF] . The pattern becomes re-entrant when

m2σ = n2π, (1.48)
where m is the number of round-trip passes and n is an integer [START_REF] Paul | Ultrasensitive absorption spectroscopy with a high-finesse optical cavity and off-axis alignment[END_REF]. Using this technique an absorption equivalent noise level of 1.8 x 10 -10 cm -1 Hz -1/2 was observed, going beyond typical ICOS performance at that time. However, as Paul, Lapson, and Anderson already note in their initial paper, the technique features an overall lower power transmission. Several other CEAS techniques have been developed over the years, of which we will discuss some interesting examples. One of those is optical feedback CEAS (OF-CEAS). The trend to higher sensitivity requires the use of cavities with higher finesse, thus narrower cavity modes. If one compares high-finesse cavity mode widths in the order of a few kHz to typical laser bandwidth in the order of 1 to 2 MHz the poor resulting coupling efficiency becomes obvious. OF-CEAS is one way to improve on this matter. In 1999, Romanini et al. proposed a method building on optical feedback to increase coupling efficiency [START_REF] Romanini | Measurement of trace gases by diode laser cavity ringdown spectroscopy[END_REF], using widely available distributed feedback diodes (DFB). The basic idea behind this method is to lock the laser to one cavity mode if the laser frequency enters resonance by feeding back photons that have already been frequency selected by the cavity to the laser. The laser will, by stimulated emission, copy the properties of those photons resulting in a line width narrowing of several orders of magnitude and consequently the coupling efficiency increases drastically. However, there are a few fundamental requirements. The laser feedback must consist of only photons from inside a resonant mode. If other light enters the laser, the laser spectrum would be disturbed. Building on earlier propositions [START_REF] Laurent | Frequency noise analysis of optically self-locked diode lasers[END_REF], Romanini et al. (1999) used a V-shaped cavity geometry, with the injection being through the folding mirror. The direct reflection is tilted away from the incident beam and only light from inside the cavity can return to the laser. Few control electronics are needed to adjust the rate of optical feedback in order to get a stable transmission. The main difference to the system by Laurent, Clairon, and Breant (1989) consists in using the cavity as a measurement rather than a reference cell, resulting in an easy setup providing highly efficient mode injection, with the precision in the initial paper reported as 1 x 10 -8 √ Hz. One beneficial side effect is the almost perfect equidistant sampling of 1.2. MEASUREMENT PRINCIPLES an absorption spectrum in frequency space due to the optical feedback locking characteristics. Another beneficial aspect is the strong locking mechanism rendering the system less sensitive to vibrations and misalignment. This technique has been used for a variety of applications in the last years, spanning ECDL based measurements of NO 2 [START_REF] Courtillot | Sub-ppb NO 2 detection by optical feedback cavityenhanced absorption spectroscopy with a blue diode laser[END_REF], monitoring of volcanoes [START_REF] Kassi | Looking into the volcano with a Mid-IR DFB diode laser and Cavity Enhanced Absorption Spectroscopy[END_REF], first tests with quantum cascade lasers [START_REF] Maisons | Optical-feedback cavity-enhanced absorption spectroscopy with a quantum cascade laser[END_REF] and SO 2 trace gas analysis with an interband cascade laser [START_REF] Richard | Optical-feedback cavity-enhanced absorption spectroscopy with an interband cascade laser: application to SO2 trace analysis[END_REF]. The technique has been further improved over the years and is currently commercially exploited in commercial instruments (AP2E, France). The last CEAS technique to be mentioned is NICE-OHMS, introduced as well in the late 1990's by Ye, Ma, and Hall [START_REF] Ye | Ultrasensitive detections in atomic and molecular physics: demonstration in molecular overtone spectroscopy[END_REF]. NICE-OHMS is arguably one of the most complex CEAS setups, while at the same time being one of the most sensitive ones, being effectively shot-noise limited. The basic principle behind NICE-OHMS is the generation of side bands by high-frequency modulation of the laser and subsequently locking the carrier and the two side bands to consecutive modes of a cavity. The output of the cavity is then demodulated, with a small absorption generating a disbalancing in the heterodyne signal. Naturally, this system requires very advanced high-frequency electronics. Several frequency locking loops and a very good knowledge of the modulation parameters then allow reaching an impressive detection limit of up to 1 x 10 -14 cm -1 [START_REF] Ye | Ultrasensitive detections in atomic and molecular physics: demonstration in molecular overtone spectroscopy[END_REF], limited to the scan of very small spectral regions, thus very suitable for Doppler-free absorption spectroscopy.

Cavity Ring Down Spectroscopy

CRDS was introduced in the 80's to determine the reflectivity of mirrors. It consists in measuring the lifetime of photons inside a cavity, given as

I(τ, λ) = I 0 exp -t/τ (λ) (1.49)
with I 0 being the intensity of light at the time of laser interruption and τ the ringdown time constant. One can relate the decay rate 1/τ to the cavity optical loss and sample absorption through

1 τ (λ) = ( L scatter (λ) + L trans (λ) + α(λ)2L τ rt ) = L cavity 2L/c + c (λ)N (1.50)
where l rt is the cavity round-trip length, c is the speed of light, L scatter is the roundtrip scattering loss of the empty cavity, L trans is the round-trip mirror transmission [START_REF] Barbara | An historical overview of cavity-enhanced methods[END_REF] and N is the sample density. Equation 1.49 shows that this technique is immune to laser intensity fluctuations. It has been shown, that besides measuring scattering losses and transmission, one can quantify additional losses, if one compares a spectrum obtained from a empty cavity to a spectrum from a cavity with an analyte gas [START_REF] Barbara | An historical overview of cavity-enhanced methods[END_REF]:

C = R(λ, C) -R(λ, 0) (c (λ)) (1.51)
where C is the concentration of the analyte gas. individual spectra is short compared to the time constant of mechanical and optical drifts, several spectra can be averaged together to ultimately increase the measurement precision. In the specific case mentioned, a laser spectrometer with a photo-detector noise limited minimal absorption detectivity of 2 x 10 -10 cm -1 for 700 averaged ring-down events has been used to rapidly record several tens of spectra. Averaging 43 successive spectra together allowed to push the detection limit down by one order of a magnitude, to 2 x 10 -11 cm -1 [START_REF] Kassi | Very high sensitivity CW-cavity ring down spectroscopy: Application to the O 2 band near 1.58 µm[END_REF]. More recently, Kassi and Campargue investigated the limits of this technique, reporting a record breaking 5 x 10 -13 cm -1 baseline absorption [START_REF] Kassi | Cavity ring down spectroscopy with 5× 10-13 cm-1 sensitivity[END_REF]. In this case, a photodetector noise limited laser spectrometer with a limit of detection about 1 x 10 -11 cm -1 has been applied to the first measurement of an electric quadrupole transition in the second overtone band of nitrogen in the near-infrared. Averaging 6220 consecutive spectra allowed reaching the record breaking baseline absorption. With a line strength of 1.5 x 10 -31 cm -1 / molecule, this is the weakest absorption line ever measured by absorption spectroscopy. Burkart demonstrated a baseline noise of 8.4 x 10 -14 cm -1 over a spectral interval of 4.7 MHz with a 50-kHz resolution [START_REF] Burkart | Optical feedback frequency stabilized cavity ring down spectroscopy -HiHigh coherent near-infrared laser sources and metrological applications in molecular absorption spectroscopy[END_REF]. To reach this noise level about 202 spectra were averaged, amounting to a total measurement time of about 24 hours. The same experiment, albeit on a shorter spectral interval of 2.5 Mhz, has been done with the instrument developed in this thesis, reaching a baseline noise of 3.4 x 10 -14 cm -1 after averaging spectra for about 10 hours (see chapter 2.4).

In this thesis we have used CRDS to measure subtle environmental effects, making use of the high sensitivity and high selectivity this technique offers if a sufficiently stable instrumental setup is provided. Isotope geochemistry offers a unique opportunity to gain insight into paleo-climates. It has been extensively used for this purpose, from the reconstruction of paleo sea-surface temperatures, over the carbonate rock formation temperatures to paleo-hydrological question sets. In this chapter, we have reviewed the history of stable isotope geochemistry, from the 1.2. MEASUREMENT PRINCIPLES first mass spectrographs by Thomson to the first modern type mass spectrometer, introduced by Nier. We have pointed out the strong linkage between the development of new isotope proxies and technological advancements offering improved precision. Subsequently, we revisited current measurement methods of which IRMS is by far the most important one today. Doing so we remarked the main limitations of mass spectrometers, that is source efficiency, which poses a fundamental limit to the systems sensitivity and the low selectivity, which hampers the discrimination of isobaric interferences and renders measurements of isobaric isotopologues (such as 636 and 627) extremely difficult. Subsequently, we pointed out a promising alternative to mass spectrometry, namely molecular absorption spectroscopy. We introduced basic principles, such as vibrational energy levels and absorption line shapes.

After revisiting the state of the art in such technologies, we concluded that CRDS appears to be the most suitable candidate for the high-precision determination of isotopologue abundance ratios in CO 2 . Fundamental limits where identified as lacking stability of currently available laser sources, as well as laser line-width, both of which result in a decreased sensitivity when probing absorption lines, due to frequency noise that will translate to amplitude noise while probing the flank of a line. Finally, we reported the current state in high-sensitivity molecular absorption spectroscopy.

The next chapter will give a thorough description of the instrument developed in this thesis. It will include descriptions of the electronics designed, the optical setup and software workflows. We will mention important quality parameters of the instrument from "house keeping" parameters such as temperature and pressure to frequency stability of our reference cell.

Chapter 2

A VCOF-CRDS Setup for CO 2 Isotope Ratio Measurements

The spectroscopic determination of isotopic ratios comes with demanding stability requirements. We will show, that a single spectrum does not reach the precision requirements of isotope ratio determinations. Therefore, the laser spectrometer has to be highly stable over extended periods of time. Temperature stability down to the mK level and pressure stability to the µbar level are two crucial requirements to be met. For instance, a measurement with our target precision of 10 ppm, would consequently require a pressure stability of 0.2 µbar for a typical measurement at 20 mbar, excluding the impact of interfering absorption lines. Furthermore, an accurate determination of isotopic ratios mandates a most accurate and precise retrieval of absorption line surfaces. Thus, a highly-stable frequency axis is a necessity. Finally, the determination of the abundance ratios of rare isotopologues of CO 2 in the nearinfrared means determining absorption lines as weak as 1 x 10 -8 cm -1 with a very high signal-to-noise ratio.

Principle of VCOF-CRDS

Assuming a laser spectrometer with infinite sensitivity, a final limitation of this spectrometer would be the conversion of frequency noise to amplitude noise when absorption line wings are probed. Such frequency noise may arise from a laser frequency jitter, drift or be related to the laser line-width or a (thermally induced) drift of the measurement cavity. One solution to improve the performance of spectroscopic instrumentation consists therefore in stabilizing and narrowing of the laser source. Coupling such a refined laser source to a highly-stable, high-Finesse ringdown cavity would drastically reduce the impact of frequency noise on absorption line surface determination. Hence, it will improve the abundance determination of a given isotopic species. V-shaped cavity optical feedback (VCOF) offers an excellent solution for those limitations.

VCOF can be considered a distant relative of the work of Morville et al., with the fundamental difference of using the V-shaped cavity as a reference cell, rather than for measurements. This has been done to overcome some of the limitations of OF-CEAS. For instance, as a result of the three-mirror setup, the Finesse of a V-shaped cavity is necessarily lower than that of a classical linear cavity. Moreover, OF-CEAS requires a variety of optical components in the beam path, giving rise to parasitic reflections. In CRDS, the amount of optical components can be reduced to 2.2. TECHNICAL REALIZATION a bare minimum. Burkart, Romanini, and Kassi therefore proposed a new technique, referred to as Optical Feedback Frequency Stabilized CRDS (OFFS-CRDS). OFFS-CRDS uses the benefits of optical self-locking of a laser diode to a reference cavity, as in OF-CEAS and combines them with the advantages of CRDS for high-precision absorption line metrology. Therefore, they locked a free-space DFB laser diode to a V-shaped reference cell. This cell, in contrast to OF-CEAS, has been evacuated down to ∼ 1 x 10 -8 mbar and been stabilized in temperature. In such way, they created a laser source with extreme frequency stability and ultra-narrow line width.

One drawback of such scheme, common to OF-CEAS, is that the laser frequency can only be changed by multiples of the reference cavities resonance modes. The authors overcame this limitation by feeding part of the light into a Mach-Zehnder modulator (MZM) wich they used as a single sideband generator (SSB, see section 2.2.1). This way, they generated a side band that can be arbitrarily tuned by applying a radio frequency to the MZM. This setup demonstrated an absorption detectivity of 5 x 10 -13 cm -1 Hz -1/2 . It has been applied to various metrological and technical studies [START_REF] Burkart | Communication: Saturated CO2 absorption near 1.6 µ m for kilohertz-accuracy transition frequencies[END_REF][START_REF] Burkart | Absorption line metrology by optical feedback frequency-stabilized cavity ring-down spectroscopy[END_REF][START_REF] Burkart | Optical phase cloning by an integrated dual-parallel Mach-Zehnder modulator[END_REF], proving the outstanding potential of this technique.

The setup introduced in this thesis can be considered as an adaption of OFFS-CRDS aiming to exploit the outstanding performance in absorption line metrology to the field of isotopic ratio measurements. In the following, we will discuss the details of the current setup. We will also discuss performance characteristics and potential improvements.

Optical self-locking of semiconductor lasers to external cavities is a well-understood and widely used technique [START_REF] Laurent | Frequency noise analysis of optically self-locked diode lasers[END_REF][START_REF] Dahmani | Frequency stabilization of semiconductor lasers by resonant optical feedback[END_REF]. Such lasers are highly sensitive to optical feedback due to coupling of the electric field amplitude and phase in semi-conductor lasers via charge-carrier fluctuations [START_REF] Henry | Theory of the linewidth of semiconductor lasers[END_REF]. In the case of optical feedback, photons are re-injected into the laser diode and counter the random-walk of the laser due to spontaneous emission. The direct impact of this is a drastic line width reduction. Furthermore, the frequency stability of the photon source, in our case a highly-stable high-finesse reference cavity, is copied by the laser diode. Hence, the laser "copies" the optical properties of the reference cavity. In fact, it even surpasses the reference cavity performance, since the laser line width is narrower than the cavity mode width [START_REF] Laurent | Frequency noise analysis of optically self-locked diode lasers[END_REF]. Therefore, the stability of the reference cavity is the most important limitation for a OFFS-CRDS system.

Technical Realization

The reference cavity used in the current setup is a composite cell as described in [START_REF] Burkart | Optical feedback stabilized laser tuned by single-sideband modulation[END_REF]. An ultra-low-expansion glass (ULE) spacer of 15 cm length is mounted inside a stainless steel vacuum chamber (see figure 2.1). An ionic pump is connected to the chamber by a KF-flange. To reduce thermal conductance from the vacuum chamber to the cell, the cavity is hold by three MACOR ceramic feet. The MACOR feet are attached to a stainless steel clamping ring, which is used to tightly fixate the cavity itself. Two Super-Invar flanges are connected to the cavity by threaded rods to further fix it. The three mirrors are fixed to those flanges by mechanically pre-aligned Super-Invar mirror holders. A high-degree of symmetry and midplane mounting reduce the susceptibility of the setup to vibration induced length changes.

The system is initially pumped down to vacuum using a turbo-molecular pump. Subsequently, the ionic pump is started and the main pumping line towards the turbo-molecular pump is permanently closed. The produced vacuum is at the 1 x Chapter 2 2.2. TECHNICAL REALIZATION 10 -8 mbar level. Initially, the cavity has been actively stabilized to 25°Celsius to avoid frequency drifts associated with thermal length changes of the cavity. The stabilization has later been disengaged, so that the system is only passively stabilized today. While this damps the temperature oscillations in the laboratory, still oscillations of up to 1°C are possible. The resulting frequency instability is compensated by referencing the laser to an optical frequency comb. The active stabilization system is currently in use on a third generation VCOF as well as in the temperature stabilization of our ring-down cavity. It will be described in great detail in this chapter. A schematic of the optical setup of our reference cavity can be found on the right side of figure 2.1. A tight feedback locking is maintained by a lock-in amplifier. For this purpose, a fibered electro-optic modulator (EOM) has been mounted on which we apply a modulation. The VCOF transmission is used as an input for the lock-in amplifier. The error signal generated by the lock-in amplifier is fed into a home-made PID board, which controls the EOM in order to maintain a stable feedback phase φ = arcsin(δν/∆ (∆ is the locking range, δν is the free running laser detuning).

A fibered beam-splitter is used to direct 90 % of the light into a Mach-Zehnder-Modulator used as a single side band generator (SSB) (see section 2.2.1). Only 10% of the light are directed towards the VCOF, of which 10 % are fed back into the laser diode to maintain the feedback lock.

Recently, we have moved to design a new cavity housing with integrated electronics.

In such way, we hope to achieve an optimal temperature stabilization of all optical parts and thus increase the robustness of the system. We have found that temperature stability of the EOM is crucial for reliable operation of the described setup.

Chapter 2

TECHNICAL REALIZATION

The same has been found for the fibered diodes, since temperature changes may cause phase changes in the fibers. Vibrations induced by wind in the laboratory is another concern, that is addressed by an integrated system. Furthermore, we have found the need to reduce the length of cables in order to reduce electric noise caused by insufficient shielding or ground loops. Therefore, we have designed a new electronic assembly, shown in figure 2.2 . The new assembly integrates five home-made laser driver stacks and fiber holders in order to securely fix all fibers. A new butterfly diode mount has been designed for the laser drivers, to reduce the need for cables in the setup. The laser drivers are used to control four laser diodes. The system is powered externally by either a power supply, or a battery pack for low noise operation. The laser stacks are controlled by four FTDI chips. Dissipators have been mounted in the system for the several transistors and operational amplifiers controlling laser-diode temperature and current. The new mount has been fitted with a home-made passive dissipation system. This dissipator is a composite system with a polished surface for tight contacting with the laser diodes and mounts for a set of standard dissipators to increase the dissipation capabilities. The new housing is shown in figure 2.3. It is built out of 5 mm thick aluminum plates and features two compartments. The lower compartment will hold the VCOF, while the electronics will be mounted in the upper compartment. A fibered connection between the two compartments is inside the box. The system can be stabilized with resistive rubber heating bands, using the temperature stabilization system described below. It features a series of analog I/O pins, a SPI bus, an I2C bus and several independent serial busses, making it a good choice for interacting with low-level electronics. The motherboard serves two major tasks: Firstly, it is handling the communication with the temperature probes (connected to the eight 6-pin MicroMatch © connectors in the center of the PCB). Secondly, it is interfacing the driving electronics for the resistive rubber heating bands (10-pin MicroMatch © connector, bottom left of the PCB). Additionally, it offers access to three additional serial busses and the I2C bus of the micro controller.

The control of the heating bands requires a 0-5 V control voltage. This control voltage is generated by a DAC8568. The PID board acts on temperatures retrieved from homemade temperature boards, consisting of a PT1000 resistance temperature detectors (RTD) in a Wheatstone-bridge, coupled to a 24-bit ADC with a maximum acquisition rate of 16 Hz. The system is interfaced by an SPI bus. In order to switch between the 8 independent temperature boards, two MC13051 multiplexers switch the SPI clock and "master in slave out" (MISO) signals between the respective probes. This pattern mandates to read the temperature boards in series rather than in parallel. For practical reasons, we limit the acquisition rate to 10 Hz in our setup.

A proportional-integral-derivative (PID) controller is used to apply the temperature

V c = K p × e(t) + K I t 0 e(τ ) + K D × de(t) (2.1)
with e(t) being the error signal and K P , K I , K D being the proportional, integral and derivative coefficients, respectively. The micro-controller features eight fully independent PID lines. One of the main benefits of a micro-controller based system is its principal independence from computer control. It allows to free valuable resources and guarantees a continuous operation in case of acquisition system shutdown, since the micro-controller would continue operation. In a high-inertia system such as VCOF or the ring down cell, this is a highly appreciated characteristic. However, a PID controller needs adjustment to operate in optimal conditions. We have therefore implemented a system to interface with the Arduino. The Arduino Due features a USB port, allowing easy connectivity with the lab computer. We constantly poll the serial communication on the micro-controller side. A simple switch-case allows to call 18 different functions listed in table 2.1. If no serial communication is detected, the PID board by default sends the recorded temperatures and the control voltage of line 1 to the host computer. On the host computer side, a homemade LabVIEW virtual instrument allows plotting of the current temperatures as well as interfacing all switch-case options.

Temperature stabilization is a crucial part of high-precision isotopic ratio determination. We therefore have to consider potential biases. In the following, we will elicit dominant sources of bias of this PID controller.

The three principal components of the temperature boards (Wheatstone-bridge, analog-to-digital-converter and voltage reference) give rise to temperature dependent errors. To evaluate exactly how the acquisition may be biased, we will have a look at the way data are retrieved. The resistance of a PT1000 element is proportional to temperature. Using a few PT1000 specific constants, the temperature can be retrieved as follows

T = -r 0 × a + r 2 0 × a 2 -4 × r 0 -r T 2 × r 0 × b (2.2)
where r 0 is the PT1000 nominative resistance, and a and b are PT1000 dependent constants. In our case those are a = 3.390802 x 10 -3 and b = -5.7750 x 10 -7 . The Wheatstone-Bridge allows to calculate the PT1000 's actual resistance r T as

r T = -R × (R W S + R C ) × dV + V × R C (R W S + R C ) × dV -V × R W S (2.3)
with R WS and R C being resistances in the Wheatstone-bridge and the centering resistance respectively. V is the reference Voltage and dV is the measured bridgevoltage.

From this it becomes obvious, that all three main components allow for a potential bias of the retrieved temperature. We therefore investigated how the temperature sensitivity of the electronics may bias the temperature acquisition. The dependencies in the system are given in table 2.2. A simulation of all the error sources reveals a potential T-bias of 119.3 ppm/°K. The bridge resistances account for the by far biggest potential bias. An error of 94.9 ppm/°K can be accounted to them. The second biggest impact is caused by the ADC offset drift, resulting in 25.61 ppm/°K. The ADC gain is as well associated with an error, albeit a negligible one.

We have used the system to stabilize our ring-down cavity. Figure 2.6 shows the temperature evolution over time in the stabilization system of the ring-down cavity.

Temperatures are recorded by four different probes throughout the system. The "PT1000 Regulation" probe and the "PT1000 CRDS 2" probe are mounted in two bores deep inside the cavity bulk, one in the right third and one in the left third of the cavity. The "PT1000 MKS Baraton" probe and the "Thermistor SuperCool" probe are mounted in the center of the isolating housing directly onto the MKS Baraton626b capacitive gauge under a protective layer of neoprene.

The system is regulated on the readings of a single probe, "PT1000 Regulation". As one can see, the system is reaching it's set point within the first hour. Computing an Allan Variance of the regulation probe temperature data reveals an instantaneous precision of 1 mK. However, a look at the second probe in the cavity bulk reveals an oscillation of about 15 mK peak to peak, following the trace of the two probes mounted on the gauge, thus following the overall isolation box temperature. The regulation probe is mounted very close to the cavity bulk, and should thus be exhibiting the temperature excursions recorded by the probe "PT1000 CRDS 2". Referring to the potential temperature bias that we remarked before, this error should be no bigger than 1.5 ppm.

The system drives an operational amplifier circuit using an OPA548T with a fixed gain of 20, delivering up to 52 Watts. Using an operational amplifier in a highvoltage, high-current setup comes with the major drawback of significant heating.

Our amplification circuit therefore has to be actively cooled by a dissipator with a fan. A way to work around this issue would consist in using pulse-width-modulation (PWM). PWM is generating an analog voltage by rapidly switching between a onand off-state, changing the length the signal is in on state, hence modulating the pulse-width determines the voltage output. This is commonly referred to as the duty cycle, given the percentage of the time that the signal is in on-state. A PWM signal with a 10-V max amplitude and a duty cycle of 50% would therefore yield Excess heat like in the present system could therefore be avoided. Additionally, extensive care must be taken towards the effects the PWM frequency may have on the measurement system.

Absolute Frequencies using a Femto Second Laser Comb

The VCOF used in the current setup shows a typical drift of 30 Hz/s and long-term oscillations with a peak-to-peak excursion of about 6 MHz, mainly due to the composite character of the cavity, involving low-expansion glass and INVAR flanges for the mirror mounts. To overcome the limitations imposed by this frequency instability, our VCOF is referenced to a GPS-referenced optical frequency comb (OFC) [START_REF] Jack | An optical frequency comb tied to GPS for laser frequency/wavelength calibration[END_REF][START_REF] Burkart | Absorption line metrology by optical feedback frequency-stabilized cavity ring-down spectroscopy[END_REF]. Optical frequency combs have become a widespread tool in absorption line metrology, offering precise and absolute frequency determination. An optical frequency comb is, at the base, a laser pulse circulating in a resonant cavity with a length L. Whenever the laser is hitting one of the cavity mirrors, a small pulse is emitted. The spacing of those pulses in the time domain is given as

T = 2L/v g , (2.4)
where v g is the mean group velocity of the cavity, that is the velocity of the pulse envelope. In the frequency domain, this relation expresses itself as

f t = n × f rep (2.5)
Where f t is the frequency of the respective tooth, and f rep is the expression of the pulse spacing in the frequency domain. However, the carrier wave travels with its Chapter 2 2.2. TECHNICAL REALIZATION phase velocity, which causes a shift of the carrier with respect to the pulse envelope with a phase angle ∆φ. In the frequency domain, this effect results in a fixed carrier envelope offset f CEO . Equation 2.5 thus simply rewrites as

f t = n × f rep + f CEO . (2.6)
One can consider an optical frequency comb as a ruler in frequency space, with the uncertainty being limited by the uncertainty on the base frequency. In our case, we have referenced f rep of the comb-laser to a multiple of a GPS disciplined rubidium oscillator (GPSDO) [START_REF] Jack | An optical frequency comb tied to GPS for laser frequency/wavelength calibration[END_REF][START_REF] Burkart | Absorption line metrology by optical feedback frequency-stabilized cavity ring-down spectroscopy[END_REF]. In this system, the output frequency of a highlystable rubidium oscillator is controlled by a servo-loop to match the frequency of GPS-signals. The basic idea behind a system like this is to correct the aging effect of a typical rubidium oscillator (1x 10 -10 /year [START_REF] Michael | The use of GPS disciplined oscillators as primary frequency standards for calibration and metrology laboratories[END_REF]) and typical drifts by steering the output frequency based on GPS timing. The short-term stability thus depends on the quality of the rubidium oscillator, while the long-term accuracy depends on the GPS signal, allowing for frequency stabilities by far outperforming stand-alone rubidium systems (stability of up to 5 x 10 -14 vs 5 x 10 -12 at one day [START_REF] Michael | The use of GPS disciplined oscillators as primary frequency standards for calibration and metrology laboratories[END_REF]). The optical frequency comb used in this setup (Menlo FC1500) has a repetition rate locked at f rep = 250 MHz. The carrier envelope offset is frequency stabilized to 20 MHz. 5% of the available laser light out of the VCOF is combined with the light from the optical frequency comb, dispersed by a 600 g/mm grating. A fast balanced detection photo detector measures the combined beam, the Fast-Fourier-Transform of this signal provides us with the detuning of the VCOF frequency to a given tooth of the comb, f bn . A Fizeau type wavelength meter (HighFinesse WS-UIR) with a precision of 10 MHz allows for determination of the respective comb tooth. The absolute frequency f absolute of the VCOF can then be determined as

f absolute = round( f wm + f CEO f rep ) × f rep -f CEO + f bn + f AOM (2.7)
Where f wm is the VCOF frequency as given by the wavelength meter, f bn is the beat note frequency and f AOM is the modulation frequency of the acousto-optic modulator between reference cell and ring-down cell to efficiently and abruptly switch off laser power. To account for the VCOF being referenced to the next or the previous comb teeth, the sign of f bn is not fixed. If the rounding of the first term yields a frequency higher than the unrounded frequency, the beat note sign is negative.

To improve the quality of the beat note signal, we employed a balanced detection scheme [START_REF] Glenn | Balanced detection technique to measure small changes in transmission[END_REF]. Light coming from VCOF and the comb light are mixed together in a 50/50 polarization maintaining fiber coupler. Each branch is optically phase shifted by ± 90°, i.e. 180°from each other. Since the optical phase of the 188 THz radiation is too fast for direct observation, only average carrier (laser and comb teeth) powers are captured by the photodiodes. Therefore the carriers optical power is identical for both branches, hence in the balanced detection scheme they cancel out. In contrast, the beatnote between the tooth and the laser falls in the RF domain (1-125 MHz), which is well captured by fast photodiodes. The total phase difference between the two branches being 180°, the subtraction of both signals (which is equivalent to an additional 180°phase shift of the branches) leads to cancellation of the phase difference. Therefore, it results in a 2-fold amplified beat note signal. The beatnote directly denotes the reference cavity frequency drift. The magnitude of this is shown in figure 2.7. In this figure we determine the line center of an absorption line by measuring its lamb dip (see section 3.2). Since this saturated In blue, apparent lamb dip position retrieved without frequency correction. In green, the same data set corrected using self-referenced optical frequency comb. The standard deviation on the line center determination is 15.2 kHz absorption feature provides us with a fixed frequency, assuming stable pressure and temperature, we can use it to confirm frequency shifts of VCOF. The blue line shows the apparent center frequency of the recorded lamb dips. An oscillation with a peakto-peak amplitude of about 6 MHz over a time scale of several days is obvious. On the short term, a maximal drift of 30 Hz/s can be observed. We corrected the same data set using the absolute frequency determination described above. The green line shows the resulting lamb dip center positions, exhibiting no measurable drift over the measured time-scale, proving the ability of the instrument to provide us with absolute transition frequency determination. There are several important aspects in this alternative frequency referencing: (1) absolute frequency determination of molecular transitions is possible (2) VCOF may act as a secondary optical frequency standard that has, in the present state, to be regularly calibrated by, for instance, a lamb dip measurement (3) VCOF is drifting at a measurable level during a single typical spectrum scan, calling for improvements on the reference cavity design. The latter point is of importance for geoscientific applications, since the precision attained with one single spectrum is not sufficient for geoscientific applications, we pursue, as discussed before, a strategy of spectral averaging. The acquisition of one spectrum takes about 47 seconds. With a drift of 30 Hz/s, this accumulates to a frequency drift of 1.4 kHz during one spectral acquisition, an effect clearly visible when fitting with fixed line positions. Freeing the line positions has proven to include measurement noise significantly. Lacking a third generation VCOF (see section 2.2) with a significantly lower drift, frequency correction is a mandatory step for isotopic ratio determination. Additionally, a possible influence on line profile definition if the laser drifts too much during successive passes cannot be excluded. Chapter 2 2.2. TECHNICAL REALIZATION Figure 2.8: VCOF 2 and VCOF 3 measurement precision over averaging time. The deviation at about 2 seconds is caused by the rubidium oscillator in our GPSDO. Reference data from [START_REF] Miles | Stability and Noise Performance of Various Rubidium Standards[END_REF] for the GPSDO performance.

We conducted a second series of measurements to further constrain the frequency stability of the system. As just described we have referenced our cell to GPS using an OFC. Additionally, we referenced a third generation VCOF (VCOF3) to the OFC. We will describe the characteristics of this cell in more detail in the next section, however we will already discuss its performances. Figure 2.8 shows an Allan Variance Plot (using an overlapping Allan-Variance) of the beating signals of both VCOFs. The difference in initial precision is due to the recording speed, which has been set to 2000 samples/second (S/s) for our VCOF (VCOF2) and 500 and 100 S/s for VCOF 3. It would have been identical for the same measurement speed as it is set by the comb tooth noise, as discussed later on. The averaging of both beat-notes assumes white-noise behaviour up to about 200 milliseconds. Then, a pronounced "bump" in becomes visible in both traces. This noise excess is due to the short term noise of the master rubidium clock which drives the comb electronics. This default of the rubidium-oscillator in our GPSDO, has been reported in the literature before [START_REF] Miles | Stability and Noise Performance of Various Rubidium Standards[END_REF]. Afterwards, the averaging again assumes white-noise behavior. For VCOF2, the point where the instrumental drift begins to dominate is at a precision of 600 Hz, after 20 seconds. This corresponds to a drift of 17 Hz/s, which is in the range of drifting rates observed from lamb-dip measurements as described in the previous section. For VCOF3, we show two data sets with different sampling rates. One data set with high sampling rate, which consequently is able to resolve the rubidium oscillator default and one with a lower sampling rate, which does not clearly show this default. The data with low sampling rate set reveals the drift of the new VCOF as about 2 Hz/s, with the final reached precision being on the order of 300 Hz. Let us reiterate that a precision of 1 kHz corresponds a relative accuracy of 5 x 10 -12 . The limitation in the current beat-note detection clearly is noise related to the OFC, which causes an artificially bad initial precision, well above the intrinsic VCOF noise. We therefore optically locked one of the comb tooth to the slowly drifting VCOF3 2.2. TECHNICAL REALIZATION while preserving the f CEO lock at 20 MHz. This allows for much narrower teeth of the comb and consequently a much more precise determination of the beatnote frequency. Using this setup, we could determine the relative beat note of VCOF2. Figure 2.9 shows the results from this experiment. Notably, a six-fold improvement on the precision at 0.02 seconds can be observed. Afterwards, a almost perfect white-noise behaviour allows averaging of the signal down to 80 Hz, or relative 4.3 x 10 -12 . The origin of the VCOF linewidth is to be searched in the mechanical design of the reference cavity, since theory predicts a Hz-level linewidth [START_REF] Laurent | Frequency noise analysis of optically self-locked diode lasers[END_REF]. The 1 kHz linewidth has to be compared to the optical frequency of ~188 THz and may thus be the result of small cavity length changes. The relation below allows us to deduce those length fluctuations must be below 1 pm

dν ν = - dL L (2.8)
Several factors can modify the length of an optical resonator. The most important ones are temperature and pressure fluctuations, acoustic noise or other vibration sources and electronic noise.

Let us shortly recapitulate the potential sources of the observed drifts. The vacuum of our VCOF is maintained by a ionic pump. The typical operating pressure is 1 x 10 -8 mbar, with fluctuations of the same level. Those fluctuations will modify the refractive index inside the cell. A pressure fluctuation by 1 mbar caused by air will result in a frequency shift on the order of 100 Mhz [116]. Thus, typical pressure fluctuations in the cell can contribute to frequency changes of about 1 Hz. Secondly, the vacuum reduces thermal convection, hence, it increases the temperature stability of the resonator. Temperature fluctuations are related to the thermal properties of the resonator materials. For this purpose, as described before, a ULE spacer has been chosen for the resonator. ULE has a thermal expansion coefficient of 10 -8 /K between 5 and 35°C [START_REF] Shaffer | Effect of thermal cycling on dimensional stability of Zerodur and ULE[END_REF]. Additionally, the whole system has been passively stabilized, to minimize the effects of temperature oscillations in the lab. However, since the oscillations in figure 2.7 are completely correlated with temperature, we can deduce this as the first sources of our instability. On the short term (<1s) the acoustic or mechanical noises of the laboratory are partly transmitted to VCOF causing vertical and horizontal acceleration, causing length changes of the spacer. Our setup has been mounted on an actively vibration damped table and as previously described, we spend attention to best practices to reduce the impact of vibration induced length changes. Tests have been carried out with a "quiet laboratory" in which all pumps and the air-conditioning are turned off and a "normal laboratory", where everything is turned on, in a situation where the OFC is locked to VCOF3. We could notice a strong improvement in the quiet situation. Most probably a maximum of the vibration sensitivity can be attributed to the composite cavity rather than the optically contacted one. However, more measurements are required to confirm this hypothesis. The observed drift in a situation where the OFC is locked to VCOF3, carries components of both VCOFs. This drift is on the order of 7 Hz/s. For the reasons discussed before and in the light of the composite character of VCOF2, we expect the dominant source of the observed drift to come from VCOF2. The comparably low drift rate of 7 Hz/s compared to the maximum temperature induced drift rate of VCOF2 (30 Hz/s) is within the range of fluctuations explainable by temperature changes in Chapter 2

2.2. TECHNICAL REALIZATION Figure 2.9: Beatnote between the two VCOFs over the OFC.

the lab, meaning that we may be on a turning point of the temperature oscillation.

In the light of these findings the afore mentioned VCOF3 has been designed, the following section will give a closer insight into the design of this superior cavity. prior to this thesis and was to be set up in the first months of the project. This new, third generation VCOF is based on an 18-cm Zerodur spacer with a slightly angled roof and ultra-polished end facets. The mirrors of this cavity have been optically contacted. Optical contact bonding is a glue-less bonding process [START_REF] Eschler | Siemens Forsch.-u[END_REF] between two perfectly plane surfaces, that occurs if the distance between the two is less than some tens of Angstroms [START_REF] Dennis | Design and fabrication of acoustooptic devices[END_REF]. This process results in a quasi monolithic cavity setup where the bonding force can be as strong as the substrate itself. The thermal expansion coefficient of Zerodur is specified to be less than 7 x 10 -9 /K. To further reduce potential thermal effects, the system has as well been shielded with a massive copper shield and is hold in place by MACOR rods, to minimize thermal conduction. It is mounted in a stainless steel vacuum enclosure and has been, as the predecessor, fitted with a ionic pump and is now operating at pressure around 1 x 10 -8 mbar. The box has been placed in a copper box, stabilized by another Arduino based system similar to the one described before. The copper box itself is protected by a wooden housing to ensure maximal temperature stability.

Frequency Tuning Using a Mach-Zehnder-Modulator

One drawback of the VCOF scheme is that the laser will be locked to one discrete mode of the VCOF. While it is possible to scan from mode to mode by changing The final setup is mounted inside a standard rack and includes a power supply that is switchable between mains and battery operation, for low noise measurements. Figure 2.12 shows the whole setup. In the upper panel the front face can be seen. In the lower panel, we show the interior of the box, including the power supply (right side) and the MZM control board, the MZM, the hybdrid coupler and a fiber optic isolator. On the software side of the setup, a LabVIEW VI allows to independently control the three electrodes. The optimal parameters for each side band can be stored and later used for easy switching between side bands, allowing a MZM scan over 40 GHz with a gap of 2 GHz in the 2.2. TECHNICAL REALIZATION center. The gap is caused by the limitations imposed by the hybrid coupler and the synthesizer. The CRDS cavity was built with the stability criteria for achieving a tight Pound-Drever-Hall lock, meaning that its length needs to be controlled on a fraction of the cavities mode width δν. At our target frequency of 1.6 µm and with a cavity finesse better than 450,000 this corresponds to a length displacement δL of :

Cavity Ring Down Setup

δL = - 1 F × λ 2 (2.9)
Amounting to less than 1.8 pm. Thus, the cavity design must aim to minimize potential effects of thermal expansion as well as mechanical vibrations. Our choice is based on previous experiences by Burkart et al. [START_REF] Burkart | Optical feedback frequency stabilized cavity ring down spectroscopy -HiHigh coherent near-infrared laser sources and metrological applications in molecular absorption spectroscopy[END_REF]. A massive, monolithic cavity design with the front mirror tightly contacted to a polished metal surface and the back mirror mounted on a piezo electric tube actuator (PZT) assembly, as well tightly contacted to a polished metal surface, has been chosen for the experiment. For ease of machining and handling, we have chosen the aluminum alloy 7075 as the base for our cavity design. This alloy provides a sufficient rigidity as well as a high thermal conductivity necessary for suitable thermal stabilization of the bulk cavity. The cavity is a hollow cylinder of 77-mm diameter and 490 mm length with an 8-mm inner drilling. Three VCR threads have been machined into the cavity body. Two of them are placed close to the flanges of the cavity and serve as gas in-and outlets. One has been placed in the middle of the cavity, and is used to connect a Baraton MKS626 capacitive gauge. On one side of the cavity, a mirror mount is machined directly into the cavity bulk. The mirror is tightly contacted to the polished metal surface and sealed by a Viton fluoroelastomer o-ring. It is tightened by a precision-machined steel-mirror holder fixed by four M3 screws. A cross-cut of the cavity can bee seen in Figure 2.13. On the other side, the mirror is mounted on a PZT assembly (see Figure 2

Locking Mechanism

The ring down cavity is weakly locked to the laser frequency. The ability of adjusting the cavity length to match the laser frequency allows continuous scanning over a spectral region and is thus of great importance for high-resolution, high-precision spectroscopy.

The cavity scans are achieved by means of one of the cavity mirrors mounted on a piezo electric tube actuator (PZT). The cavity length displacement δL is proportional to the voltage change applied to the PZT δV. The stability in maintaining a given voltage on the PZT defines the quality of injection in the cavity. During this thesis, two different locking schemes were used. The first scheme we used was based on a Pound-Drever-Hall (PDH) lock of the cavity [START_REF] Rwp Drever | Laser phase and frequency stabilization using an optical resonator[END_REF]21]. The PZT was driven by the potential difference between the output of a computer-driven, homemade high-voltage board and a homemade analog PID controller operated in low voltage mode. The effective voltage range we used in this setup was -120 V to 0 V. In this scheme, the computer would set a high-voltage setpoint by supplying an analog voltage between 0 and 5 V to the homemade high-voltage board. For 2.2. TECHNICAL REALIZATION this purpose we used a NI-6281 I/O, with an output resolution 20 bit and an RMS noise level of about 7 µV. The plus pole of the experiment was then used to acquire the actual lock of the cavity, by means of a PDH lock using the MZM to generate 400 kHz RF sidebands and a fiber-optic circulator. For a closer discussion of the technique, we refer the reader to reference [START_REF] Burkart | Absorption line metrology by optical feedback frequency-stabilized cavity ring-down spectroscopy[END_REF]. A fiber-optic circulator was used to capture the back-reflection of the cavities front mirror and direct it towards a fibred photodiode. This signal was then filtered by a 350-450 kHz band-pass filter, subsequently amplified and then demodulated by mixing it together with a local oscillator sine wave supplied from our RF-Synthesizer. The retrieved PDH signal was directly fed into the analog PID controller. This way an unbroken chain of stability transfer from VCOF to the CRDS is guaranteed. While this locking mechanism yielded high repetition rates (200 RD/s) and constantly high transmission rates, optical fringes associated with the fiber optic circulator forced us to change the technique. The second technique in this thesis uses a PDu150 (Piezodrive) ultra-low noise high-voltage amplifier with a constant gain of 20 to drive the PZT. We have also developed low noise electronics for this purpose, however, those electronics proved to be not resistant to repeated failures of our battery system and have thus been exchanged with the aforementioned commercial system. The high voltage amplifier is controlled by a homemade analog PID controller, which supplies 0-5 V voltage ramps if no passage through resonance is detected.

To allow for a high repetition rate we developed dedicated electronics to weakly lock the cavity to the laser frequency. The scheme consists in applying a constant, 100 Hz, symmetric modulation with an amplitude of 60 mV on the PZT, amounting to about 0.075 % of the cavity FSR. Simple electronics consisting of an operational amplifier comparator, a sample-and-hold amplifier (SAH), and a monostable multivibrator are used to maintain the cavity lock after the PID ramp has detected a passage through resonance. The SAH on the locking board constantly monitors the symmetric modulation applied to the PZT, see figure 2.15 for an illustration. The comparator constantly compares the photodiode signal to a locking-threshold set by a NI-6218 I/O card. If a signal passes the threshold, the SAH is triggered by the monostable multivibrator and passes the current modulation voltage as an error signal to the analog PID board. The PID board then centers this voltage around 0 V, thus maintaining a stable lock. We have noticed subsequently, that we can significantly decrease the re-lock times by increasing the modulation voltage during resonance search to 400 mV. We could show, that as soon as the lock is acquired we can regulate the modulation voltage down to 30 mV or 0.0375% of the cavity FSR without losing the lock. This allows for a better cavity injection and thus higher transmission rates. The regulation of the modulation voltage is handled automatically by our acquisi-2.2. TECHNICAL REALIZATION tion software, using as well a NI-6281 I/O card. This technique guarantees high transmission rates and a repetition rate of 200 RD/s, while showing an astonishing robustness to temperature or pressure drifts of the cavity. We acknowledge, that it would be possible to generate this modulation as well by means of an operational amplifier differentiator, a monolithic waveform generator (e.g., EXAR XR-2206) or direct digital synthesis (DDS) in order to make the system fully independent from the lab computer. One may also consider employing a microcontroller to handle the lock acquisition and modulation voltage regulation.

Vacuum System

VCOF-CRDS is a highly sensitive measurement technique, able to detect lowest gas concentrations. It is therefore mandatory to ensure an optimal pressure regulation to not limit the performance. As mentioned earlier, the ring-down cavity is equipped with three Swagelok VCR ports. Three VCR-to-6mm-tubing adapters have been fitted directly into the cavity bulk without a gasket by deforming the aluminum. Swagelok VCR has an ensured maximum leak rate of 4 x 10 -9 std. cm 3 /s if used with silver-plated or copper gaskets and up to 4 x 10 -11 std. cm 3 /s for unplated gaskets. In our case silver-plated Nickel gaskets are used. The connection between the cavity VCR ports and the inlet system is realized using Swagelok UltraTorr connectors, rated with a maximum leak rate of 4 x 10 -9 std. cm 3 /s as well. Towards the pumping system, KF flanges are used. In the sample gas line we currently use standard Swagelok connectors to connect to the CO 2 tank, which are rated to a maximum leak rate of less than 2.8 x 10 -3 std. cm 3 /s, clearly being the weak point in the current system. The inlet system consists of several pressure-actuated, diaphragm sealed 2-valve, 3-port monoblocks (Swagelok 6LVV-P1D222P-AA), as shown in figure 2. 16. The pressure actuacted valves are controlled by a homemade system. Using an FTDI chip to interface with the lab computer and a series of 2N2222 NPN bipolar junction transistors, we control a series of ASCO DC-solenoid valves to switch compressed air towards the respective pressure-actuated valve. The system is set in a normal off setting, such that it isolates the cell in case of a power outage.

TECHNICAL REALIZATION

Two different inlet system layouts have been used during this thesis. The first system (figure 2.16, left side) consists of four valve-blocks. On the inlet side, a valve allows switching between a line controlled by an electro valve, and a main line for efficient pumping. On the top left, a second valve block allows switching between either the pumping line or the sample line. On the right side, a valve block allows to switch the cavity either to a capillary, for low pumping rates, or to a main line for high pumping rates. A second valve-block allows switching between the pump line or a flow regulated line. All valve blocks can be used in a configuration that is open on both lines, for efficient pumping. While this first setup serves all necessary tasks, there is a dead space between electro valve and one of the valve blocks that we cannot control, and that frequently had caused problems when not sufficiently pumped.

Therefore we decided to use a simplified scheme for easier operation (Figure 2.16, Figure 2.17: Pressure evolution in the CRDS cavity after isolation. Note the discrete leakage events every 9 hours. We determined a leakage/outgassing rate of 1.01 x 10 -7 mbar×l×s -1 . The gauges zero has been set to 0.08 mbar.

right side). This system consists of only two valve blocks and one electro valve. On the inlet side, a block allows to switch between the pumping side and the sample, while the electro valve is mounted in line towards the measurement cell. On the other side, a valve block allows switching between a capillary towards the pumping side, for restricted pumping rates, or directly to the pumping side, for strong pumping. This setup allows us, as does the first, to rigorously pump the sample line, as well as the cell. It allows switching between different pumping rates using a capillary. And, with the electro-valve being mounted directly in front of the cavity, it minimizes the risks associated with an uncontrolled dead space between electro valve and one of the valve block valves. Pressure regulation is realized by opening the cell to the pumping side, either through a capillary or the main pumping line and regulating the inflow of analyte gas by Chapter 2

2.2. TECHNICAL REALIZATION means of an electro-valve, with a maximum opening diameter of 0.1 mm. It is important to ensure that no effusion effects take place to prevent the associated fractionation. To reach an effusive state two conditions must be met. (1) the mean free path

λ = RT √ 2πd 2 N A P (2.10)
(where T is the temperature, N A is Avogadro's number, R is the universal gas constant, d is the particle diameter and P is the pressure), must be greater than the opening hole diameter, so that the molecules act independently while passing through the pinhole and (2) the inlet pressure must be much greater than the outlet pressure, so that back flow can be excluded. The mean free path for pure CO 2 at 29.405°Celsius and 1 mbar is on the order of 1.89 x 10 -4 mm, thus being roughly three orders of magnitude smaller than the hole at maximum opening. The sensitivity of electro valve is given as 0.1% of the full span, resulting in an minimum opening of 1 x 10 -4 mm. Thus, for very low pressures and very low flow measurements effusion may occur. A study of the valve opening as a function of voltage should be carried out in the near future.

The electro-valve is regulated by home-made amplification electronics, driven by a NI-6281 card and controlled by a dedicated LabVIEW VI using a PID algorithm.

The typical stability reached by this stabilization system is on the order of 10 ppm. Figure 2.17 shows the pressure evolution of the cavity used in this thesis after shutting of the pumping side, and closing the electro valve on the inlet side. The cavity exhibits a combined outgassing/leakage rate of 3.43 x 10 -6 mbar/s. There are discrete leakage events of 5 x 10 -3 mbar of unknown origin to be observed with a stable periodicity of 9 hours. The effective cavity volume is the sum of the volume of the cavity, the piping and the PZT V eff = V cavity + V pipe + V PZT sums to approximately

V ef f = 24.9cm 3 + 4.2cm 3 + 0.3cm 3 = 28.8 cm 3 .

(2.11)

Taking the pressure increase Ṗ given above, the combined outgassing/leak rate R amounts to

R = V ef f × Ṗ = 1.01 × 10 -7 mbar × l s (2.12)
Thus, being about 25 times higher than the maximal leak rate associated VCR or UltraTorr connections. However, since we have used an uncoated cell, this may very well be related to outgassing effects.

We have evaluated spectra acquired during a period of 48 hours, where we isolated the cell and observed the outgassing behavior. We could identify CO 2 , H 2 O, CH 4 and C 2 H 2 . During this time interval, we evidenced a total increase in pressure of 0.55 mbar. Of this we could attribute .5% to C 2 H 2 , .9% to CH 4 . CO 2 accounts for 2.7%, while water is by far the biggest contribution, amounting for 27%. Therefore, we can only attribute 30% of the total pressure increase that was observed, forcing us to resort to flow measurements for the time being. As for the periodic leaks, they contribute a total volume of

V periodic = Ṗperiodic × V ef f = 1.47 × 10 -4 l. (2.13)
Considering the PZT assembly, we mounted a mirror with a radius of 12 mm in a mirror mount with a inner radius of 6.4 mm, amounting to a dead volume of 0.1 2.3. VCOF-CRDS cm 3 . The mirror is tightly contacted to a polished steel surface towards the cavity. This space may potentially be at atmospheric pressure, therefore it could supply N = 1013.25 mbar × Ṗperiodic /V cav /V P ZT = 689.29 (2.14) leakage events, or more than 250 days of periodic leaking. Another possible explanation for the leakage would be the permeability of Viton to carbon dioxide. Sturm found the permeation coefficient for CO 2 through Helium to be in the order of 5.8-6

x 10 -15 / m 2 s -1 mbar -1 [START_REF] Sturm | Permeation of atmospheric gases through polymer O-rings used in flasks for air sampling[END_REF] ,too low to explain leakages of the observed magnitude.

In any case, periodic leakage events are hardly explained by the permeability to gases. It should be noted though, that the literature describes several more suitable materials that exhibit lower CO 2 permeability, such as polytetrafluoroethylene, polychlorotrifluoroethylene [START_REF] Sturm | Permeation of atmospheric gases through polymer O-rings used in flasks for air sampling[END_REF] or polysulfide [START_REF] Seals | Parker o-ring handbook (ORD 5700)[END_REF]. A change of materials may thus result in better performance. Another factor to consider is the O-Ring compression. Currently, our O-rings are compressed by 30 % and are not lubricated.

It has been shown that a compression rate of 50 % is necessary to achieve lowest permeability without lubrication [START_REF] Seals | Parker o-ring handbook (ORD 5700)[END_REF].

A new, coated cavity has been thoroughly leak-tested using a helium leak detector.

The helium flow rate is found to be smaller than 8 x 10 -10 mbar × l × s -1 .

VCOF-CRDS

The main difference to previous work by Burkart, Romanini, and Kassi is the partly broken stability transfer chain from VCOF to the ring-down cavity, and the suboptimal coupling of the laser into the cavity. Therefore, the setup presented here should not be called "Optical feedback frequency stabilized cavity ring-down spectroscopy", but rather VCOF-CRDS. In the following, we will describe the workflows of the system, we will discuss the experimental performance, error sources and the fitting procedures employed for isotopic ratio measurements and spectroscopic studies.

Software and Workflow

The current setup is a highly decentralized system with only very few controls to be handled by the operator himself. The VCOF lock is, as described earlier, maintained by means of a lock-in-amplifier and a homemade analog PID controller, thus fully autonomous. The locking of the CRDS, as described earlier, is maintained automatically by dedicated analog electronics, and just requires a transmission threshold to be defined by the user.

In the following, we will describe the workflows of the current system and have a deeper look into the different software to be used in day-to-day operation, all of which are LabVIEW virtual instruments (VI).

The core of the current setup is the "Ring-down-Server". Here, all acquisition parameters can be adjusted, including the fitting parameters for ring-down fitting. It allows adjustment of the locking threshold for the CRDS. This VI automatically adjusts the modulation voltage applied to the CRDS PZT for optimal locking, ensuring always the smallest possible modulation. Furthermore, it allows to manually control the synthesizer. The adjustment of the MZM is as well accessible in the RD server.

After adjustment of the MZM, the optimal parameters can be stored. House-keeping data from the experiment , such as pressure readings, the laser frequency, temperature readings, MZM-photodiode readings, VCOF-Transmission readings and beatnote readings (see section 2.2) are supplied by dedicated acquisition servers. The pressure regulation is handled by a dedicated system (see section 2.2.2). The temperature control of the ring-down cavity is as well handled by another VI (see section 2.2).

The acquisition of spectra is handled by a dedicated acquisition VI (see figure 2.19). This VI controls the experiment fully automatically in several different acquisition modes.

The first acquisition mode that has been used during this thesis acquires simple spectra with an evenly spaced grid of spectral points. This method requires the user to define a frequency range, the grid spacing or resolution, and the number of ring downs to be averaged at baseline absorption. The method then generates a grid that allows for an interlaced measurement. This form of measurement generates a grid of spectra points separated by one cavity FSR, then shifts that grid by the defined measurement resolution and so on, based on the chosen resolution, a certain number of cavity sweeps is required to construct a full spectrum, as shown in figure 2.20. This scheme allows maximum acquisition speed, since frequency jumping the laser from cavity mode to cavity mode does not require re-locking of the cavity. An important task shared by all acquisition modes is the dynamic adjustment of the number of ring-downs to be averaged. If an equal number of ring-downs would be averaged for all spectral points, the points on absorption lines would exhibit a noise excess compared to those on the baseline, because a shorter ring-down time results in a diminished signal-to-noise ratio. The software therefore considers the user specified number of ring-downs as a base and adjusts it according to the detected absorption following the equation

N opt = N 0 (τ 0 /τ act ) 3 (2.15)
Where N opt is the adjusted number of ring-downs to be averaged, τ 0 is the ringdown time of the empty cavity and τ act is the current ring-down time. The quality of the ring-downs is tightly controlled based on statistics on the measurement series, so that bad ring-down events are immediately rejected and are not considered for averaging. The rejection is solely based on the ring-down fit residual RMS, mostly caused by electronic noise or polarization mismatching. It has been observed, that after disbalancing of the MZM the system may lock to the wrong sideband thus generating "good" ringdowns, that are however to be rejected. Typically, those events can be identified by a biased ring-down time or a very poor repetition rate.

In the first case they are caught by a spike-filtering algorithm, in the second case the re-locking mechanism initiates re-locking.

VCOF-CRDS

The second adjustment common to all acquisition mode is the adjustment of the RFpower applied to the Mach-Zehner-modulator. To compensate increased losses at higher frequencies, the RF power needs to be ramped as a function of frequency. This ensures that the transmission rate of the cavity stays constant during a measurement, thus allowing one constant cut-off voltage for all measurement frequencies. The second measurement mode is adapted for saturation absorption spectroscopy and consists in determining line centers and thereafter recording their center with an increased resolution. This mode, at the base, shares the same basic functions as the previous one, generating an interlaced grid over a certain spectral region and adjusting the amount of ring-downs and the RF power. This method is used to measure single absorption peaks, which it fits after the first spectrum is acquired.

It then determines the center frequency and adds a second, high-resolution grid around the peak-center (dν around 50 kHz) to reveal saturation effects (see chapter 3.2) on the peak top. It then moves to fit those saturation effects to determine the center accordingly. Note, that the high-resolution grid cannot be used in an interlacing manner, since it typically has a width of about 3 MHz, that is a 100th of a FSR. However, due to the close spacing of spectral points the cavity lock is typically able to "follow" the laser frequency. This method also supports the use of line lists for consecutive, automated acquisition of different absorption lines. The line list is supplied in .txt format. In this case, the VI takes control over laser-current and laser temperature and adjusts it to move the VCOF to a suitable frequency for measurement. It aims to move VCOF to a mode about 4 GHz from the line to be measured, to be able to measure in the optimal frequency range of the MZM. The third measurement mode has been developed very recently and makes use of our ability to place spectral points arbitrarily. The software will again generate a grid for interlaced measurement and acquire one first spectrum. Subsequently, it detects absorption lines in the spectrum based on a user defined threshold. It then generates a second, high-resolution grid (dν in the order of a few MHz) on each peak top. This allows for an excellent constraining of absorption line shapes and is the method currently used for isotopic ratio determination. Summarizing, the current acquisition scheme exhibits a high degree of automatization as it is, and usually requires very few input of the operator. It has proven to be a reliable measurement protocol for time periods reaching up to months of continuous measurement. However, one main limitation must be acknowledged. The current system is not yet able to handle the pressure regulation of the cell in a fully automated manner. Once the cavity is filled, the PID regulation on the electro valve has proven to be highly reliable but unfortunately the filling of the cavity in an automated way has not yet been proven to be safe. This would be an important -and necessary -improvement do be done for future high-throughput analysis of environmental samples, requiring repetitive filling and pumping of the measurement cell. If the measurement pressure is always identical, this task is easy to solve by storing suitable PID parameters and define a safe filling speed for the cavity in terms of e.g. a voltage applied to the proportional electric valve, with all physical parameters of the pumping system identical, this should ensure safe operation. It should however be noted, that all critical processes should, if possible, be out-sourced from the laboratory computer and be defaulted to a safe state if the laboratory computer fails. This has already been achieved for the temperature regulation by means of an autonomous micro-controller and should certainly be considered for the pressure regulation. To determine the minimum detectable absorption level we evacuated our ring down cell. We recorded about 2232 spectra within less than ten hours, with an average acquisition time of 16 s per 2.5 MHz spectrum. Figure 2.21 shows the results for narrow scans like this, typically used for the acquisition of lamb dips. The single-shot minimum absorption detectivity is about 2 x 10 -12 cm -1 . Averaging was carried out for a growing number of spectra. We then removed a linear slope from the spectra to account for the mirror baseline. The standard-deviation of the remaining baseline noise then represents a detection limit α min of our spectrometer. Figure 2.21 shows the evolution of the baseline noise as a function of averaged spectra. After less than 10 hours of averaging, a record baseline noise of 3.8 x 10 -14 is reported. To our best knowledge this is the lowest absorption detection limit ever reported. It is important to notice, that the averaging exhibits white-noise behavior until we stopped the experiment, implying a even lower absorption detection limit being possible.

Error sources 2.5.1 Time Base Error

CRDS is fundamentally built on measuring the time that light leaks out of an optical resonator. Therefore we need to consider errors associated to an inaccurate time base. Introducing a time based error into cavity ring-down measurements means generating a pseudo-second. Since the absorption coefficient is defined as relative intensity loss per unit of length, this would, via the definition of the meter in terms of speed of light, ultimately cause an alteration of the absorption coefficient. The Chapter 2 Figure 2.22: Baseline for one acquisition and for 2232 averaged baselines after removal of linear background. A single scan exhibits a noise of 2 x 10 -12 cm -1 . After less than 10 hours of averaging, a record baseline noise of 3.8 x 10 -14 cm -1 is reported. effect of a time bias γ on the retrieved absorption coefficient can be expressed as

α = 1 1 + γ α (2.16)
In our experiment we are using a National Instruments PCI-6281 acquisition card with a specified internal accuracy of the timebase of 5 x 10 -5 . For signal-to-noise ratios exceeding 5 x 10 5 the time base accuracy thus becomes the limiting factor. In order to ensure traceable unbiased measurements, it is therefore obligatory to reference the time-base to the SI-second, which in our lab could be realized by a GPS-disciplinied rubidium timebase. Non-linearities in a CRDS system can arise from several sources. On the technical side, there may be non-linearities associated with the photodiode, the amplification circuit or the analog-to-digital (ADC) conversion. Seperating those error sources from another is a highly complex task. One of the most obvious sources of non-linearities on the technical side is the digitization of the photodiode signal. A system that includes ADC conversion can generate non-linearities in the conversion process. The non-linearity associated with an ADC is typically given as the 2.5. ERROR SOURCES icant trends can be observed with the choice of measurement parameters, consistent with the observations shown in figure 2.24 [START_REF] Wójtewicz | Line-shape study of self-broadened O 2 transitions measured by Pound-Drever-Hall-locked frequency-stabilized cavity ring-down spectroscopy[END_REF]. Figure 2.25 shows the fit residuals for ring downs recorded by our instrument. The blue trace shows the fit residuals for one single ring down event. Note the quantization effects towards the left side. The red trace shows the residuals for 10000 averaged ring downs. The fine chaotic structures, clearly visible on the red trace, are most likely linked to non-linearities during digitization, well within the specifications of our acquisition card. One way to improve the performance of ADCs is the use of differential detection systems, rejecting common-mode noise and interference as well as allowing for balanced signal detection. ADC driver circuitery is widely available today offering bandwidths up into the GHz region. Those circuits allow preconditioning of the signal to ensure optimal conditions for acquisition. Note, that some of the possible non-linearities may carry physical information, such as intensity dependent losses, associated with saturated absorption, as shown in section 3.2. Temperature dependent variations of the losses in the highly reflective dielectric mirror coatings may cause non-linearities due to the exponential decrease of dissipated power in the coating during ring down events, however, this has not yet been experimentally observed.

Non-Linearities

Bandwidth

Any system that aims at transferring a measurement of amplitude into the time domain may be limited by the systems bandwidth. Burkart provided a concise analysis of the effect of bandwidth limitations in CRDS systems [START_REF] Burkart | Optical feedback frequency stabilized cavity ring down spectroscopy -HiHigh coherent near-infrared laser sources and metrological applications in molecular absorption spectroscopy[END_REF]. His findings show, that a certain amount of RD points at the beginning of a ring down event have to be rejected. In a dection system with a low pass filter having an angular cut-off frequency ω c ω c = 2πν c (2.17)

and ω c 1/RD time, the minimal waiting time can be calculated as follows:

t w ≈ - lnp 2πν c (2.18)
where p is the target accuracy. This shows, that as long as ω c τ 1 the minimal waiting time is nearly independent of τ . The analog bandwidth of the National Instruments PCI-6281 card used for ring-down acquisition amounts to 750 kHz, however, we typically use a 40 kHz filter. According to equation 2.18 this leads to a minimal waiting time of 40 µs between ring down triggering and exponential fitting, if the accuracy goal is 1 x 10 -6 . If the filter is not used, a minimal waiting time of 3 µs is required. This means for the two measurements, in our case of 240 µs ring downs, a ring down threshold of 88 % and 98% has to be implemented.

Frequeny Bias By dither-lock

As discussed before, VCOF-CRDS is using a dither-lock scheme to achieve passages through resonance. In this scheme, the cavity length is adjusted in order to match the laser frequency. A symmetric 100 Hz triangle modulation with an amplitude of 60 mV is applied on the PZT, amounting to an FSR modulation δν of 223 kHz. where the sign is dependent on the sign of the modulation. Averaging an even amount of ring-downs should average out any Doppler-effect. However, missing one ring down event would create a random bias. Since we typically average about 50 ring-down events per spectral point this effect should play no role down to the sub-kHz level.

Imperfect Signal Extinction

One fundamental underlying assumption in CRDS is an instant interruption of laser light upon ring-down triggering, implying an infinitely fast switch-off time and a infinitely high extinction ratio after switching. Since those two requirements cannot be fulfilled in experimental setups, a residual cavity mode injection exists after switching and interferes with the resonant cavity field, hence biasing the ring-down decay signal.

A theoretical analysis of this has been provided by Huang and Lehmann [START_REF] Huang | Noise caused by a finite extinction ratio of the light modulator in CW cavity ring-down spectroscopy[END_REF]. In their analysis the authors consider the case of a noisy laser with a line-width much wider than the cavity mode width. For this case the authors deduce the single shot RMS noise σ k in the cavity decay rate k = τ 1 as a function of the inverse power extinction ratio r during ring-down triggering. For ring down fitting with equal weights they find:

( σ k k ) 2 = 64 27
I 0 I thresh r (2.20)
In the case of shot-noise limited ring-down acquisition a weighted least-square fit of the decay signal is necessary, changing the relation to

( σ k k ) 2 = 4 I 0 I thresh r (2.21)
Contrary to the analyzed case, VCOF-CRDS utilized a laser source with a line-width smaller than the cavity mode width injecting the cavity by scanning its length by a fraction of its FSR. Therefore, the injection is significantly less noisy. Let us note, that a single-shot ring-down noise of about 1 x 10 -12 cm -1 would require an extinction rate of almost 100 dB in the framework of a noisy laser scenario proposed by Huang and Lehmann.

Transverse Modes

High-finesse optical cavities exhibit a complex transverse mode structure [START_REF] Fabre | Ultrahigh-finesse optical cavities[END_REF]. Diffusive scattering on the mirror surfaces may couple light into higher order transverse modes, resulting in a sharp increase in the ring-down noise. [START_REF] Huang | Noise in cavity ring-down spectroscopy caused by transverse mode coupling[END_REF] gave an exhaustive account of those effects.

ν lmn = c 2n 0 L × (l + m + n + 1 π × arccosg) (2.22)
where n 0 is the refractive index of the intra-cavity medium, l is the longitudinal mode number, L is the length of the cavity and the cavity stability criterium g given as

-1 < g = (1 - L r ) < 1 (2.23)
2.5. ERROR SOURCES with r being the mirror radius of curvature. Coincidences of a longitudinal mode with the mode number l can thus occur when the second term in equation 2.22 is an integer j:

m + n = j × π arccosg (2.24)
The required precision for such coincidence is given by the laser line width, the Figure 2.26: Ring-down acquisition by Huang and Lehmann, carrying a heterodyne beat note between a TEM 00 and a higher order TEM mn mode.

width of the cavity modes and thus the cavity finesse. It should be noted though, that the cavity finesse is much lower for higher order modes than for the TEM 00 mode due to increased losses, effectively facilitating the occurence of coincidences. A manifestation of such a coincidence can be observed in Figure 2.26, where the beating between two modes alters the ring-down signal, which is not a pure exponential anymore. The ring-down signal can be fitted by a fit based on a mode-beating function, assuming a dominant light field originating from an excited TEM 00 mode and a small contribution from higher-order transverse modes,

y(t) = A + B 1 exp(-k 1 t) + B 2 exp(-k 2 t) + 2 B 1 B 2 exp( -k 1 t 2 )cos(2π∆vt + ∆Φ)
(2.25) where B 1 and B 2 are the initial amplitudes of the two modes, k 1 and k 2 their respective power decay rates, ∆v the difference in frequency of the two modes and ∆Φ the difference in the initial phase [START_REF] Huang | Noise in cavity ring-down spectroscopy caused by transverse mode coupling[END_REF]. In the current setup, we tried to circumnavigate the problem by setting the ratio g/π to 0.93, by choosing a cavity length of 49.5 cm and mirrors with radii of curvature of 100 cm. This setup reduces coincidences to very high order modes and thus effectively prevents higher order transverse modes to affect the spectra. Chapter 2

Polarization Mode Mismatch

CRDS is fundamentally based on the use of of highly reflective mirrors. Such mirrors exhibit dichroism, the loss rate thus changes as the polarization stated evolves, resulting in a deviation from a normal exponential decay signal during ring-down measurements [START_REF] Huang | Effects of linear birefringence and polarization-dependent loss of supermirrors in cavity ring-down spectroscopy[END_REF]. They also exhibit birefringence (e.g. [START_REF] Jacob | Supermirror phase anisotropy measurement[END_REF]) causing a turn of the lights polarization at each reflection. Huang and Lehmann noted that a drifting polarization state of the incident light may thus cause a base line drift by affecting the ring-down decay signal. This effect typically expresses itself as an oscillation in the ring-down fit residuals. However, these issues can be avoided by tightly controlling the polarization of the incident light before injection into the cavity. In our case this is realized by a half-wave plate. This way, we ensure excitation of only one of the two polarization eigenmodes of the cavity, thus masking a potential drifting of the incident lights polarization state.

Interference Fringes

Interference fringes are one of the most commonly encountered limitations in cavity ring down spectroscopy. They origin from parasitic reflections of optical components and express themselves as a low finesse etalon. In fact, the parasitic fringe forms a virtual new cavity between an optical component and one of the cavity mirrors, which therefore has a periodicity analogous to the one for the resonant modes of the cavity itself:

∆ν

F ringe = c/(2D) (2.26)
where D is the distance between the cavity and the origin of the parasitic reflection. Thus, taking an absorption spectrum and computing a Fast-Fourier-Transform (FFT) allows to characterize the distance to the reflection source D

D = c ∆ν F ringe (2.27)
In the current system, interference fringes mostly arise from optical components behind the measurement cell, notably a focusing lens and the detection photodiode front surface. We address the induced problems by a "fringe-scrambling" scheme as explained in reference [START_REF] Burkart | Absorption line metrology by optical feedback frequency-stabilized cavity ring-down spectroscopy[END_REF]. In this scheme, the steering mirror on the back-face of our ring-down cavity has been mounted on a piezo electric actuator. Applying a triangle modulation on the PZT effectively changes the phase of the optical fringe, which leads to a sign change in the fringe associated bias of the ring down time if the PZT displacement is sufficiently big, allowing for unbiased averaging.

Sample Refractive Index

The refractive index of a medium alters the phase velocity of light traveling through a medium. By doing so, the lifetime of photons inside the cavity is prolonged. This is confirmed by the explicit dependence in the computation of the ring-down time

τ = ( 1 τ 0 + αc n ) -1 = ( (1 -R)c nL + αc n ) -1 (2.28)
where c is the speed of light, α is the absorption coefficient, and R is the mirror reflectivity. Thus neglecting the change in refractive index between the empty cavity 2.5. ERROR SOURCES and a cavity filled with analyte gas, can introduce a bias. However, the amplitude of this bias strongly depends on the way in which acquired spectra are treated. Commonly, n is considered to be 1, and any deviations from this are neglected. Let us explore how this could bias the quantification of molecular absorption. In most cases, we determine τ 0 by fitting a baseline in an absorption spectrum rather than taking it from empty cavity measurements. The previous equation then simplifies to

τ -1 = τ -1 0 + αc n = t -1 0 + αc (2.29)
where α is a biased absorption coefficient. Defining an altered sample refractive index as ñ = 1 + (2.30)

yields δα α = - (2.31)
The systematic error in this case is thus 1 -n. If the baseline is determined from empty cavity measurements, for instance for the determination of the continuum absorption, the biased absorption coefficient is computed as

τ -1 = (1 -R)c nL + αc n = (1 -R)c L + αc (2.32)
In this case, the absorption error can be computed as

δα = - 1 cτ (2.33)
and amounts to the total fraction of the intra-cavity losses per length [START_REF] Burkart | Optical feedback frequency stabilized cavity ring down spectroscopy -HiHigh coherent near-infrared laser sources and metrological applications in molecular absorption spectroscopy[END_REF].

Background Absorption Spectrum

One major source of bias in spectroscopy does in fact not arise from technical imitations, but expresses itself in a seemingly chaotic baseline structure. This is due to background absorption by other molecular species, most notably water but also probably organic molecules with a diffuse absorption pattern. Figure 2.27 shows three spectra recorded in our main region of measurement. The spectra have been recorded in our first, uncoated cavity and characterize a continuous outgassing process over two days. In this period, the pressure inside the cavity rose from 0 to 0.55 mbar. The two most dominant absorption lines can be attributed to CO 2 (6284.81905 cm 2 ) and HDO (6285.1079 cm -1 ). The remaining absorptions are most probably a mix of CH 4 and organics absorption lines. The pressure increase may in fact have several origins. Desorption from the cell walls, outgassing of o-rings and micro-leaks are certainly the most prominent ones. Quantifying those processes is a difficult task, since desorption rates may change as a function of cell temperature and prior pumping. The same is true for the outgassing rates of o-rings. It is imperative to consider the background structure in metrological applications, since it may affect line-profiles in many ways, effectively biasing the physical value of retrieved parameters. Several strategies exist, one of which consists in determining the background composition, and subsequently monitor strong absorption lines in order to scale accordingly. This is a convenient way to assess the impact of water desorption from cell-walls. An other option consists in empirically determining the Chapter 2 background structure and subtract it from measured spectra. However, this method is prone to create biases as soon as either the background composition changes, or the outgassing rates vary. An efficient solution to diminish the impact of background absorption are flow measurements, flushing out unwanted species. However, especially for environmental samples or highly concentrated gases, sample sizes are often small and thus flow measurements are not realistic. An optimized vacuum system and surface-treatment of the measurement cell is therefore the best choice to tackle background interferences.

Fitting and Data Treatment

The fitting of absorption line surfaces is done using the Minuit library [START_REF] James | MINUIT, Function Minimization and Error Analysis[END_REF]. Minuit is a numerical function minimization program originally written in FORTRAN by Fred James at CERN in the 1970's. The code has later been ported to C++. The line profiles have been implemented by Serge Beguier in our group. Typically, a dynamic link library (DLL) is used with LabVIEW code to generate a user interface for fitting. In our case this interface handles the computation of absolute frequencies, allows manipulation of fit parameters and deals with several data conversions to optimize the efficiency of the fit routine. The starting parameters are retrieved from the Hitran [23] database and are prepared by a dedicated script to be used by the fitting software. In our main region of analysis, between 6285.01 cm -1 and 6285. three main lines, all lines are fitted with Voigt-Profiles, using the complex probability function (CPF) routine proposed by Humlìček [START_REF] Humlìček | An efficient method for evaluation of the complex probability function: the Voigt function and its derivatives[END_REF]. This choice fulfills the needs for lines with low S/N and allows for fast line profile calculation. The three main lines are fitted with a qSDNGP Profile, again using the CPF subroutine. To receive the most accurate line surfaces, it is obligatory to use advanced fit models to capture subtle effects, affecting the broadening of an absorption line (see also section 3.1). We have confirmed in several tests that the precision, however, is not affected by using a insufficient line-model, an option to be considered if processing time needs to be limited. In any case, the mentioned cross correlations between different collisional and speed dependent parameters necessitate the use of a multi-fit approach in order to determine physical meaningful values for those parameters. In a multi-fit approach, spectra at several pressures are fitted simultaneously in order to retrieve the pressure dependence of each parameter. Knowing the pressure dependence of every fit parameter is a requirement for static measurements, since small pressure drifts mandate adjustments in a controlled manner in order to not hamper accurate line surface retrieval. Parameters determined from a multi-fit would also significantly improve the accuracy of the fit. The current fitting procedure consists in fitting a high-resolution calibration spectrum and subsequently fixing all parameters except the peak amplitude of the three main peaks. The other peaks are adjusted in relation to those three driving peaks. We conducted several tests, where we measured a spectrum and shifted the grid of measurement points between two consecutive spectra. We could not evidence any impact on our measurement results associated to this. For isotopic ratio measurements, except spectra fitting, all data treatment is done by a dedicated Python script. The script conservatively filters out outliers, then computes the temperature gradient exhibited by the cell, smooths this trace for temperature correction of the retrieved spectra (see section 2.7). It then computes all required isotopologue ratios and does the temperature correction based on the T-dependence of the line intensity as retrieved from Hitran. Finally, several correlation matrices are computed. We look at a Pearson correlation (see figure 2.28), a measure of linear relationship and a Spearman's rank correlation coefficient which benchmarks the monotonic relationship. Finally, we compute the difference between the two correlation matrices as an indicator of correlations that are monotonic but not linear. Figure 2.28 shows that the partial pressure of 627 is anti-correlated to the cell temperature gradient, while the partial pressures of 628 and 626 are correlated with the cell gradient. Those findings are backed by line intensity temperature dependencies retrieved from HITRAN2012 [23]. Additionally, the strong temperature dependence of the 626 absorption line, a "hot band", is highlighted. A comparison between the correlation values for ∆ 17 O and the temperature corrected ratio, ∆ 17 O T corr , reveals already that our temperature correction cannot completely correct for temperature induced effects. Most likely, this is due to temperature ef-Chapter 2 2.6. FITTING AND DATA TREATMENT Figure 2.28: Pearson correlation matrix as routinely computed in post-fitting datatreatment. The data set used here is the one used in [22]. Correlated elements are the three partial pressures (627, 626 and 628), the raw and temperature corrected ∆ 17 O, the temperature gradient of the cell, the cell pressure, the temperature of the pressure gauge and the integral value of the PID governing the pressure-regulation electro valve.

2.6. FITTING AND DATA TREATMENT fects on the MKS Baraton capacitive gauge, as indicated by the correlation between the partial pressures and MKSTemp, which is a reading of a probe placed on the gauge. Finally, PressPID I is the integral value on the PID controlling the electrovalve which regulates the pressure in the cell. Monitoring this value allows to assess gas-density fluctuations, also it For a long time, 17 O anomalies have been considered a somewhat exotic circumstance restricted to extraterrestrial materials, such as meteorites (e.g. [START_REF] Robert | Oxygen isotopes in eucrites, shergottites, nakhlites, and chassignites[END_REF][START_REF] Robert N Clayton | A classification of meteorites based on oxygen isotopes[END_REF]), arising from special processes in outer space. This was mostly due to the assumption that the ratio between 17 O/ 16 O and 18 O/ 16 O is completely governed by mass-dependent fractionation and thus does not carry any further information of interest. Terrestrial non-mass-dependent fractionation has therefore not been in the focus of active research for a long time. Gradually, more and more non-mass dependent signatures have been observed on earth. In the 1980's mass independent fractionation was observed for stratospheric ozone [START_REF] Mauersberger | Measurement of heavy ozone in the stratosphere[END_REF][START_REF] Mauersberger | Ozone isotope measurements in the stratosphere[END_REF]. Later, mass-independent fractionation has been observed for stratospheric oxygen [START_REF] Mark | The mass-independent fractionation of oxygen: A novel isotope effect and its possible cosmochemical implications[END_REF] and finally for stratospheric CO 2 [START_REF] Mh Thiemens | Oxygen isotope fractionation in stratospheric CO2[END_REF]. Subsequently, Luz and Barkan (2000) discovered a difference in the relationship between δ 17 O and δ 18 O for processes governed by equilibrium fractionation compared to evaporation regimes [START_REF] Luz | Assessment of oceanic productivity with the triple-isotope composition of dissolved oxygen[END_REF]. 17 O anomalies were consequently proposed as a unique tracer for evaporation processes [START_REF] Angert | Kinetic 17 O effects in the hydrologic cycle: Indirect evidence and implications[END_REF]. 17 O anomalies in CO 2 are disparately more difficult to measure. The most commonly used measurement method for such analysis is IRMS. However, due to a isobaric interference of 627 and the much more abundant 636 isotopologue, IRMS is not able to perform direct measurements. Several techniques to circumnavigate this problem have been proposed, all of them relying on transferring the information of interest to other molecules, which in turn could be measured by IRMS. The publication below [22], result of the current work, offers a new solution to this problem, allowing direct measurements on CO 2 . The article starts by giving a comprehensive summary of the current understanding of ∆ 17 O anomalies. Subsequently, the current analytical state of the art for IRMS based measurements as well as spectroscopic measurements is recapitulated. This letter features a description of the full optical experiment, albeit deliberately omitting the use of a highly fibered VCOF cavity. The measurement parameters and processes are described and the current data processing including a necessary correction for an observed temperature bias are explained. Finally, the current performance is discussed. This letter is, to our best knowledge, the first documentation of a laser based system for the analysis of non-conventional isotopologue abundance ratio measurements, which yields a precision level comparable with state-of-the-art IRMS technology, with a 20-fold reduction in measurement time. N on-mass-dependent stable isotopic anomalies are devia- tions from an assumed mass-dependent fractionation law (e.g., Young et al. 1 ). 17 O anomalies can be observed in a variety of environments, associated with different processes. Commonly, 17 O anomalies are expressed in the Δ 17 O notation. In this study, we use a logarithmic expression, 1,18,19 where λ R denotes the slope of a reference line R:

δ λ δ Δ = + - × + O ln( O 1) ln( O 1) 17 17 R 18
Several values for λ R have been reported, each adapted for or coming from different environmental systems. In this study, we have chosen a value of 0.528. δ 17 O and δ 18 O are referenced to arbitrary fixed values for now, as we solely intend to prove the instrumental precision of our prototype. Δ 17 O of CO 2 has been proposed to be used as a proxy for terrestrial gross carbon fluxes 2,3 or marker for deep stratospheric intrusions. 4,17 O anomaly in water bodies are an established tracer for evaporation processes, 5,6 which has been used extensively in geoscientific studies. The 17 O-anomaly of carbonate rocks, in turn, reflects the anomaly of the respective parent water, thus constituting a valuable tracer for paleo-hydrologic processes. High-resolution terrestrial archives such as speleothems or limnic carbonates therefore could give extensive insight into past moisture sources and/or atmospheric convection regimes.

The determination of Δ 17 O in CO 2 requires precise measurements of three isotopologues: 16 O 12 C 16 O, 16 O 12 C 18 O, and 16 O 12 C 17 O. Typically, the required precision levels call for the use of state of the art isotopic ratio mass spectrometry (IRMS) techniques. However, because of isobaric interferences of 16 O 13 C 16 O (1.1%) and 16 O 12 C 17 O (0.076%), 17 O measurements in CO 2 have so far remained highly challenging. Several methods have been developed in previous years, mainly based on IRMS methods following oxygen exchanges through fluorination, 7 exchange with solid (cerium or copper) oxide, 8-10 CO 2 -water equilibration. 3,11 An analytical challenge is also to be able to measure this anomaly in small stratospheric samples (e.g., Mrozek et al. 12 ). The best precision reported until now is 10, 30, and 5 ppm for δ 17 O, δ 18 O, and Δ 17 O of CO 2 11 , respectively (1000 ppm = 1 ‰). Those methods come at a significant cost of time and resources.

Spectroscopic methods offer an appealing alternative in this field, since they probe absorption frequencies unambiguously associated with the internal distribution of mass rather than the total mass of an isotopologue, so they are unaffected by isobaric interferences. The precise spectroscopic determination of isotopologue ratios, however, requires an accurate and precise determination of absorption line shapes.

Only few approaches toward high precision measurements of δ 17 O in CO 2 have been made. 13,14 The highest precision reported to date is 590 ppm, by Long et al. in 2011. 14 Note that a spectrometer with infinite signal-to-noise on the y axis would finally be limited by the conversion of laser frequency noise to amplitude noise as it probes absorption line wings. Our work builds on previous work by Burkart et al., 15 which offers exceptional laser frequency stability by using a new kind of laser source obtained by optical feedback locking of a distributed feedback laser (DFB) to an ultrastable V-shaped optical cavity. We describe several improvements to the original setup and report on the performance levels of a prototype with a relative frequency-stability better than 2 × 10 -12 and an absorption detection limit of 5 × 10 -13 cm -1 , allowing for high-precision determination of isotopic ratios.

■ EXPERIMENTAL SETUP

The experimental setup comprises of a very narrow and stable V-shaped optical feedback source (VCOF) 15 lasing in the nearinfrared around 1.6 μm, which provides a sub-kHz laser line width with a typical drift of 30 Hz/s. Locking of a distributed feedback diode laser to the cavity is realized by a mirror mounted on a piezo-electric actuator (PZT1), which is controlled by a lock-in-amplifier regulating on the transmission signal of VCOF. 80% of the emitted light is collimated (L1) in an optical fiber. To allow continuous frequency tuning over a 19 GHz range, a fibered multiple Mach-Zehnder modulator (MZM, Photline MXIQ-LN40), used as an optical Single-Sideband generator (SSB), 15 is modulated by a radio frequency. This solution allows arbitrary distribution of spectral points on the frequency axis and therefore focusing on regions of importance for line shape definition, to increase measurement precision. The frequency shifted light is amplified by a boost optical amplifier (BOA) and can be interrupted by an acoustooptic-modulator (AOM). Finally, a second collimator (L2) allows free-space coupling to a high-sensitivity, high-stability cavity ring down spectrometer (CRDS) setup. The CRDS cavity is made of a massive aluminum rod (70 mm outer diameter, 8 mm inner diameter, 490 mm length) fitted with two high reflectivity mirrors (Layertec GmbH). The optical resonator exhibits a finesse of 450 000 with an FSR of 297 MHz. The rear mirror is mounted on a piezo-electric tube actuator (PZT, Physikinstrumente P-016.10H) to allow for length dithering of the cavity. The alignment of the cavity is realized by acting on 8-push-and 8 pull-screws. Two external mirrors mounted on piezo-electric-actuators (PZT2, PZT3) allow to average out effects of spurious reflections on optics elements. The reader will find a detailed description of the technique in Burkart et al. 23 The whole CRDS setup is mounted in a temperature stabilized enclosure, and the cavity itself is further stabilized at a level of a few mK. The cavity temperature is recorded by two PT1000 elements embedded in the aluminum body.

CRDS Stability. A major difference to the setup proposed by Burkart et al. 16 is the simplification of the optical resonatoroptical source locking scheme, by abandoning a complex Pound-Drever-Hall locked system and switch for a simpler weak-locked system, satisfactory for isotopic ratio measurements. It results in a more robust and faster system at the price of a negligibly imperfect optical phase transfer resulting in higher demands in system stability. Active temperature stabilization of the CRDS cavity is realized by a homemade, stand-alone, PID system based on an Arduino Due microcontroller. The PID receives temperature readings from one of the PT1000 probes embedded in the aluminum body, close to the analyte gas, and acts on a resistive heating band (OMEGA SRFG-XXX/10-P). To minimize environmental influence, the whole CRDS-setup is mounted inside an insulating wooden enclosure. This limits temperature gradients in the gas cell to less than 10 mK. Pressure stabilization for flow measurements is done by a (Burkert 2/2) proportional valve, acting on readings from a (MKS Baratron 626B, 100 Torr) capacitive gauge. Control of the electro valve is done by homemade control electronics working with a LabVIEW VI. Using this system, we reach a precision of the pressure regulation of 0.2 μbar.

Comb Referencing. The VCOF used in the current setup shows a typical drift of 30 Hz/s and long-term oscillations with a peak-to-peak excursion of about 6 MHz, mainly due to the composite character of the cavity, involving low-expansion glass and INVAR flanges for the mirror mounts. To overcome the limitations imposed by this frequency instability, our VCOF is referenced to a GPS-referenced femtosecond comb 20,21 with a repetition rate of 250 MHz. In total, 5 % of the available laser light are used to set up a beat-note with the comb. A fast Fourier transform of the beat note signal provides us with the distance in frequency space between our laser source and the closest comb tooth. A Fizeau type wavemeter (HighFinesse WS-UIR) with a precision of 10 MHz allows for determination of the respective comb tooth used for referencing. This referencing of our laser source allows for instantaneous correction of the observed drift. This level of frequency stability allows an optimal retrieval of line surfaces and thus gives the long-term stability needed for spectral averaging.

Locking System. The cavity length is weak-locked to the laser frequency. The lock is reached and maintained by a homemade system comprising of three principal components. A piezo-electric tube actuator (PZT, see Figure 1) is dithering the length of the optical resonator on the pm scale. The PZT is driven by an ultralow noise (PDμ150, PiezoDrive) piezo driver over a range of 100 V. Control is realized by an analog PID board triggered by the photodiode output. A constant, symmetric, 100 Hz triangle modulation with an amplitude of 0.2 V is added on the PZT. The modulation amounts to an effective length dithering of the cavity of about 0.3% of the FSR, allowing the generation of passages through resonance. A signed error signal is derived from the sign and amplitude of the modulation voltage at the moment the passage through resonance occurs.

The error signal is sent to a PID that keeps the modulation centered over extended periods of time. The relocking time of this system is on the order of 2 s. Once locked, the system reaches a typical repetition rate of 200 ring-downs per second.

Acquisition and Spectral Treatment. In order to exclude potential effects of gas exchange or adsorption on the cell walls, measurements are currently performed using a stable flow of pure CO 2 at 20 mbar. The flow rate is 0.6 mL/min which corresponds to 25 μmol/min. The fully automatic spectral acquisition follows an interlacing scheme to minimize time losses. In this scheme, the cavity is locked to the laser frequency and the MZM is used to jump over multiples of the CRDS FSR subsequently. To increase the resolution this pattern is shifted. This restricts the necessary relocking of the cavity to the laser

Analytical Chemistry

Letter DOI: 10.1021/acs.analchem.7b02853

Anal. Chem. XXXX, XXX, XXX-XXX B frequency to a minimum, when the pattern is shifted, making the amount of relocks a function of the spectral resolution. Additionally, because our setup is able to arbitrarily place spectral points, we constrained the top of absorption peaks by increasing the spectral density. This results in an average acquisition time of 47 s per spectrum, dominated by the fact that adding constraining points on the peak implies a series of additional relocks. Part of the lost time is due to a diminished repetition rate at strong absorptions, which can be optimized by using an adaptive system. The data is then fitted using the Minuit2 (CERN) function minimizing tool to retrieve absorption line surfaces, which gives the base for the described ratio calculations. The line shape of the absorption profile is fitted using a speed-dependent-Nelkin-Ghatak profile (SDNGP 17 ). It has been shown in previous studies, that SDNGP is well suited to account for collisional narrowing and speed dependent collisional broadening effects in the present pressure regime 14 in order to increase the accuracy of ratio determination. The pressure broadening coefficients are provided by the HITRAN2012 database and scaled according the gas pressure. The Doppler width is fixed according molecular mass and cell temperature. The other parameters, proportional to pressure, have been determined experimentally. Only the line amplitude is kept free. Using this procedure, we reach a standard deviation of the fit of 4.2 × 10 -12 cm -1 , see Figure 2. Since the precision of the retrieved line profiles from one single spectrum is not sufficient for the subtle changes that need to be resolved, we average the values from several subsequent spectra.

■ EXPERIMENTAL PERFORMANCE

Figure 3 shows the instrumental precision of our instrument in terms of an Allan-standard deviation plot (using an overlapping Allan-Variance for increased statistical confidence) for a Δ 17 O measurement series.

Figure 3 shows the evolution of the measurement precision over averaging time. The green trace shows the simulation of an ideal, unbiased, and purely statistical behavior. In blue we show untreated Δ 17 O values from a typical measurement series, with the points marking individual spectra. Exhibiting an initial precision of 31.5 ppm, the maximum precision is reached after 16 min with a precision of 10.3 ppm. From there onward the precision oscillates marking an underlying bias which prohibits further averaging of measurement values but also showing a stability at a level significantly below 15 ppm. Figure 4 shows the raw Δ 17 O values and the temperature gradient.

A correlation of the two parameters is observed. A direct correction using the correlation factor between ratio and gradient would, however, not be sufficient, since from a physical point of view the three absorption lines involved exhibit different temperature sensitivities. The retrieved line surfaces are thus affected to a different extend. We therefore implemented a temperature correction of the retrieved line surfaces based on T-dependencies retrieved from the HITRAN 22 database. The orange curve in Figure 3 shows the Allan-Variance of the same data set after temperature correction. An improvement of the data quality is clearly visible, with the instrumental precision reaching 10 ppm after 10 min of measurement time. The Allan SD finally starts oscillating between 5.5 and 9 ppm, which is likely due to very small temperature effects that we do not yet sufficiently account for. Both curves show the rolling mean over 15 samples of the raw data. A clear correlation of both parameters becomes obvious. Note that the gradient is retrieved within two drillings inside the massive aluminum body. While this allows correcting for biases caused by temperature changes in the gas, it will be less suitable for corrections of biases introduced by affected pressure gauges or valves. We developed a new instrument for the direct measurement of Δ 17 O in CO 2 . This instrument is based on optical feedback frequency stabilized cavity ring down spectroscopy near 1.6 μm 16 and incorporates an ultrastable and ultranarrow laser source, coupled with a high stability CRDS setup. We demonstrated an instrumental precision of better than 10 ppm within 10 min of measurement time, requiring 300 μmol of pure CO 2 . The predominant current limitations arise from the temperature sensitivity of absorption lines. However, we identified alternative absorption lines of a comparable signal/ noise ratio with a reduced temperature sensitivity and envision using those together with an improved cell temperature management to limit the need for temperature corrections in routine measurements. To our best knowledge, this is currently the fastest method for such measurements and the way to quick and direct routine measurements of Δ 17 O in CO 2 .

Analytical Chemistry

■ AUTHOR INFORMATION

Corresponding Author *E-mail: samir.kassi@univ-grenoble-alpes.fr.

ORCID

Tim Stoltmann: 0000-0002-3047-128X

Notes

The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

This work was supported by the Agence Nationale de la Recherche (Grant ANR-13-JS060005), Institut National des Sciences de l'Univers (LEFE/CHAT) and Labex OSUG@2020 (Grant ANR10 LABX56

Identification of Suitable Absorption Lines

The identification of suitable absorptions lines is one of the most important aspects in the development of a new spectrometer. Choosing a "bad" line, can drastically impair measurement precision and accuracy. Choosing an optimal absorption line is of even greater importance for isotopic ratio measurements, since the need for spectra averaging increases the demands towards long-term stability of the instrument. Aiming at precision of 10 ppm, even subtle changes in temperature or pressure may deteriorate the results of an experiment. Having an instrument that is stable on the short-term and may be able to generate high-quality spectroscopic data is therefore not necessarily sufficient for isotopic ratio measurements. Modern spec- troscopic databases, such as Hitran2012 [23], allow to simulate absorption spectra under various conditions and investigate to which degree they may be influenced by experimental constraints such as pressure or temperature stability. There are some main factors that determine the quality of an absorption line for isotopic ratio determination:

1. Temperature sensitivity pressure noise is given by each lines pressure related coefficients. However, this assumes complete isolation, without any influence from neighboring absorption lines.

In practice, background absorption by other molecules, in our case mainly water and other CO 2 isotopologues, affects the line of interest. Interfering absorptions in the base of a line will compromise the quality of the line surface determination, since their contribution may be difficult to estimate and varies with pressure. A well isolated line is therefore a direct way of reducing the effects of pressure noise, by minimizing the interaction with other species, for instance in the foot of the absorption line, hence hard to precisely determine. The signal-to-baseline-ratio gives constraints of the required averaging for a precise measurement, thus it is an indicator of the required time for a given target precision. For this project, three isotopologues are of interest: 626, 627 and 628, required for the computation of ∆ 17 O. In the reflectivity region of our setups mirrors from 6060 cm -1 to 6900 cm -1 , Hitran contains 32,800 CO 2 absorption lines, rendering a comprehensive manual analysis impossible. We made use of HAPI, a python-based interface to HITRAN2012, developed by Kochanov et al. in 2016 [24]. HAPI allows to parse HITRAN2012 and simulate absorption spectra and retrieve line parameters. Using the functionalities of HAPI, we wrote a Python-script which analyses all given absorption lines in a region and determines the best possible line for measurements. The script characterizes every line by the three main criteria that we already discussed. The temperature sensitivity is empirically estimated by simulated absorption spectra at two different temperatures and comparing the retrieved peak absorptions. The absorption line isolation qf b is determined as

qf b = α∈St α./ α∈S b α. (2.34)
with S t and S b referring to the sets target isotopologue and background absorption, respectively and where α is the absorption coefficient. The signal-to-noise ratio,

IDENTIFICATION OF SUITABLE ABSORPTION LINES

which equals the signal-to-baseline ratio in regions where the background absorption is stronger than our baseline determination, was determined as shown in equation 2. 35.

qf = max(α ∈ S t ) max(α ∈ S b ) (2.35)
To increase computation efficiency, lines having absorptions weaker than our detection limit were omitted.

The script allows the user to specify a set of parameters, such as pressure, temperature, maximum and minimum absorption (to account for the instruments dynamic range) and the frequency range to investigate. measurements, we investigated 638, a doubly-substituted, so called clumped isotopologue [40]. All simulations are for 20 mbar of pure CO 2 at 29.5 • C. The upper plot in Figure 2.29 shows qf for all investigated isotopologues. It is evident, that the optimal region for 627 measurements is centered at 6285 cm -1 . In this region, a widespread abundance of 628 and 626 lines makes single-diode measurements of ∆ 17 O feasible, meaning that regions exist in which both species can be addressed within the range of one MZM scan. Another interesting point is the abundance of suitable 638 lines around 6730 cm -1 , reaching a comparable quality as the best 627 lines. The lower plot shows qf b . This plot shows globally similar patterns as qf.

It indicates, however, that the line isolation is a restricting factor at 20 mbar, in particular for 638. Two main options for increasing the isolation of an absorption line exist. One consists of decreasing the measurement pressure. As the effects of collisional broadening decrease, the overall line width decreases and consequently the influence of neighboring lines. We therefore analyzed the evolution of the isolation parameter and the temperature sensitivity in a range from 1 to 20 mbar, seen in figure 2.30 at the example of 627. It is evident, that a reduction in pressure Chapter 2

2.8. IDENTIFICATION OF SUITABLE ABSORPTION LINES indeed results in a better isolation of the lines. The result of this analysis has to be considered with respect to experimental constraints: While a reduction in pressure diminishes the influence of neighboring absorption lines, it does as well decrease the signal-to-noise ratio of a given absorption line. Also, the relative noise on the pressure regulation may increase in certain pressure ranges. The benefits and drawbacks therefore have to be carefully evaluated as a function of the absolute pressure noise in the system. The second option to increase isolation consists in changing the measurement temperature. As the effects of thermally induced line broadening decreases, line isolation increases. Therefore, low temperature measurements are an interesting option for increased spectral quality. Figure 2.31 shows the evolution of qf b at the example of 638 in a range from -80 gular momentum quantum number, there are lines which exhibit this phenomenon to a lower extent and may thus be chosen for this purpose. This is true for the best lines in the case of 638. In practice, as mentioned earlier in this chapter, precise temperature control is one of the most challenging tasks in the experimental setup. For this reason, a diminished isolation is to be preferred over a more temperature sensitive line. Table 2.4 shows the best lines identified by the script for our available laser diodes. Note, that the region used for most of the initial measurements (around 6285.20846 cm -1 ) is only considered by the algorithm for the 627 absorption lines. Still, a factor of three is to be gained for 627, compared to our current measurement zone, by using an optimal line. 626, due to its very strong abundance, is very difficult to be treated by the algorithm, mostly due to the extent of absorption line wing and are thus excluded from analysis. Note, that an identification like this only makes sense, if isolated lines can be targeted. Since this was not initially the case, we were forced to use a compromise spectral region for measurements. This is because aiming for a region in which all isotopologues of interest exist in one 19 GHz range adds severe constraints and, in the end, requires compromises on line quality. A second script has been written to propose optimal regions for the analysis of several isotopologues in one single measurement of 0.6 cm -1 . The script applies a qf b threshold that is applied to only look at absorption lines of a certain quality. This way, the script ensures a certain line isolation and strength before considering a region for measurements. Table 2.5 shows three distinct regions that have been identified for multi-isotope analysis.

Having the same isotopologue in several regions allows to estimate potential errors during multi-diode measurement and is thus an option to assess the impact of possible fluctuations between consecutive measurements.

Chapter 3 Applications

D 2 Measurements

Molecular hydrogen and its isotopologues are the simplest of all neutral molecules. With their rotational constant and extremely simple spectrum they are molecules of choice for testing advanced line profiles and testing ab-initio calculations. The rise of high-precision spectroscopic tools in recent years has allowed for very precise measurements of H 2 and its isotopologues, including the very rare D 2 (e.g. [START_REF] Kassi | The absorption spectrum of D2: Ultrasensitive cavity ring down spectroscopy of the (2-0) band near 1.7 µ m and accurate ab initio line list up to 24 000 cm-1[END_REF][START_REF] Mondelain | Sub-MHz accuracy measurement of the S (2) 2-0 transition frequency of D 2 by Comb-Assisted Cavity Ring Down spectroscopy[END_REF], enriched samples). With line-shape models and ab-initio calculations of transition frequencies and strengths getting extremely accurate, accurate experimental determinations of transition frequencies is mandated to validate highly refined simulations. A precise recording of the absorption line-shape is necessary to test line-shape models of growing complexity, a prerequisite to reliable determination of transition strengths and frequencies. Hydrogen and its isotopologues are one of the best candidates for such assessments due to several characteristics: (1) a single, high-energy vibration (since it is a diatomic molecule) (2) a very high rotational constant (since it consists of two light atoms) (3) only three stable isotopologues. All together, it results in a very simple spectrum. However, due to the absence of a dipole moment, the P and R transitions are forbidden. Only Q (∆J=0), O and S (∆J = ±2) transitions are allowed due to the electric quadrupole moment, resulting in very weak transitions. Hence, a particularly sensitive instrument is needed to precisely determine the line shape of those transitions. With our VCOF-CRDS setup, we combine high sensitivity with high frequency accuracy, thus we have an optimal tool to analyze D 2 transitions.

Having acquired a suitable diode, we have conducted a series of measurements on the S(2) transition of D 2 (99.98 % purity) with pressure ranging from 1 to 75 mbar at 302.555 kelvin. The transition frequency at zero pressure has been determined with a precision on the order of 32 kHz, showing a pronounced model dependency.

Line Profile Analysis

Molecular absorption spectroscopy relies on the correct modelling of the line profile. The profile carries information on intramolecular processes such as vibration, rotation and vibrational mode interactions and inter-molecular processes, such as collisions. Therefore, proper modeling can give access to physical parameters, such as, e.g. the temperature either directly from the profile or by looking at relative

3.1. D 2 MEASUREMENTS
intensities of transitions originating from different energy levels. The accurate retrieval of absorption line areas is of crucial importance, e.g. for earth observation missions and the assessment of other planets atmospheres. A good understanding of spectral line shapes is therefore mandated. In section 1.2.3, we introduced several profiles that go far beyond Voigt. Hydrogen is a good option to investigate the validity of such models, due to its simplicity, and, as we will show later, the fact that it's line profile is strongly affected by different processes. and 1 mbar and normalized by amplitude. In the lower panel, the amplitude difference between the amplitude-normalized spectra of 50, 25 and 1 mbar with the amplitude normalized spectra at 75 mbar has been computed. It is clearly visible, that the character of the wings changes significantly (4 %) with increasing pressure. A more detailed investigation of those effects requires fitting of the line shape.

We have thus investigated the line profile of this transition using four different line profiles, (1) the Nelkin-Ghatak Profile (NGP), (2) the Quadratic-Speed-Dependent-Voigt profile (qSDVP), (3) the Quadratic-Speed-Dependent Nelkin-Ghatak profile (qSDNGP) and finally, (4) the HTP-Profile. We have chosen those profiles to cover a broad range of available models, one including only velocity changing events (in addition to Voigt profile) (1), one including only speed dependence (and Voigt) (2) as well as two higher order models (3,4). To reduce possible correlations between parameters, we used a technique close to the multi-fit technique, as first proposed by Benner et al. [START_REF] Benner | A multispectrum nonlinear least squares fitting technique[END_REF]. Our fit is still sequential, however, one set of pressure driven coefficients is fitted for all spectra. We 2) transition of D 2 . The mirror baseline has been subtracted. Clearly visible, an additional slope remains, diminishing towards spectra at higher pressure. Also, a quadratic dependence of the baseline with pressure is obvious. We assume this being a signature of the collision induced absorption band. Note, that the spectra at 25 and 50 mbar carry a distinct signature of an HDO absorption at 6241.244 cm -1 . The contribution diminishes with increasing pressure, as the flow increases. The 1 mbar spectrum was acquired with a fully open pumping line, thus exhibiting significantly higher flow. This was not possible for the other three spectra due to a limited amount of sample. excluded the amplitude and line center, which were fitted independently from pressure. We subtracted the empty cavity baseline from all spectra. It was necessary to still fit an additional baseline with a slope of 2, 4, 5 and 6 x 10 -12 cm -1 /wavenumber. In Figure 3.3, we show a zoom of the foot of the investigated transition at different pressures, clearly showing the baseline slope diminishing with increasing pressure.

Fitting Procedure

The noise level on the 1 mbar spectrum did unfortunately not allow us to fit the line center precisely enough, therefore its position in the fit was imposed by a linear extrapolation from the line center determinations at three other pressures. This does not impair our ability to test the pressure dependence as well as the robustness of our line center determination, since those parameters do still rely on three different pressures. The iteration on all fit parameters but position and amplitude, which were optimized using the Minuit2 routine [START_REF] James | MINUIT, Function Minimization and Error Analysis[END_REF], was realized by an inverse hill-climbing type optimization method, searching for a decrease in overall residual RMS of all fits at different pressures. Iteration over all parameters was repeated 3.1. D 2 MEASUREMENTS until the residual RMS was minimized. Several tests have been performed for each spectrum and resulted in the same outcome. The possibility of converging on a local minimum is therefore unlikely. Ten spectra were fitted for each pressure. One HDO transition at 6241.244 cm -1 and one CO 2 transition at 6241.09 cm -1 present in low flow conditions (at low pressures, except for 1 mbar, where a higher flow could be set) were fitted and subtracted from the data, prior to the fit of the D 2 absorption line. CO 2 has been evaluated to contribute a partial pressure of up to 23 µbar. The HDO partial pressure was evaluated to a maximum of 0.6 µbar, observed for the spectrum at 25 mbar. Let us underline that we recorded an HDO line. If water was present in natural abundance, the fitted line area would translate in an unrealistic overall water concentration of 1.94 mbar, accounting for a water contribution of 7.7%. Such a strong water contribution has never been observed in our system before. Practically, the biggest water contribution ever observed in our system amounts to 5

for very low flow CO 2 measurements at 10 mbar, attributed to outgassing processes. Since the flow rate increases with pressure, thus counteracting the outgassing, we conclude that the water present in the cell arises from outgassing but is highly enriched in HDO, due to exchange with pure D 2 . In that case, assuming 50% exchange between D2 and water, the total water pressure would amount to 1.2 µbar accounting for a water contribution of about 50 ppm. Given that we have pure D 2 exchanging with water this contribution we can expect an almost complete water-D 2 exchange, due to the extremely high collision probability. Thus, the real water contribution could very likely be rather on the order of 25 ppm.

Fit Results

As mentioned before, after removal of the mirror baseline we had to fit an additional baseline, we attribute this to collision induced absorption (CIA) and Rayleigh scattering. Abu-Kharma et al. recorded the CIA spectrum of the 2-0 band of D 2 [START_REF] Abu-Kharma | Collision-induced absorption by D 2 pairs in the first overtone band at 77, 201 and 298 K[END_REF]. CIA was first described by Van Kranendonk and Bird in 1951. He described an absorption resulting from an induced dipole moment due to charge distortion produced by electron exchange in a colliding pair of molecules or a distortion arising from the polarizing effect of the permanent quadrupole moments of the molecules [START_REF] Van Kranendonk And R Byron | Pressure-induced absorption I: The calculation of pressure-induced absorption in pure hydrogen and deuterium[END_REF]. The resulting spectrum is dominated by broad absorption lines and is therefore of a generally diffuse structure [START_REF] Frommhold | Collision-induced absorption in gases[END_REF]. It scales as the square of the gas density [START_REF] Van Kranendonk And R Byron | Pressure-induced absorption I: The calculation of pressure-induced absorption in pure hydrogen and deuterium[END_REF]. In Abu-Kharma et al. one can see from the experimental spectrum (p. 63, figure 3), that the S(2) band of D 2 is positioned in a region where CIA creates a slope opposite to our empty cavity slope. It may therefore explain the diminishing baseline slope with increasing pressure. Unfortunately, the quality of the published data does not allow us to quantitatively correct for it. A fitting of the baseline offset reveals a quadratic trend with a small linear contribution, which we attribute to Rayleigh scattering. Figure 3.2 shows the fit residuals for fits of the same transition at four different pressures using four different models. For 1 mbar the residuals are below the experimental noise level. For higher pressures one can note clearly, that the NGP is not able to correctly capture the line profiles. This profile develops a residual signature with a significant asymmetry, which cannot be accounted for in this kind of symmetric model. On the contrary, the three others, including speeddependence, capture the line-shape significantly better. Nevertheless, the qSDVP results in bigger residuals than the two other profiles for higher pressure. This is re-Chapter 3 lated to the fact that it does not account for Dicke-Narrowing, which is well marked and increases with pressure [START_REF] Rh Dicke | The effect of collisions upon the Doppler width of spectral lines[END_REF]. To test how well the models capture the line profile asymmetry, we have folded the fit residuals at the line center. Figure 3.4 shows those folded residuals for the case of NGP and HTP for an absorption spectrum recorded at 75 mbar. It becomes very clear, that the NGP does not capture the asymmetry of the line shape, while the HTP does. However, an asymmetry is still present, albeit at a level almost in the measurement noise. Summarizing, it should be stated, that the NGP is not capable of capturing the complete physics behind the investigated transition, evidenced by a pronounced, asymmetric residual structure. This was expected, since NGP does not include speed-dependent effects. The qSDVP results in a better fit than NGP, however, at higher pressures a characteristic W-shaped residual structure becomes visible. We attribute this to the absence Dicke-Narrowing, which is not modeled in the qS-DVP. Both, qSDNGP and HTP fit the whole pressure range very well, with the HTP model having a slight advantage. Both models include hard-collision Dicke-Narrowing and Speed-dependence. As mentioned in section 1.2.3, HTP includes an additional correlation parameter η, which has been arbitrarily fixed to 0.5. Even at high pressures, those models generate fit residuals at the level of 3 x 10 -12 cm -1 , very close to our single-spectrum noise level of 10 -12 cm -1 . The retrieved fit-parameters are given in table 3

.1 3.1. D 2 MEASUREMENTS Profile Γ ζ Γ 2 ∆ 2 η NGP
2.4891 x 10 -11 1.8507 x 10 -8 0 0 0 qSDVP 6.9114 x 10 -9 0 1.3273 x 10 -5 8.4722 x 10 -7 0 qSDNGP 4.1766 x 10 -9 1.8752 x 10 -8 7.8572 x 10 -6 8.7950 x 10 -7 0 HTP 0.0000 x 10 -8 1.8752 x 10 -8 0 0 0.5 Table 3.1: Parameters as retrieved for this study. For definitions, we refer to section 1.2.3. For speed-dependent models, Γ means Γ 0

Accurate Determination of Transition Frequencies and Pressure Shift

Furthermore, we analyzed the impact of those line profiles on the retrieval of some key parameters, that is the pressure shift and the calculation of the line intensity.

The upper panel of figure 3. transition frequencies thus all agree quite well, a strong discrepancy becomes evident when examining the determined pressure shifts. The qSDVP and qSDNGP yield results that agree well with each other (see also table 3.2). HTP yielded the best overall fit, thus we will consider it as a reference profile for comparison. The NGP overestimates the pressure shift 2.7-fold compared to HTP. qSDNGP overestimates still 1.8-fold. An amplification of the deviation as a function of pressure is an intuitive result which had to be expected from the line-profile study in the previous section. We see, that the degree of over-estimation is very significant for higher pressures, based on the choice of models. The pressure shift of this transition has already been determined in previous studies, however, the given values differ dramatically. Kassi and Campargue found a pressure shift of -2.5 x 10 -3 cm -1 /atm [START_REF] Kassi | Cavity ring down spectroscopy with 5× 10-13 cm-1 sensitivity[END_REF], while Gupta et al. found a pressure shift of -1.536 x 10 -3 cm -1 /atm [START_REF] Gupta | Quantitative determination of the (2, 0) band of deuterium in the near infrared via off-axis ICOS[END_REF]. It is interesting to look at the line profiles used in those studies. While Kassi and Campargue used a GP, Gupta et al. used a SDVP. The GP, as mentioned before, is a soft-collision model which does not include speed-dependence, needed to take line asymmetry into account, whereas the SDVP does not consider Dicke-Narrowing, but does take line asymmetry into account. While we did not evaluate the GP profile in this study, we know from the NGP results that ignoring speed-dependence does result in a strong over estimation of the pressure shift, even though his estimate is 20 % higher than our NGP result. The second study used a qSDVP, yielding a pressure shift about 10 % lower than what we retrieved for the qSDVP. The trends in the literature hence agree with the trends we found for different models. It appears that there is a significant over estimation associated with the choice of the line-profile. This should be considered for future studies, especially if the signal-to-noise of a measurement does hide those effects.

We also investigated the impact of line-profiles on the retrieval of line-intensities. Line intensities can be derived from the line area A as

I = A P D 2 × N (3.1)
where, P D 2 is the partial pressure of D 2 and

N = n 0 /760 × 273.16/T (3.2)
where T is the temperature and n 0 is the Loschmidt constant,

n 0 = P N A RT (3.3)
where P is the pressure, N A is the Avogadro constant and R is the gas constant. In the Hitran database, line intensities are reported for 296 Kelvin, therefore all line intensities mentioned here are given for 296 K as well.

In the lower panel of figure 3.5 we show the deviation of the retrieved line surfaces as a function of pressure. Again, HTP was our reference profile, since it yielded the best fit. For the determination of line intensities, we see deviations of up to 7.6 (for the NGP) from the HTP result. Moreover, there are significant deviations to be observed at higher pressures. Therefore, it seems to be mandatory to determine line intensities based on several measurements at different pressures to determine a slope A vs P, since A = P x S, where S is the line strength. In this case, high confidence can be attributed to the results, even though speed-dependent models should be preferred, since they yield significantly lower deviations (maximal 5 for the qSDVP). The study shows, that determining line intensities from measurements at one single pressure may introduce significantly bigger errors and should thus be avoided, it is therefore advised to test the linearity of the pressure-area relation.

From the results found above, it became clear that the HTP seems to be the best candidate for reliable measurements. We thus conducted a study on this profile. The main difference of this profile to the qSDNGP profile, which consistently yielded the second best results, is the presence of the correlation parameter η. Therefore, we have investigated the impact of this parameter on the retrieval of the values discussed before. Figure 3.6 shows the fit residuals of HTP fits for different values η, where the other parameters have been freely iterated, just as in the example before. A first fitting session was done with a free η, to determine a possible optimal value for η. This yielded a correlation value of 0.23986. Figure 3.6 shows the impact of η on the fitting at various pressures. At 1 mbar, the fit residuals are indistinguishable, at 25 mbar this is still the case, except for the full-correlation case (η = 1), in which a very subtle deviation becomes obvious, this deviation amplifies with increasing pressure and creates an asymmetric structure with a strong influence on the baseline, indicating a bias of the retrieved line center. All other cases from no correlation to semi-correlation, remain barely distinguishable even at higher pressures. However, they do create slightly asymmetric residual structures. In Figure 3.7, we compare the residuals of an HTP fit with η = 0 and η = 0.23986 (best fit). There is no strong difference observable between the two fits, however, a slightly stronger asymmetry seems to be present for the zero correlation case. We subsequently investigated the impact of the correlation choice to the determination of pressure shift, zero-Chapter 3 pressure transition frequency and line intensity. Figure 3.8 shows, in the upper panel, the line center frequency as a function of pressure, fitted with four different correlation values. All zero-pressure transition frequencies fall in a range of 16 kHz, with standard errors of 32 kHz. Again, while the determination of the zero pressure value is largely unbiased, the range of pressure shifts amounts to 25 % of the best fit value. We determined as well the bias on line intensity determination. The lower panel of figure 3.8 shows the bias for surface retrieval. In this case, a strong bias is obvious for the fully correlated case, amounting to an offset in the line intensity of 23 compared to the best fit value, in addition to a strongly non-linear behavior. Again, our results highlight the need for a well constrained correlation value and show that in any case, line intensities should be derived from measurements at several pressures to limit potential biases. Finally, we report the best-fit values we retrieved for this transition. For the line center we found a frequency of 187104299.848 MHz with a standard error of 31 kHz, this is 334.47 kHz higher than found by Mondelain et al., who reported 187104299.51 +/-500 kHz [START_REF] Mondelain | Sub-MHz accuracy measurement of the S (2) 2-0 transition frequency of D 2 by Comb-Assisted Cavity Ring Down spectroscopy[END_REF]. For the pressure shift, we report -1.1388 x 10 -3 cm -1 /atm with a standard error of 0.015 x 10 -3 cm -1 /atm. We determine the line intensity at 296 K as 4.777 x 10 -28 cm/molecule, with an estimated error of up to 1.5 %, assuming a worst case scenario due to outgassing and accounting for the 0.5% accuracy of the pressure gauge as well as a possible temperature error of 0.5%. The retrieved value lays within 1 of theoretical calculations by Kassi et al. [START_REF] Kassi | The absorption spectrum of D2: Ultrasensitive cavity ring down spectroscopy of the (2-0) band near 1.7 µ m and accurate ab initio line list up to 24 000 cm-1[END_REF]. There are several issues to be addressed in this study. For instance, we need to do scans with a broader range, to better constrain the baseline. This appears to be necessary, since the baseline was shown to be very sensitive to the choice of the line profile (see figure 3.2). Secondly, to get a more precise insight into other gas species present in the measurement cavity, it is necessary to monitor absorption lines of interfering species. Finally, Γ has to be further constrained. For this, we propose to perform a few high-pressure measurement in the near future in order to constrain this parameter more, and in turn, inject it into the fit. This way the impact of the speed-dependent parameters should be further constraint.

SATURATED ABSORPTION SPECTROSCOPY

Saturated Absorption Spectroscopy

In CRDS, the saturation of a transition (the fact that absorption reduces as the higher level of a transition gets populated) expresses itself as a deviation from a purely exponential behavior of the ring-down signal. CW-CRDS, with its capability of providing very high intra-cavity power, is a suitable tool for the observation of saturated features and has been used for this purpose for about two decades now. The first observation of saturation effects using CRDS was done by Romanini, Dupré, and Jost, who observed lamb-dips on NO 2 transitions near 12562 cm -1 [START_REF] Romanini | Non-linear effects by continuous wave cavity ringdown spectroscopy in jet-cooled NO 2[END_REF]. Bucher et al. conducted a comprehensive study on the power dependence of lamb dips on an ethylene transition near 941.855 cm -1 , investigating effects on the lamb dip shape [START_REF] Bucher | Doppler-free nonlinear absorption in ethylene by use of continuous-wave cavity ringdown spectroscopy[END_REF]. Lisak, Hodges, and Ciury lo observed a lamb dip on a strong H 2 O transition at 10687.36 cm -1 [START_REF] Lisak | Comparison of semiclassical line-shape models to rovibrational H 2 O spectra measured by frequencystabilized cavity ring-down spectroscopy[END_REF]. Finally, Burkart et al. used an OFFS-CRDS setup to accurately determine line centers of CO 2 absorption lines around 6250 cm -1 . An interesting effect arising from saturation is the so called lamb dip [START_REF] Ra Mcfarlane | SINGLE MODE TUN-ING DIP IN THE POWER OUTPUT OF AN He-Ne OPTICAL MASER[END_REF], appearing at the center of an absorption line. This effect arises when a molecule interacts with the counterpropagating light between the cavity mirrors. This selection criteria is only met by the zero-velocity class of molecules, i.e. the class of molecules with no longitudinal velocity component. Those molecules undergo no Doppler-effect and thus receive twice the intensity in comparison to molecules with longitudinal velocity. In this case, providing that the laser beam is sufficiently strong, the excited state is populated and the ground state is depopulated, twice as much as other velocity classes, forming a Doppler free lamb-dip. This dip is three orders of magnitude narrower than the Doppler-broadened absorption line. The Gaussian broadening associated with the thermally induced Doppler effect is one of the main limiting factors in the high-precision determination of absorption line centers. Lamb dips are unaffected by this broadening and as well unaffected by speed dependent effects observed in the inhomogeneously broadened absorption line ( [START_REF] Hartmann | Collisional effects on molecular spectra: laboratory experiments and models, consequences for applications[END_REF] and references therein), hence excluding potential sources of bias. Therefore, Doppler-free lamb-dips are an excellent alternative, providing highly precise center frequency determinations. With the advent of optical frequency combs (see section 2.2) those measurements have gotten a tightly controlled frequency axis. Thus, saturated absorption spectroscopy has become a formidable tool for the precise and accurate determination of absorption line centers, evidenced by several publications (e.g. [START_REF] Galli | Absolute frequency measurements of CO2 transitions at 4.3 µm with a comb-referenced quantum cascade laser[END_REF][START_REF] Amy-Klein | Absolute frequency measurement of 12 C 16 O 2 laser lines with a femtosecond laser comb and new determination of the 12 C 16 O 2 molecular constants and frequency grid[END_REF][START_REF] Burkart | Communication: Saturated CO2 absorption near 1.6 µ m for kilohertz-accuracy transition frequencies[END_REF]).The benefits are particularly helpful to resolve blended transitions, whose line centers are extremely hard to accurately determine with conventional molecular absorption spectroscopy. Lisak and Hodges used saturated absorption spectroscopy to precisely constrain the line centers of four blended H 2 O transitions near 7100 cm -1 with an uncertainty better than 400 kHz. Other exciting applications include the observation of the hyper-fine structure of 627 by Giusfredi et al. near 2.3 µm.

Comb-Assisted Cavity Ring Down Lamb-dip Spectroscopy

of 13 CO 2 Near 1.6 µm

We have recorded a set of 14 transitions of the 3001200001 band of 13 CO 2 in natural abundance near 6250 cm -1 . The transition frequencies have been determined with kHz accuracy. Figure 3.9 shows such a lamp-dip recording, at the example of the R4 transition of 13 CO 2 of this band, acquired at a pressure of 25 µbar. The scan is done in two steps. First, we do a rough scan of the absorp- tion line. The line is then fitted to determine the line center, a second measurement grid is then placed around the center to do a high resolution recording of the lamb dip. In such way we retrieved a list of 15 transitions frequencies, with precision on the kHz level. We should reiterate that our accuracy it limited by the dither lock scheme, with a bias expected to be on the kHz level (see section 2.5.4). The energy of a given ro-vibrational transition depends on the constants of its upper and lower state. The method of combination differences depends on using transitions that share the same upper or lower state. The benefit of this methods lied in that it allows for unbiased determination of energy gaps in either the upper or lower level of an absorption band.

The energy of a given transition is given in Equation 1. 16. In Figure 3.10, two transitions, one from the P branch and one from the R branch are shown. Both transitions share a common lower state. The combination difference can thus be used to gain access on the energy distribution of the upper level. In such way, all P and R lines of a given band can be represented as

ν = ν 0 + (B + B )m + (B -B -D + D )m 2 -2(D + D )m 3 + (D -D )m 4 (3.4)
where B', D' and D", D" refer to the upper and lower state constants respectively [START_REF] Tellinghuisen | Combination differences: victim of false charges?[END_REF]. In this case, m is -J for P lines and (J+1) for R lines. The given polynomial 3.2. SATURATED ABSORPTION SPECTROSCOPY accounts includes the rotational and quartic constant, omitting the sextic constant for clarity. We used PGopher, a program for the fitting and simulation of rotational, vibrational and electronic spectra [START_REF] Western | PGOPHER: A program for simulating rotational, vibrational and electronic spectra[END_REF]. We did two fitting runs, in both fitting runs, we retrieved the rotational constant B and the vibrational and rotational distortion constants D and H. The first run, is a general global optimization, regardless of the actual physics. We injected the parameters in equation 1.16, we recalculated the transition frequencies which we measured in this study. The results are shown in column 3 of Table 3 x 10 -7 cm -1 x 10 -7 cm -1

x 10 however, the combination differences enforce a certain level of physics, rather than generating a tuned fit realized in the global fit. The increasing noise towards higher J corresponds to the computation method, where the error on the measurement parameters accumulates during the calculation of the transition frequencies. However, further constraining measurements towards higher J are necessary to further constrain the fit. As a side project, in close collaboration with the Combiniso Project from Dr. Amaelle Landais, a second setup was realized, using a third generation VCOF source, referenced to an OFC for accurate frequency determination. The CRDS side of the setup is identical to the one described in this thesis before, however, this setup is devoted to the measurement of water absorption lines around 1.4 µm. The ring-down cell used for this setup exhibits a finesse of 129000, with a calculated intra-cavity power on the order of 40 W/cm -2 per V measured. Using the acquisition scheme described in section 2.3.1, we acquired lamb dips of a set of highly K-type blended doublets, exhibiting an Einstein coefficient in the 1-10 s -1 range, about three orders of magnitude higher [START_REF] Galzerano | Absolute frequency measurement of a water-stabilized diode laser at 1.384 µm by means of a fiber frequency comb[END_REF] than the ones used in a previous OFFS-CRDS study by Burkart et al. [START_REF] Burkart | Communication: Saturated CO2 absorption near 1.6 µ m for kilohertz-accuracy transition frequencies[END_REF] Therefore being , to our best knowledge, the highest saturation level for which lamb dips were reported, clearly resolving the blended components, which were found to be separated by about 10 MHz. We discus our results in the context of widely used water line lists, revealing significant deviations.

1

Lamb dip CRDS of highly saturated transitions of water near 1.4 µm S. Kassi1 , T. Stoltmann 1,2 , M. Casado 1,2 , M. Daëron 2 , and A. Campargue 1 *

Introduction

The accuracy of the determination of the center of an absorption line depends on the accuracy of the calibration of the frequency axis and on the precision of the line center determination. In recent years, the measurement of absolute frequencies has greatly benefited of the advent of self-referenced optical frequency combs (OFCs) [1]. For instance, frequencystabilized cavity ring-down spectroscopy (CRDS) referenced to a Cs atomic clock through an optical frequency comb was applied to the measurement of 12 C 16 O2 transition frequencies with combined standard uncertainties of a few tens kHz over the large 1.6-7.8 µm range [2].

In a very recent study, Bielska et al. measured the frequency of a B-band transition of oxygen near 690 nm with kHz level of accuracy by using a Pound-Drever-Hall-locked frequencystabilized cavity ring-down spectrometer referenced to an 88 Sr optical atomic clock via an optical frequency comb [3]. These state-of-the-art results are limited to a few very well isolated spectral lines recorded with very high signal to noise ratio through dedicated experimental setups. In general, due to the Doppler broadening in the near-infrared amounting to several hundred MHz at room temperature, typical line center accuracy in the Doppler regime hardly reaches the MHz (3×10 5 cm -1 ) level [4][5][6]. This is typically the case for the comb-assisted cavity ring down spectroscopy (CA-CRDS) approach that we developed recently [7]. This method relies on "on the fly" measurements of the beat note frequency between one of the modes of the frequency comb and a small part of the light emitted by a Distributed Feedback (DFB) laser diode used as a source of our cavity ring down spectrometer. CA-CRDS has provided slightly sub-MHz accuracy of CO, D2 and water line centers in routine over broad spectral regions between 1.7 and 1.3 µm [7][8][9].

Saturation spectroscopy is a powerful method to overcome the limitation due to the Doppler broadening [10]. Saturated transitions exhibit a Lamb dip at their line center with a width several orders of magnitude narrower than the Doppler broadening. The increased intracavity power provided by cavity enhanced absorption spectroscopy techniques makes them a very well-suited method to saturate rovibrational transitions in the near infrared and visible ranges [11,12]. For instance, Lisak and Hodges measured Lamb dips of four closely spaced rovibrational water vapor absorption transitions near 7100 cm -1 using frequencystabilized CRDS [13]. In absence of OFC, absolute transition frequencies were not determined but a 50 kHz resolution was achieved and relative transition frequencies were determined with an uncertainty better than 400 kHz. Galzerano et al. used the Lamb dip of an H2 17 O transition near 1.384 µm to frequency stabilize an external-cavity diode laser [14]. The same group reported a Lamb dip center frequency of a H2 18 O transition near 1.38 μm with 10-kHz accuracy by OFC assisted cavity-enhanced saturated absorption spectroscopy [15]. This transition which is selected to obtain an accurate spectroscopic determination of the Boltzmann constant is very strong (line intensity on the order of 2×10 -20 cm/molecule).

Recently, Burkart et al. used an optical feedback frequency-stabilized cavity ring-down spectrometer (OFFS-CRDS) to further enhance the intracavity power [16]. Doppler-free Lamb-dips were measured with kHz accuracy on ten lines of the 30013←00001 band and two lines of the 31113← 01101 hot band of 12 C 16 O2 near 1.6 μm, among the weakest ever studied by saturation spectroscopy (line intensity as weak as 5×10 -25 cm/molecule [17]). More recently, Gatti et al. [18] Furthermore, the three highly blended K-type doublets are used to discuss the accuracy of various recent high-quality ab initio water line lists.

Experimental

The present instrument combines an ultra sensitive cavity ring down spectrometer and a very narrow, highly stable V-cavity-based optical feedback (VCOF) type light source [21][22][23]. The reader is referred to Refs. [16,[22][23][24] for a detailed description of the first version of the experimental setup. The present OFFS-CRDS setup differs in different aspects from that applied to the measurement of saturated-absorption Lamb dips of CO2 near 1.6 μm [16]: the working range is centered at 1.39 µm (215 THz), the VCOF source has been improved, it is faster and easier to operate and its long-term reliability has been improved. In particular, the RD cavity is robustly dither-locked to the source rather than tight-lock using the Pound-Drever-Hall locking technique [16], prone to frequent unlocking.

Fig. 1

Schematic of the experimental setup. A VCOF source is made from a laser that is locked by optical feedback to one chosen TEM00 mode of a V-shaped cavity made of three mirrors optically contacted on a precisely machined low-expansion material. The cavity is kept at constant temperature and under ultra-vacuum (see picture in right inset). The relative phase between the laser and the cavity is precisely controlled (ctrl) by monitoring the cavity transmission and consequently acting on the laser-cavity distance. Its very stable emission frequency is accurately determined using both a precise Fizeau wavemeter and the BN obtained against a GPS-stabilized auto-referenced OFC. A MZM, configured as a single side band modulator (SSBM), allows the laser emission to be subsequently precisely tuned to an arbitrary wavelength by adding or subtracting a GPS-referenced radiofrequency in a range of 2-18 GHz. The shifted laser is used to sequentially probe the TEM00 modes of a massive CRDS cell, which are actively kept in resonance with the source using a dither-lock tracking scheme.

1 Laser source

The new VCOF reference cavity is made of a low expansion spacer, which has been machined and polished to be fitted with three mirrors by optical contact bonding. This source, hosting a DFB laser (Eblana Photonics), has sub-kHz emission line width, 10 mW output power, and exhibits a maximum frequency drift of 7 Hz/s. Its emission frequency is constantly monitored with both a wavemeter (HighFinesse, 20 MHz accuracy, 5 MHz resolution) and a GPS disciplined, selfreferenced OFC (250 MHz repetition rate, -20MHz carrier offset Frequency) in order to determine its absolute optical emitting frequency with sub-kHz accuracy [16]. This frequency measurement was used in several of our previous studies [7][8][9]16]. It consists in refining the wavemeter readings by additionally measuring the beat note (BN) between the laser and the closest tooth of the OFC. The BN is recorded 100 times per second using a fast acquisition card (2 15 samples recorded at 2.5×10 8 samples/s). A real time Fast Fourier Transform of this signal is computed, leading to a 7.6 kHz resolution spectrum of which only the lowest frequency peak detected, i.e. in the 0-125 MHz range, determines the so-called BN frequency. The precision of this method is exposed in Fig. 2 in an Allan deviation plot of a BN frequency series. It shows that the BN is determined within 42 kHz in a single shot (10 ms), and down to 700 Hz after 60 s averaging, which corresponds to a relative frequency determination of 2×10 -10 and 3×10 -12 , respectively. The GPS-disciplined Rubidium clock driving the OFC electronics induces a bump at 2 second averaging. After about 80 seconds, the VCOF frequency drift is visible, which is accounted for in the frequency calibration process. According to literature [25], the present GPS referenced setup allows for absolute frequency determination with a relative accuracy better than 10 -12 , i.e. 200 Hz. The wavemeter readings allow for a quasi-unambiguous determination of the OFC tooth index (N) beating with the VCOF, which frequency reads VCOF=N×250±BN-20 [MHz], where the sign is determined based on a determination of the relative position of the tooth frequency towards the VCOF frequency. In case of ambiguity, the sign can be explicitly deduced from the BN obtained by briefly locking the VCOF to an adjacent mode of its very stable reference cavity.

In OFFS-CRDS experiments [16,23,24,26,27], the frequency tunability of the light source is obtained by adding or subtracting a radio frequency (RF) to the fixed laser frequency. A fibered I/Q modulator (iXblue) used as a single side band modulator (SSBM), is inserted in-between the VCOF and the CRD cell. It allows for fine and arbitrary tuning of the laser frequency within a range of ±2 to ±18 GHz, by applying clean GPS-referenced-RF (SMF100A, Rohde & Schwarz) and a series of static voltages to the modulator driving inputs. The SSBM efficiency is close to 10 % and the carrier and other sidebands suppression ratio reaches 30 dB. Allan variance plot of a series of beat note measurements (black curve) recorded 100 times per second with 7.6 kHz FFT resolution (see text). The single shot precision is 42 kHz, due to OFC noise. The precision reaches 700 Hz after 60 s averaging, closely following the ideal t -1/2 random noise averaging (blue dashed curve). However, a bump is observed after 2 s averaging time and is attributed to noise excess in the Rubidium reference clock driving the OFC electronics. After 80 s averaging, the VCOF frequency drift is clearly visible. The effect of a 7 Hz/s drift, which is the worst expected case, is plotted (red dot line).

In OFFS-CRDS experiments [16,23,24,26,27], the frequency tunability of the light source is obtained by adding or subtracting a radio frequency (RF) to the fixed laser frequency. A fibered I/Q modulator (iXblue) used as a single side band modulator (SSBM), is inserted in-between the VCOF and the CRD cell. It allows for fine and arbitrary tuning of the laser frequency within a range of ±2 to ±18 GHz, by applying clean GPS-referenced-RF (SMF100A, Rohde & Schwarz) and a series of static voltages to the modulator driving inputs. The SSBM efficiency is close to 10 % and the carrier and other sidebands suppression ratio reaches 30 dB.

2 Ring down cavity

This precisely frequency shifted fully-fibered laser carrying about 1 mW power is finally freespace coupled to a ring down cell (Fig. 1). The mode matching is achieved with a single lens and two steering mirrors. In order to record ring down events, the side band generation can be efficiently interrupted within 60 ns by switching the radio frequency off, using a high isolation fast PIN switch (> 60 dB). A free space optical isolator is inserted between the two steering mirrors. The ring-down cell is made of a massive 30 cm long, 70 mm outer diameter, 13 mm inner diameter copper tube fitted with two highly reflective mirrors. One mirror is mounted on a piezoelectric tube actuator (10 nm/V expansion coefficient), so that the whole assembly forms a 32 cm long high finesse optical cavity (468 MHz FSR, F= 129,000). The two cavity mirrors can be precisely aligned by acting on two sets of 8 push-and pull-screws. The transmitted light is focused on a fast photo-detector (2 MHz band pass, 300,000 transimpedance gain) using a steering mirror and a lens. It allows for monitoring the cavity transmission and recording the ring down events. To keep the setup simple and make the locking/relocking mechanism more robust, the cavity is dither-locked. Tracking electronics keep the cavity modes in coincidence with the laser by applying a 60 mV, 100 Hz triangular modulation on the mirror piezoactuator. With 44 µs maximal ring down time and an excursion of about 400 kHz around the cavity modes, the Doppler effect associated with the cavity mirror displacement introduces a cavity mode frequency sweep of ±3.5 kHz per ring down, the sign being associated with the scan direction. Theoretically, the drift cancels out if one averages an even number of ring downs equally distributed amongst upward and backward scanning direction. Despite our efforts, a few spectral points may still be randomly biased by a fraction of ±5 kHz if a ring down event was missed.

However, given that the Lamb dip absorption features considered below are typically described by 40 spectral points, the dither-lock mechanism is expected to bias their center frequency to sub-kHz level.

Saturated ring downs

Combining a very narrow laser and a stable high finesse cavity ensures an efficient lasercavity coupling. Consequently, very high intracavity fields can be reached thanks to intra-cavity electric-field buildup. The photodetector has a photosensitivity of 1 A/W and the transimpedance gain was set to 300,000. With a cavity finesse of F~129,000, corresponding to a mirror reflectivity of 99.9976%, supposing no additional losses and according to a beam waist of 400 µm, the intracavity power is calculated to be on the order of 20 W/cm² per V measured. The ring-downs are typically triggered at a threshold of 1.5 V, i.e. 40 W/cm 2 . This value is 25 times lower than that used by Burkart et al. [16,22] to saturate CO2 transitions but the water transitions probed here have an Einstein coefficient that is 3 orders of magnitude higher [15]. To the best of our knowledge, none of the previous studies has reported CRDS Lamb dip measurement at such level of saturation. This is illustrated in Fig. 3 where the photodiode signal (in logarithm scale) is plotted versus time for three spectral points located out of the line profile, at about half width and near the line center. In nonsaturated regime, the light intensity decreases according to the cavity loss rate, 1/0+()c, which obviously varies over the frequency range of the line profile. This is not the case in the present recordings: The RD at the line center starts with a time constant close to that of the empty cavity. In other words, the saturation is so high that, at the beginning of the RD, the gas looks sort of transparent, over its whole line profile. The absorption line leads to an increase of the loss rate only after about 100 µs when the intracavity power has been decreased by about a factor of 10.

Fig. 3

Ring down photodiode signals recorded on the baseline (blue dots), the wings (green dots), the maximum (orange dots) and dip center (red dots) of the water line doublet at 7185.596 cm -1 . Ring downs were acquired with a different CRDS cell (51cm, F= 180000). Each curve corresponds to an average of 1000 ring down events. The photodiode voltage (left scale) could be roughly converted to intracavity power (right scale) based on the mirror reflectivity and the photodetection chain gain. The green and red dashed lines indicate the saturation-free ring down behavior expected on the wings (green) and on the top (red) of the absorption line, respectively. Effect of induced transparency is obvious within the first 100 µs of the event where intracavity power is in excess of 10 W/cm 2 .

Let us highlight that in a two-mirror optical cavity configuration, the TEM00 resonant mode is made of two contra-propagative optical waves perfectly overlapping each other. Optical cavities are thus an ideal tool to observe Lamb dip feature that appear at absorption line center, due to the twofold optical power experienced by molecules having zero velocity along the optical axis [10][11][12]. Because the present study is focused on accurate position measurement and not on a quantitative transition strength evaluation, we did not implement a non-exponential fit of the ring down events that would explicitly take saturation into account [21,26]. The ring down events were simply fitted with an exponential, therefore leading to strongly non-flat residuals (Fig. 4). Nevertheless, line profiles exhibit a well marked Lamb dip feature at their center, with up to 14% contrast allowing for a precise line center determination. The dip center is retrieved by fitting the dip absorption using a Lorentzian function (see inset in Fig. 5). The typical half-width at half-medium (HWHM) of the Lamb dip profile is 250 kHz. No evidence of asymmetry was found in the residuals. Therefore, although imperfect, the line fit model is expected to deliver unbiased line center determination.

Fig. 5

Line profile and Lamb dip recordings with adaptive resolution. A first low resolution (50 MHz) survey scan is recorded, from which the line center is roughly determined using a Gaussian profile. The spectrum is immediately supplemented with a high resolution (25 kHz) scan around the center presented in the inset. The inset includes the residuals of the two observed Lamb dips using Lorentzian profiles leading to 1.5×10 -10 cm -1 standard deviation of the residuals. No sign of profile asymmetry is observed.

In order to test the reproducibility of the experiment, we measured the   101-110 water line around 7182.2 cm -1 (215.5 THz) for several days. The CRD cell was continuously turbo pumped and outgasing water was probed at a residual pressure of less than 0.2 µbar. As depicted in Fig. 6, without OFC calibration the apparent dip center is fluctuating over a 50 kHz range within two days. This drift is exclusively due to the VCOF imperfect stability, as revealed by comparison with the BN monitoring, which exactly follows the same trend (red curve in Fig. 6). The (BN-dip) difference frequency is constant over time and shows 2.5 kHz RMS white noise, principally arising from the dip center fit precision. The Allan plot of this measurement series (Fig. 6) shows a quasi-perfect random noise type averaging, down to a statistical precision of 100 Hz, i.e. 5×10 -13 relative to transition frequency. The self pressure line shift, on the order of 300 kHz/Torr [28] is expected to account for about 100 Hz, i.e. our measurement precision level. Because of the high symmetry of the experimental setup -two identical mirrors on a symmetry axis and laser off during the ring-down event -the geometry is not expected to induce frequency bias [29]. Thus, the main source of uncertainty remains the locking scheme even though we could not evidence it. Therefore, we indicate a conservative 1 kHz (~4×10 -8 cm -1 ) accuracy for this line as an upper limit. No averaging was performed for the other lines, despite they are weaker and recorded at the same pressure. Therefore, due to a lower signal to noise, we estimate their position to be determined with an accuracy of 12 kHz (~4×10 -7 cm -1 ).

Fig. 6

The upper left panel shows a calibration free measurement series of a Lamb dip center. The blue curve corresponds to the evolution of the RF tuning frequency corresponding to the Lamb dip position. The red curve corresponds to the relative beat note between the VCOF and the GPS disciplined OFC, shifted up by 50 kHz on the plot for clarity. The difference is plotted (black dots) in the lower left panel revealing a perfect agreement with each other. The right panel is an Allan deviation plot of the difference. It shows firstly, that a single Lamb dip position is determined with 2.5 kHz accuracy in a single scan and, secondly, that successive measurements average as 1/N 1/2 and, thirdly, that a precision better than 100 Hz is reached after averaging 500 measurements (about 8 hours). This corresponds to a relative precision of 5×10 -13 of the absolute Lamb dip position determination.

3-Results

Table 1

Assignments, HITRAN line parameters and Lamb dip measurements of the ten studied water transitions near 1.39 µm. Doppler-free saturated-absorption Lamb dips were measured at sub-Pa pressures on eight rovibrational lines of water near 7180 cm -1 (see Table 1).

Fig. 7

Absorption line and Lamb dips for the JJ 0 ← JJ 1 and JJ 1 ← JJ 0 doublets of H2 16 O (J= 6, 7). On the lower panels, individual measurements points are showed to illustrate the higher resolution to sampling the dips range.

The measurements include three K-type doublets of H2 16 O. Two of them are [JJ 0 ← JJ 1, JJ 1 ← JJ 0] doublet of the 3 band with J= 6 and 7. The corresponding spectra are presented Fig. 7. The ½ nuclear spin of hydrogen leads to total nuclear spin of 0 and 1 corresponding to para-and ortho-water, respectively. Transitions are observed either between para or between ortho levels. Para and ortho energy levels in water can be classified according to the parity of the quantity (Ka+Kc+V3). Then, a JJ 0 ← JJ 1 and JJ 1 ← JJ 0 doublet involves a transition between para-energy levels and a transition between ortho-energy levels, the latter being three times stronger due to the spin statistics (ortho levels have a degeneracy of 3 while para levels are not degenerate). More precisely, for cold bands (V3= 0), the JJ 1 ← JJ 0 component is the strongest when J is odd and the weakest when J is even. Thus, for the two studied doublets, the 771←770 and 660←661 dips are the strongest. Considering the close degeneracy of the two components, the relative intensity is the only criterion to discriminate the transitions corresponding to the two dips. We have included in Table 1, the relative intensity of the studied doublets obtained from a Lorentzian fit of the dip profiles together with the corresponding relative depth. The obtained intensity ratios are very close to 3.

Fig. 8

Energy level scheme and relative intensity of the JJ 0 ← JJ 1 and JJ 1 ← JJ 0 doublets in water, according to the J parity.

Fig. 8 presents the expected appearance of the JJ 0 ← JJ 1 and JJ 1 ← JJ 0 doublets in absence of perturbation. The separation between the JJ 0 and JJ 1 energy levels is decreasing sharply with J. As the unperturbed JJ 0 energy level is higher than the JJ 1 level, the JJ 1 ← JJ 0 transition is always observed at lower frequency. In the JJ 0 ← JJ 1 and JJ 1 ← JJ 0 series of doublets of the 1+3 band of H2 16 O, only the J= 1-4 doublets have been resolved (in Doppler regime) and the measured frequency splittings were found to decrease from +10.47 cm -1 down to +0.106 cm -1 [30]. For comparison, the presently measured splittings are -2.9×10 -4 and -8.5×10 -4 cm -1 , for J= 6 and J= 7, respectively. We note that the sign of the J= 6 and 7 splittings is opposite to that of the J≤ 4 doublets and the relative position of the two components is inverted compared to the unperturbed case. In addition, the amplitude of the frequency splitting is larger for J= 7 than for J= 6. This situation is attributed to small perturbations of the considered energy levels of the (101) upper vibrational state, the [START_REF] Romanini | Diode laser cavity ring down spectroscopy[END_REF] state being involved in the strong and complex interaction scheme of the first hexade of water {(040), ( 120), (200), (002), (021), (101)} [31].

The Lamb dips of the 76 1 ← 7 6 2 and 7 6 2 ← 7 6 1 doublet were also resolved and assigned according to the relative intensity of the two components (Fig. 9).

Fig. 9

Absorption line and Lamb dips for the 76 1 ← 7 6 2 and 7 6 2 ← 7 6 1 doublet of H2 16 O.

4-Line position accuracy of water spectroscopic databases

Experimental and empirical databases

The eight H2 16 O dip positions measured with 12 kHz accuracy (4×10 -7 cm -1 ) provide an accurate set of data for comparison to various spectroscopic databases of water vapor. Fig. 10 shows the overview of the deviations from our measured dip values. The different data sets considered for the comparison are: (i) line positions calculated using the energy levels recommended by an IUPAC task group (IUPAC-TG) from an exhaustive review and evaluation of rovibrational line positions, energy levels and assignments for all the main isotopologues of water [30]. By using the procedure and code MARVEL (Measured Active Rotational-Vibrational Energy Levels) [32], all the high-quality absorption or emission line positions available in the literature were used to determine and validate the energy levels together with their self consistent uncertainties. MARVEL uses a reweighted inversion process to determine the uncertainties which are given at 2. The IUPAC-TG used several hundred transition wavenumbers to derive the upper energy levels of each of the eight H2 16 O transitions measured in this work [30]. As a result, these levels are reported with the best quality grade in the IUPAC-TG gradation (A+) and their uncertainty values (included in Fig. 10) range from 10 -9 (!) to 3×10 -5 cm -1 . The IUPAC-TG line positions are observed to deviate from our measurements by much larger values, up to 1.8×10 -3 cm -1 . In our opinion, the main reason of this strong disagreement is that the considered IUPAC-TG energy levels have an uncertainty which is underestimated by several orders of magnitude. This may be due to underestimated error bars provided by some of the sources used by MARVEL or to some problems with the inversion process. In particular, the three K-type H2 16 O doublets were resolved in neither experimental source used by the IUPAC-TG and the error bar of the upper levels cannot be smaller than the doublet reparation, (ii) Line positions retrieved in Doppler regime from Fourier Transform spectra recorded by Toth [33] and Régalia et al. [34],

(iii) The HITRAN spectroscopic database [17] which uses different sources for the considered transitions. Six transitions have frequencies calculated from the IUPAC-TG levels, the two others being experimental values by Toth [33] and Jenouvrier et al. [35]. The error code ( 4) is attached to all but one HITRAN2012 positions and corresponds to an uncertainty better than 10 -3 cm -1 . This value is much larger than the corresponding IUPAC-TG error bars.

We have included in Figs. 7, 9 and 10, the HITRAN stick spectrum for the three studied Ktype doublets. In the three cases, the frequency ordering of the ortho-and para-components is inverted compared to the observations. Nevertheless, the HITRAN2012 and dip position values are mostly consistent within the 10 -3 cm -1 HITRAN error bar, the largest discrepancies concerning the weakest component of two K-type doublets.

(iv) Transition frequencies provided in the near infrared spectroscopic database constructed by Mikhailenko et al [37]. The frequency values were obtained from empirically determined energy values mostly based on extensive investigations of water spectra by high sensitivity CRDS [38][39][40] complemented with literature data (in particular the FTS data by Toth [33] and Régalia et al. [34]) (v) H2 16 O line positions measured in Doppler regime at low pressure (<0.2 Torr) by CA-CRDS of water highly enriched in 17 O [41].

Fig. 10

Differences of the line positions to the dip center for the eight water lines measured near 7170 cm -1 (The ranking number in ordinate is the line number given in Table 1). The light grey zones indicate the three K-type doublets. From left to right, the comparison applies to HITRAN2012 [15] and IUPAC-TG line positions [30] (left panel), FTS values by Toth [33] and Régalia et al. [34] and empirical values of Ref. [36] (center panel) and the recently obtained position values measured by CA-CRDS in Doppler regime [41] (right panel, the S symbol indicates the strongest of the doublet components).

It is worth underlining that in the case of the three K-type doublets (light grey zones in Fig. 10), the three experimental works in Doppler regime by FTS [33,34] and CA-CRDS [41] provide a single line position for the two components. As expected, for the three K-type doublets, the reported line position is closer to the dip center of the strongest component.

Interestingly, the CA-CRDS values [41] are intermediate between the two dip centers and the amplitude of the deviation of the weaker dip is not far from three times that of the stronger dip, as expected from their relative intensity. Two factors contribute to the higher accuracy of the CA-CRDS values: the referencing of the laser source to the optical frequency comb and the higher sensitivity of the CRDS technique allowing for measurements at very low pressure.

Table 2

Comparison of the Lamb dip centers of the three measured K-type doublets to the predictions of various variational calculations [44][45][46][47][START_REF] Black | Trapped neon in meteorites-II[END_REF].

Band 𝐽𝐾 𝑎 ′ 𝐾 𝑐 ′ -𝐽𝐾 𝑎 ′′ 𝐾 𝑐 ′′ Lamb dip center (cm -1 )
Variational-dip (10 -3 cm -1 ) Doublet separation (10

Variational line lists

High-quality-computed water line lists are available since two decades. Since the pioneer works by Partridge and Schwenke [42,43], the collaboration between University College London and the Institute of Applied Physics in Nizhny Novgorod have produced various line lists based on different versions of the potential energy and dipole moment surfaces [44][45][46][47]. They differ in terms of accuracy and completeness (maximum energy of the levels, maximum J values). In Table 2, we compare the line positions of the three H2 16 al. [44]. For SP values, we used the values computed by S. Tashkun, available in Ref. [START_REF] Black | Trapped neon in meteorites-II[END_REF]. In terms of absolute position values, no clear improvement is noted for the three considered doublets, the deviations being in the 0.01-0.10 cm -1 range except for Ref. [46] for which larger differences are noted (contrary to the others, the values of Ref. [46] are pure ab initio values without any experimental corrections). However, the improvement is obvious for the K-type doublet separations. While SP separations show large differences including for the sign, the POKAZATEL separations show an impressive agreement with the measured values, at the 10 -5 cm -1 level. It would be interesting to trace the origin of such achievement in order to identify which family of levels has energies predicted with such high relative accuracy.

5-Conclusion

An ultrasensitive cavity ring down spectrometer injected by a very narrow, highly stable V-cavity-based optical feedback type light source [22] has been developed for accurate spectroscopy in the near infrared [21][22][23]. The V-shaped optical feedback source (VCOF) provides a sub-kHz laser linewidth with a very high stability (typical drift of 10 Hz/s) which makes the setup particularly suitable for line shape studies and precise measurements of isotopologue abundances [27]. Very high intracavity fields are obtained by this combination of a very narrow laser and a stable high finesse cavity. In the present OFFS-CRDS setup, the obtained intracavity power (about 40 W/cm 2 ) was used to induce a high saturation of strong rovibrational lines of water vapor (Einstein coefficient in the 1-10 s -1 range). At the ring down starting point, the intra-cavity power was roughly estimated to be 10 times higher than the saturation intensity. Therefore, an almost completely induced transparency regime was reached, so that, at the early stage of the ring down the decay time is identical to that of the empty cavity. By referencing the laser source, the developed setup allows determining line centers of highly K-type blended doublets from their much narrower Lamb dips signatures, having 250 kHz HWHM. As the component separation is about 10 MHz to be compared to a HWHM Doppler width on the order of 300 MHz, our measurements contrast with previous experimental studies where the doublets were observed as single lines. The chosen examples illustrate the advantage of Lamb dip spectroscopy for accurate measurement of line centers. In Doppler regime, line center determination with kHz accuracy requires a precise modeling of the full line profile and the absence of interfering line with a very high contrast, while in Lamb dip spectroscopy these requirements are much relaxed. In particular, we demonstrate that averaging measurement series allows for line position to be statistically determined to 100 Hz precision, i.e. to the remarkable 5×10 -13 relative precision.

The obtained position measurements have been discussed in relation with widely used water line lists. In particular, the error bars provided by the IUPAC-TG for the energy levels involved have been found considerably underestimated. The comparison to variational line lists indicates that absolute positions deviate from the measurements by 0.01-0.1 cm -1 for all the considered lists but the recent POKAZATEL list [44] provides an impressive agreement at the 10 -5 cm -1 level, for the three studied K-type doublets splitting. To date, directly measuring the isotopic composition of a carbonate mineral is not possible with the necessary precision for clumped-isotope-palaeothermometry. Therefore, carbonates are converted to CO 2 using acid digestion in phosphoric acid [START_REF] Morden | On the isotopic chemistry of carbonates and a paleotemperature scale[END_REF][START_REF] Pn K Swart | Fractionation of the stable isotopes of oxygen and carbon in carbon dioxide during the reaction of calcite with phosphoric acid as a function of temperature and technique[END_REF]. The fractionation associated with this process is a matter under active debate in the clumped isotope community, (e.g. [START_REF] Guo | Isotopic fractionations associated with phosphoric acid digestion of carbonate minerals: insights from first-principles theoretical modeling and clumped isotope measurements[END_REF][START_REF] Müller | Clumped isotope fractionation during phosphoric acid digestion of carbonates at 70°C[END_REF][START_REF] Fernandez | Are acid digestion styles responsible for differences in clumped isotope calibrations?[END_REF]). The abundance of 13 C- 18 O bonds has been shown to be proportional to the abundance in the original carbonates with an offset [START_REF] Ghosh | 13 C-18 O bonds in carbonate minerals: A new kind of paleothermometer[END_REF]. Guo

H 2 CO 3 → H 2 O + CO 2 (3.12)
where two oxygen isotopes form CO 2 while one forms water. This process is common to all current methods employing this proxy, since all methods rely on the conversion from carbonates to carbon dioxide. Besides the limitations of mass spectrometry for the measurement of 17 O anomalies, mainly the difficulties in resolving isobaric interferences, two other important limitations arise for the measurement of clumped isotopes. Non linearities are a common problem in the measurement of isotopic ratios and it is not surprising that they are a major limitation in clumped isotope measurements as well. It has been observed, that there is a linear relationship between the ∆47 value and the δ47 value of the CO 2 gas. δ 47 is more or less representative of the bulk isotopic composition of a sample. Several observations towards this have been made. Huntington et al. proposed the relationship being tied to a correlation between the calculated R 47 values and the current ratio between the mass 47 and the mass 44 ion beams [START_REF] Kw Huntington | Methods and limitations of 'clumped'CO2 isotope (∆47) analysis by gas-source isotope ratio mass spectrometry[END_REF]. Rosenheim, Tang, and Fernandez noted large changes in the relation after filament changes for an Isoprime 5kV sector mass spectrometer [START_REF] Rosenheim | Measurement of multiply substituted isotopologues ('clumped isotopes') of CO2 using a 5 kV compact isotope ratio mass spectrometer: Performance, reference frame, and carbonate paleothermometry[END_REF]. The findings in this problem field led to the development of the pressure baseline correction when He, Olack, and Colman noted a negative offset in the faraday cup amplifier upon presence of analyte gas in the IRMS [168]. Finally, few IRMS systems seem to not exhibit a linear relation ship like this, one of which has been described by [START_REF] Yoshida | Precision and long-term stability of clumped-isotope analysis of CO2 using a small-sector isotope ratio mass spectrometer[END_REF] who used a Thermo Fisher DeltaXP, which mainly differs in the geometry of the ion chamber, affecting the width of the beam. Likely, this problem is related to ion-beam geometry, causing more or less scattering ions depending on the quality of the beam focus.

Electron impact, used in the source of most IRMS systems used in clumped isotope studies, has a potential to lead to fragmentation and recombination of iso-Chapter 3 3.4. FIRST DETERMINATION OF 16 O 13 C 18 O ABUNDANCE topologues. This "scrambeling" has been observed to lead to a reduced difference in ∆47 between analyte gas and working standard [START_REF] Kw Huntington | Methods and limitations of 'clumped'CO2 isotope (∆47) analysis by gas-source isotope ratio mass spectrometry[END_REF] and then produces a scale compression in clumped isotope measurements. The exact source of this process remains under debate. Dennis While this effect plays no significant role when measuring bulk isotopic compositions, since associated fractionations should affect samples and references equally, it does pose a problem if one is trying to measure the isotopic ordering between sample and standard. This is because those effects should drive samples to stochastic compositions, thus the effect will depend on the initial composition of a sample or reference and hence they may not be equally affected [START_REF] Dennis | Defining an absolute reference frame for 'clumped'isotope studies of CO 2[END_REF]. A third limitation is very similar to the limitations affecting IRMS measurements of 17 O anomalies, that is interfering molecular species of the same mass than the species of interest. The measurement of ∆47 is fundamentally based on the measurement of mass 47. Mass 47 includes three isotopologues: 638, 827 and 737, the latter 2 make up 3.4% of all mass 47 isotopologues. The same problem exists for mass 45, where 627 contributes roughly 6.7%. Those isobaric molecules thus constitute a big potential bias, since they cannot be discriminated using current IRMS techniques. Molecular absorption spectroscopy offers several advantages in this case due to the selectivity and non-destructive nature of the measurement method. Laser based measurements of ∆47 would therefore be a valuable complementary technique subject to very different limitations. In the following, we will demonstrate first tests on laser based measurements of clumped isotopes using VCOF-CRDS. Using the line identification script described in chapter 2, we have identified several absorption lines of the rare clumped isotope 638 (see table 2.4 and Figure 3.11) all of which falling in the region around 6241 cm -1 . Additionally, we have identified several regions in which we can address 638, 636 and 626 simultaneously (see table 2.5). There are several limitations to the identified region. On the technical side, we are not able to use our boost optical amplifier in this region, forcing us to work with a six fold lower optical power, thus diminishing the sensitivity. From a spectroscopic point of view this region is the optimal region for the determination of 638 abundance in the near-infrared. However, it is as well a spectral region with very strong H 2 O transitions. Figure 3.12 shows the absorption spectrum for 5 mbar of CO 2 and 50 µbar H 2 O, retrieved from Hitran [23]. Such high water concentration has been found for very low flow regimes. In this case, a steady state situation is reached, keeping water at the same partial pressure over prolonged times, revealing a permanently outgassing water source, or a undetected leakage. We have conducted a series of tests at different pressures to identify the optimal pressure regime and evaluate the possible precision of clumped isotope measurements in two distinct spectral regions

Measurements

The attainable precision of our laser spectrometer has been tested in two distinct spectral regions at pressures of 5 and 10 mbar. The pressure regulation had a precision of 40 and 20 ppm respectively, for a single spectrum. The average precision of the pressure regulation was in the order of 15 For 5 mbar measurements, our precision is currently limited to about 100 ppm for both regions. For the 10 mbar measurements, we could reach a maximum precision of 20 ppm after about 30 spectra in region 1. Currently, this relates to about one hour of measurement. It should be noted, that the current spectral acquisition is not yet optimized for speed of acquisition. A close look at the spectrum of region 1 in figure 3.13 already indicated the potential for time gains by optimizing the acquisition interval. Using the Mach-Zehnder modulator we are able to precisely target the region around the 638 absorption and the region around the 636 absorption. However, for a first proof of concept, it is useful to monitor a wider spectral interval, hence the increased acquisition time. We are therefore very confident to be able to realize clumped isotope measurements with the current instrument in the very near future. Main issues to be addressed to increase the performance will be related to an optimized gas-handling, to allow static measurements and reduce the sample size. In this light, we have recently mounted a cavity which has been treated with SilcoNert (Restek). This Silicon coating should diminish outgassing drastically and reduce adsorption and desorption processes in the cell. However, a thorough testing of this cavity is yet to come.

Chapter 4 Conclusion

The prime target of this thesis was the development of a new OFFS-CRDS setup for high-precision measurements of isotopologue abundance ratios in pure CO 2 based on the thesis work of Johannes Burkart [START_REF] Burkart | Optical feedback frequency stabilized cavity ring down spectroscopy -HiHigh coherent near-infrared laser sources and metrological applications in molecular absorption spectroscopy[END_REF] and the validation of its performance. We have set up a new OFFS-CRDS spectrometer, coupling a VCOF source with a maximum drift of 30 Hz/s to a high-stability ring-down cavity, which exhibits a finesse in excess of 450,000. Contrarily to the original OFFS-CRDS setup, we abandoned the complex and somewhat fragile PDH locking scheme for a robust dither lock, better adapted to the requirements of geoscientific applications. This lead us to new developments, in which we designed robust locking electronics, allowing ring-down rates on the same level as the PDH lock (200 RD/s), with the benefit of being less sensitive to noise, temperature and pressure drifts. Also, we did not have to compromise on the transmission threshold, therefore not loosing sensitivity. Most importantly, the re-locking speed increased, diminishing the acquisition time for spectra significantly. However, the stability transfer chain from VCOF to CRDS was somewhat broken, thus the name OFFS-CRDS was not absolutely valid anymore. We chose to name this new, closely related technique, VCOF-CRDS. A second problematic was encountered with the very specific and demanding requirements the optical determination of isotopic ratio imposes, in particular in terms of temperature stabilization. We spent a significant amount of time on the development of a new temperature stabilization system, minimizing temperature excursion and gradients. The system is based on a micro-controller to render it autonomous from the lab-computer, ensuring continuous temperature stabilization. We could reduce the temperature excursions exhibited by the ring-down cavity to less than 15 mK, with oscillations following a day-night cycle, imposed by the laboratory airconditioning system. A few technical issues remain to be solved in the future. For instance, our reference cavity is currently only passively stabilized, exhibiting a clearly temperature related frequency drift. While this is less problematic in the presence of an OFC referencing scheme, it permits the use of our instrument in a geoscientific laboratory. We foresee the need for active stabilization to be able to run the system without an OFC. For this purpose, a new housing has been designed. Both, the VCOF and all laser driving electronics will be included into this new housing. Active stabilization of the whole system will ensure a maximum stability of our reference system. Already, such a system is in place for another VCOF, and is able to ensure a stabilization on the 10 mK level. A further important difference to the previous system is that the current VCOF is using fibered DFB lasers. Five diodes have been acquired, allowing us to address several spectral regions of interest. To further automatize the instrument, we did first tests with a fiber optic 1x4 switch. First tests, show that it is feasible to record multi-diode spectra, addressing distinct absorption lines. However, more work is needed before this technique can be considered fully operational. Significant effort has been been devoted to automatize the MZM based single side-band generation. Home-made control electronics have been designed to control a commercial iXblue MXIQ-ER-LN-30-PD nested MZM, controllable via USB. The system allows for easy adjusting on the lab-computer, storage of optimal parameters and automatized switching between side bands, which would allow for a 38 GHZ scan, in total. VCOF-CRDS reached a record breaking detection limit of 3.8 x 10 -14 cm -1 for a narrow scan of 2.5 MHz, with a frequency stepping of 50 kHz. This value was reached after less than 10 hours. To our best knowledge, this is the lowest detection limit ever reported in absorption spectroscopy. It should be noted, that this is not the maximum attainable precision by VCOF-CRDS, since we could not evidence a deviation from white noise behavior when we stopped the averaging. The singlespectrum detection limit is 2 x 10 -12 cm -1 , sufficient for a wide range of spectroscopic applications as well as isotope ratio determination. Several applications were realized during the course of this thesis. One publication resulted from this work so far. The paper "Direct, Precise Measurements of Isotopologue Abundance Ratios in CO 2 Using Molecular Absorption Spectroscopy: Application to ∆ 17 O" [22], gives a comprehensive technical description of the development work done in this thesis and reports on our results on the determination of ∆ 17 O. We have shown, that our instrument is able to reach a precision on 10 ppm within 10 minutes of measurement, about 20 times faster than current state of the art IRMS, with the benefit of direct measurements, without chemical pre-treatment.

In the paper we have shown that a distinct temperature bias of our isotope ratio determination is evident, but can be partly corrected for by using line-strength temperature sensitivity data from Hitran [23]. Since we cannot completely correct all temperature biases our final precision is limited to 6 ppm. The temperature sensitivity problems motivated us to do a thorough analysis of the absorption lines which fall in the reflectivity zone of our current reference cell. For this purpose we created a Python script, which uses HAPI, a python library to interface Hitran [24]. This allowed a more stringent test of every absorption line in the range, for a set of quality parameters. Resulting from this we found a set of absorption lines that are of significantly higher quality than the ones currently used. However, the use of a switching scheme is mandated for this approach, since those lines are separated by more than 19 GHz. The script also generates a list of spectral zones which allow the measurement of several absorption lines within one 19 GHz scan. We envision using those optimized lines in the future to further increase the performance. One already realized outcome of this exercise is the measurement of the rare, clumped isotope 638 near 6707 cm -1 . We have performed several tests in this region and could show a precision of 10 ppm on the measurement of 638/636 for a measurement in a very small flow at 10 mbar, limited by 638 determination. We already identified a better line with roughly twice the SNR and envision testing this line in the very near future. However, it should be noted that the measurement of the classical clumped isotope paleothermometer ∆47 requires a laser source switching approach, since no 628 transitions of sufficient quality are present in the specified region. We believe that a multi-source approach would drastically increase the potential of VCOF-CRDS. Indeed, both, our reference and ring-down cell cover a broad region between roughly 6060 and 6720 cm -1 . Exploiting this huge range to target the best absorption lines for each CO 2 isotopologue can drastically increase measurement precision, or, for a given precision target, reduce measurement time. Furthermore, optimal regions for H 2 O, CO or CH 4 can be identified and adressed by dedicated diodes. This would be a promising way forwards to a multi-species instrument, a further step on the way to a real alternative to IRMS systems. One major advantage of VCOF-CRDS is the very high frequency stability, unleashing its full potential when probing absorption line wings, where the benefits of a stable laser are more pronounced. We performed an intensive line-profile study on the S(2) transition of D 2 in a pressure range from 1 to 75 mbar, using the extreme sensitivity and frequency stability to test how well available line profiles can model the line shape of this transition. Finally, the VCOF-CRDS presented here -dedicated to high quality and accurate spectroscopy -is the most sensitive absorption spectrometer to date. It proved to be a very versatile tool with application that encompass fundamental and applied science. Certainly, there is still potential for improvements, but the technique has reached sufficient maturity for extensive spectroscopic and geoscientific studies.

Chapter 4 133 First and foremost I want to express my sincere gratitude to my PhD supervisor Samir Kassi. By sharing your vast technical and scientific knowledge you convinced a Geologist to let go his hammer and find joy in electronic design, optics and spectroscopy. Thank you for always being open to new ideas, sharing your thoughts and optimism when things got stuck. The skills I learned from you opened many new doors for me. I will miss the evening rides back home. I would also like to thank Mathieu Daëron for ensuring the financing of the project within the framework of the ANR project "LITOS" and having allowed me to be part of this great project. I hope there will be great applications in the future. I want to thank Erik Kerstel for proposing this project to me. Without you, I would probably still be analyzing drill cores. I have to thank the work-shop for realizing so many parts of my experiment and always sharing their experiences with me to improve the experiment. I also want to thank my family. Without your constant loving support on so many levels I would not be where I am now. Furthermore, I want to thank my friends, who made my time in Grenoble amazing. I will miss all the lunches, evenings and hikes with you. I want to especially thank Adel, Mathieu and Joe, whom I owe thanks for a lot of great times. I sincerely hope our ways will keep crossing each other. And finally, I want to thank Morgane. You made my time in Grenoble unforgettable and somehow managed to endure me during thesis writing. I can't wait for our next step in Aix-en-Provence!

Figure 1 . 2 :

 12 Figure1.2: Schematic of dual-inlet gas-source IRMS system. Modified from[START_REF] Ghosh | Stable isotope ratio mass spectrometry in global climate change research[END_REF]

Figure 1

 1 Figure 1.3: Masses and coordinates of a linear triatomic molecule [67].

Figure 1 .Figure 1 . 4 :

 114 Figure 1.4 shows a comparison of the three line shapes. One can see, that the flanks of a Doppler broadened line shape are significantly more suppressed than the ones of a pressure broadened line shape. Since in most experimental setups the pressure effects are dominating, the Lorentzian contribution dominates the Voigt-Profile in

Figure 1 . 6 :

 16 Figure 1.6: Idealized transmission function of an optical cavity (Airy function).Different reflectivities are given. The width of the mode is a function of the mirror reflectivity R. The transmission is periodic, separated by the FSR. Graphic from[START_REF] Berden | Cavity ring-down spectroscopy: techniques and applications[END_REF]

Figure 1 . 7 :

 17 Figure 1.7: Basic setup making use of an optical resonator. (1) Mode matching optics consisting of two steering mirrors and a lens, (2) optical cavity with wavelengths proportional to L/2, (3) cavity output showing three successive resonant modes.

Figure 2 . 1 :

 21 Figure 2.1: Left panel: Picture of the VCOF assembly. MACOR machinable glass ceramic feet hold a system of INOX rings, that is spaced by threaded rods to keep the cell in place. Two INOX mirror holders hold the mirrors in position. The whole setup is to be mounted in a vaccuum chamber, additionally shielded by a copper shield. Right Panel, schematic of VCOF setup..

Figure 2 . 2 :

 22 Figure 2.2: Computer-assisted drawing of the second generation electronic setup for VCOF. Five laser driver stacks are included into this setup. Fiber holders are firmly fixed in order to reduce potential vibrations. The connection to the VCOF setup is made by a fiber connection on the right back side.

Figure 2 . 3 :

 23 Figure 2.3: New VCOF housing with two compartments. 5 mm thick aluminum plate shield the interior thermally.

2. 2 .

 2 Figure 2.4: 8-Channel, 16-bit, PID stack on board for Arduino Due © .

Figure 2 . 5 :

 25 Figure 2.5: LabVIEW interface for the Arduino based PID controller.

Figure 2 . 6 :

 26 Figure 2.6: Temperature excursions at various points inside the temperature stabilization system, in this case for the CRDS cavity. The system is reaching its set point with the first 2 hours

Figure 2 . 7 :

 27 Figure 2.7: Frequency stability of VCOF as determined by lamb dip measurements. In blue, apparent lamb dip position retrieved without frequency correction. In green, the same data set corrected using self-referenced optical frequency comb. The standard deviation on the line center determination is 15.2 kHz

2. 2

 2 Figure 2.10: Picture of VCOF 3 Zerodur spacer with optically contacted mirrors, forming a quasi-monolithic cavity.

Figure 2 .

 2 Figure 2.12: Rackable MZM Control unit. Upper Panel: Front Face, Lower Panel: Interior with control electronics and power supply.

Figure 2 . 13 :

 213 Figure 2.13: Schematic of the currently used CRDS cavity.

  .14). The PZT assembly consists of a metal disk with a groove machined into it. The groove is Chapter 2 used to host a Viton o-ring. Four M2 threads in the cavity bulk allow fixation of the steel disk. A piezo electric tube actuator has been glued onto the steel disk using the ultra-low vapor pressure epoxy resin TorrSeal. In the same manner, a mirror mount receptor is glued on the other side of the PZT. This receptor is threaded on the outside and has a o-ring groove on the front. The mirror is then mounted in a mirror assembly, where it is tightly contacted to a polished steel surface on the cavity side, and tightened by a Viton-oring on the other. The mount is then screwed on the receptor, tightened by another Viton o-ring. Fine adjustment on the mirrors is realized by means of adjusting two cavity flanges. The flanges have been machined by cutting a 6-mm trench into the cavity bulk, leaving a wall thickness of about 0.6 mm at the thinnest point. This creates a weakspot that allows adjusting of the flanges. The adjustment can be done by means of four push-and four pull-screws on every flange. The screws are mounted in pairs of two, enabling counter-balancing and aligned along two orthogonal cavity axes. Note that counter-balancing of the screws allows to fix the mirror position firmly. For temperature control, two 3-mm drillings have been machined 20 mm deep into the cavity bulk. This allows placing temperature probes deep inside the cavity to check the homogeneity of temperature stabilization during operation.

Figure 2 .

 2 Figure 2.14: Half-section view of the PZT assembly. In red, the piezo electric tube actuator.

Figure 2 . 15 :

 215 Figure 2.15: Simulation of the error signal generation for the cavity lock. Blue curve shows the symmetric modulation applied to the PZT, green, dotted curve shows the corresponding error signal. Black, dotted line indicates passages through resonance.

Figure 2 . 16 :

 216 Figure 2.16: Sample inlet system version 1 (left side) and the recent version 2 (right side).The CRDS indicated as dashed line, the flow direction is indicated by arrows.

Figure 2 . 18 : 2 2. 3 .

 21823 Figure 2.18: Schematic of free space VCOF CRDS.

Figure 2 . 19 :

 219 Figure 2.19: Screenshot of the spectra-aquisition software.

2. 3 .Figure 2 . 20 :

 3220 Figure 2.20: Construction of an interlaced spectrum. The frequency is swept over multiples of the FSR in a range of 14 GHz for four time for construction of the full spectrum.

Figure 2 . 21 :

 221 Figure 2.21: Absorption detection limit over number of averaged spectra for a recording over a span of 2.5 MHz, as used for lamb-dip recordings.

Figure 2 . 23 :

 223 Figure 2.23: Ring downs recorded by Wójtewicz et al. (2011)(a,b). Fit residuals for single ring down event (c,d) and for 3000 averaged events (e,f) [123].

  Integral non-linearity (INL). The INL is defined as the integral deviation of an ADC transfer function from an ideal straight line. The NI-6281 acquisition card states a full range INL of 10 ppm. The impact of non linearities on the ring-down determination has been investigated by Wójtewicz et al. on a PDH-locked FS-CRDS [123]. The authors compared two different ADC acquisition cards (ADC1: Gage Applied, CompuScope Octopus 8327, 14-bit vertical resolution, 125 MS/s max sampling rate, 100 MHz bandwidth and ADC2 Gage Applied, CompuScope 14200, 14-bit vertical resolution, 200 MS/s max sampling rate, 100 MHz bandwidth). Panel a and b of Figure 2.23 shows ring down acquisitions with ADC1 and ADC2. The panels c and d show the fit residuals of a single fitted ring down event. A difference between the two ADCs is not obvious. Panels e and f show fit residuals for 3000 averaged ring down events. It becomes obvious, that ADC1 exhibits strong non-exponential behavior while ADC2 exhibits almost perfect exponential behavior.

Figure 2 .Figure 2 . 24 :

 2224 Figure 2.24: Fractional difference between ring down time constants as obtained by different measurement conditions and reference time constants from Wójtewicz et al. (2011). Panels a and b correspond to baseline measurements (τ = 9.5µs) and panels c and d to the line center (τ = 5.2µs)

Figure 2 . 27 :

 227 Figure 2.27: Spectrum of evacuated cavity and spectra after one and two days. Note the strong CO 2 absorption at 6284.81905 cm -1 and the strong water absorption at 6285.1079 cm -1 . The remaining lines are a complex mix of H 2 O, CO 2 , CH 4 and possibly higher order organics absorption lines.

  Direct, Precise Measurements of Isotopologue Abundance Ratios in CO 2 Using Molecular Absorption Spectroscopy: Application to Δ 17 O Tim Stoltmann, †, ‡, § Mathieu Casado, § Mathieu Daeron, § Amaelle Landais, § and Samir Kassi* , †, ‡ † CNRS, LIPhy, F-38000 Grenoble, France ‡ UniversitéGrenoble Alpes, LIPhy, F-38000 Grenoble, France § Laboratoire des Sciences du Climat et de l′Environnement, LSCE/IPSL, CEA-CNRS-UVSQ, UniversitéParis-Saclay, F-91191 Gif-sur-Yvette, FranceABSTRACT: We present an ultrasensitive absorption spectrometer based on a 30 Hz/s stability, sub-kHz line width laser source coupled to a high-stability cavity-ring-down-spectroscopy setup. It provides direct and precise measurements of the isotopic ratios δ 17 O and δ 18 O in CO 2 . We demonstrate the first optical absorption measurements of17 O anomalies in CO 2 with a precision better than 10 ppm, matching the requirements for paleo-environmental applications. This illustrates how optical absorption methods have become a competitive alternative to state-of-the-art isotopic ratio mass spectrometry techniques.

Figure 1 .

 1 Figure 1. Experimental setup of a VCOFCRDS system. On the lefthand side is a v-shaped, evacuated cavity in a thermalized enclosure. On the right side is a CRDS-setup in a thermalized enclosure.

Figure 2 .

 2 Figure 2. Typical absorption spectrum and the corresponding fit and fit residuals. Frequency is given as detuning from 188,421,366 MHz. The standard deviation of the fit is 4.2 × 10 -12 cm -1 .

Figure 3 .

 3 Figure 3. Allan standard deviation of a typical Δ 17 O measurement series. Denoted in blue, the uncorrected data set. Denoted in orange, the same data set with a temperature gradient correction applied.

Figure 4 .

 4 Figure 4. In blue, the raw Δ 17 O values used in this study. The red curve shows the temperature gradient measured on the CRD-cell.Both curves show the rolling mean over 15 samples of the raw data. A clear correlation of both parameters becomes obvious. Note that the gradient is retrieved within two drillings inside the massive aluminum body. While this allows correcting for biases caused by temperature changes in the gas, it will be less suitable for corrections of biases introduced by affected pressure gauges or valves.

Letter DOI: 10

 10 .1021/acs.analchem.7b02853 Anal. Chem. XXXX, XXX, XXX-XXX C ■ CONCLUSION

Figure 2 . 29 :

 229 Figure 2.29: Quality parameters for four CO 2 isotopologues of interest at 20 mbar and 302.555 Kelvin. Upper plot shows the signal-to-baseline ratio, lower plot shows the isolation indicator.

2 . 2 2. 8 .

 228 Absorption line isolation from other lines 3. Signal-to-noise or signal-to-baseline ratio The temperature sensitivity refers to the relative change in the retrieved line surface due to temperature fluctuations and is linked to the originating energy level of the considered transition. Absorption line isolation is a way of estimating the influence of pressure fluctuations and interaction with other species. The lower estimation of Chapter IDENTIFICATION OF SUITABLE ABSORPTION LINES

Figure 2 . 30 :

 230 Figure 2.30: Pressure dependence of qf, qf b and Tsen for the case of 627.

Figure 2 .Figure 2 . 31 :

 2231 Figure 2.31: Temperature dependence of qf, qf b and Tsen at 20 mbar for the case of 638.

Figure 3 . 25 Figure 3 . 1 :

 32531 Figure 3.1: Upper panel: D 2 absorption line recordings normalized by amplitude, acquisition pressures are given in the legend. Lower panel: Differences towards 75 mbar spectrum.

3. 1 . D 2 MEASUREMENTSFigure 3 . 2 :Figure 3 . 3 :

 123233 Figure 3.2: Fit residuals for fits of the S(2) transition of D 2 for four different spectra. The SNR after fitting reaches from 115, 2390, 4922 and 7055 for 1, 25, 50 and 75 mbar respectively for a fit with the HTP. For the NGP 115, 1688, 1236, 891 for 1, 25, 50 and 75 mbar respectively are reached. The baseline noise for those measurements was 2.6 x 10 -12 cm -1 , thus the maximum attainable SNR would be 125, 2702, 5450, 8262.

3. 1 . D 2 MEASUREMENTSFigure 3 . 4 :

 1234 Figure 3.4: Residuals folded at line center for fits at 75 mbar. Upper panel NGP, lower panel HTP. Frequency axis shows detuning from the line center. Note the four-fold zoom on the y-axis between the two profiles.

Figure 3 . 5 :

 35 Figure 3.5: Upper panel: Pressure shift of the S(2) transition determined with four different fit models. Middle Panel: Line area versus pressure. Lower panel: Relative deviation of the retrieved line surfaces from the line area retrieved by HTP. HTP was used as a reference profile, since it yielded the best overall fit.

2 : 3 3. 1 . D 2 MEASUREMENTSFigure 3 . 6 : 3 3. 1 . D 2 MEASUREMENTSFigure 3 . 7 :

 23123631237 Figure 3.6: Four spectra at different pressures fitted with HTP. η has been fixed, while other parameters where let free for iteration.

3. 1 . D 2 MEASUREMENTSFigure 3 . 8 :

 1238 Figure 3.8: Pressure shift of the line center of the S(2) transition of D 2 as retrieved from fitting with an HTP profile with fixed η. In the lower panel, differences in the determined line surfaces to the one retrieve by HTP (η = 0.23987, best fit). Note the strongly non linear behavior of the full correlation case.

3. 2 .Figure 3 . 9 :

 239 Figure 3.9: R4 transition of 13 CO 2 in the 33312 03301 band, with the corresponding lamb dip. Measurement at 25 µbar.

Figure 3 . 10 :

 310 Figure 3.10: Schematic showing two transitions originating from the same lower level.

3. 3 .

 3 LAMB DIP CRDS OF HIGHLY SATURATED TRANSITIONS OF WATER NEAR 1.4 µM 3.3 Lamb Dip CRDS of highly saturated transitions of water near 1.4 µm

  used a comb-locked Lamb-dip spectrometer to determine the centers of three strong lines of acetylene near 1.54 µm with 2 kHz accuracy. Those lines have previously been measured by Madej et al.[19]. A Lamb dip center accuracy on the same order (a few kHz) was achieved by Twagirayezu et al. for more than 130 relatively weak lines of the 10110-00010 and 10101-00001 hot bands of acetylene[20].In addition of facilitating the line center determination, saturation spectroscopy allows for resolving highly blended lines. An attractive application of saturated CA-CRDS is the partial resolution of the hyperfine structure of the 17 O 12 C16 O R(0) fundamental transition near 2340 cm -1 and the measurement of the absolute frequencies of the hyperfine triplet with an accuracy of a few kHz[21]. In the present work, we use a modified version of the combassisted OFFS-CRDS setup developed by Burkart et al.[16] to accurately measure Dopplerfree saturated-absorption Lamb dips of eight water lines near 7170 cm -1 . The targeted transitions were chosen to illustrate the advantages of the system in terms of both frequency accuracy and spectral resolution. Three highly blended K-type doublets with frequency separation of a few MHz are fully resolved while they appear as single lines in Doppler regime. The 12 kHz frequency accuracy of the retrieved line centers allows discussing the quality of the line centers in the most commonly used spectroscopic database of water vapor.

Fig. 2

 2 Fig. 2Allan variance plot of a series of beat note measurements (black curve) recorded 100 times per second with 7.6 kHz FFT resolution (see text). The single shot precision is 42 kHz, due to OFC noise. The precision reaches 700 Hz after 60 s averaging, closely following the ideal t -1/2 random noise averaging (blue dashed curve). However, a bump is observed after 2 s averaging time and is attributed to noise excess in the Rubidium reference clock driving the OFC electronics. After 80 s averaging, the VCOF frequency drift is clearly visible. The effect of a 7 Hz/s drift, which is the worst expected case, is plotted (red dot line).

Fig. 4

 4 Fig. 4Ring down signal (upper panel) and corresponding exponential fit residuals (lower panel) observed at different spectral points of the line profile (see inset in Fig.3): baseline (blue), wings (green), dip center (red) and close to the maximum (orange) of the 1+3 [66 0 ← 661, 661 ← 660] line. at 7185.596 cm -1 Deviation to standard exponential (lower panel) increases with absorption. In the region of the dip, smaller residuals are observed as expected from a longer pseudo transparent regime induced by the higher effective incident optical power seen by zero z-axis velocity molecular class.

20

 20

  O Ktype doublets to the computed values of five variational calculations, from the list released by Schwenke and Partridge (SP) in 1997 up to the very recent POKAZATEL list by Polyansky et

126 Chapter 3 3. 4 .Figure 3 . 11 :

 12634311 Figure 3.11: qf and qf broad for 638 in the range covered by our laser diode.

Chapter 3 3. 4 .Figure 3 . 13 :

 34313 Figure 3.13: Region 1 and region 2 for 638 measurements at 5 and 10 mbar at a temperature of 29.405°Celsius.

Figure 3 .

 3 Figure 3.14: Allan Variance plots for Isotopologue Abundance Ratio measurements in 2 different regions. For region 1, 638/636, for region 2 638/626.

Table 1 .

 1 O 12 C 16 O with a mass of 44, but about 1 % exists in the form of the 16 O 13 C 16 O isotopologue with a mass of 45. There are twelve stable isotopologues of CO 2 , given in table 1.1. The most commonly used 12 C 17 O 7.339890 × 10 -4 44.994045 627 16 O 13 C 18 O 4.434460 × 10 -5 46.997431 638 16 O 13 C 17 O 8.2462300 × 10 -6 45.9974000 637 18 O 12 C 18 O 3.9573400 × 10 -6 47.9983220 828 17 O 12 C 18 O 1.4718000 × 10 -6 46.9982910 827 17 O 12 C 17 O 1.3684700 × 10 -7 45.9982620 727 18 O 13 C 18 O 4.4460000 × 10 -8 49.0016750 838 18 O 13 C 17 O 1.6535400 × 10 -8 48.0016460 837 17 O 13 C 17 O 1.5375000 × 10 -9 47.0016182 737

	Formula	Abundance	g × mol -1	AFGL code
	16 O 12 C 16 O 0.984204	43.989830	626
	16 O 13 C 16 O 0.011057	44.993185	636
	16 O 12 C 18 O 0.003947	45.994076	628
	16 O

1: Isotopologues of CO 2 with their relative abundances, molecular masses and AFGL codes.

Table 2 .

 2

	2.2. TECHNICAL REALIZATION
	Case Function
	1	Activate/deactivate PID
	2	Enable/disable Communication
	3	Modify K P values
	4	Modify K I values
	5	Modify K D values
	6	Modify probe offset values
	7	Modify temperature setpoints
	8	Change sampling rate
	9	Save values to EEPROM
	10	Activate/deactivate software reset (Arduino Mega only)
	11	Detect active probes
	12	Show all PID values
	13	Show offset values
	14	Read status
	15	Reinitialize DAC
	16	Modify integral value
	17	Define number of averaged samples
	18	Define probe centering resistance
	Error source	Temperature dependence Resulting T-drift
	Bridge resistances	10 ppm/°K	94.9 ppm/°K
	ADC gain		2 ppm/°K	-1.2 ppm/°K
	ADC offset drift	1 × 10 -6 V/°K	25.6 ppm/°K
	Voltage reference error 4 ppm/°K	0 ppm/°K

1: Callable functions of the micro-controller based PID board.

Table 2 .

 2

2: Error budget for the Wheatstone bridge circuit boards used in the temperature stabilization system.

Table 2 .

 2 3: Main absorption lines used in this thesis.

	2.6. FITTING AND DATA TREATMENT

28 cm -1 , we fit twelve CO 2 absorption lines. The lines are grouped by species, with each group driven by the corresponding main line. Additionally, one line outside the region is adjusted in amplitude proportionally to retrieved values inside the fitted region for the same species. Moreover, the positions of all absorption lines are fixed relative to the strongest

  gives an indication if the regulation has entered a potentially effusive state (see section 2.2.2).

	ISOTOPOLOGUE ABUNDANCE RATIOS IN CO 2 USING MOLECULAR ABSORPTION SPECTROSCOPY: APPLICATION TO ∆ 17 O 2.7 Publication 1: Direct, Precise Measurements of Isotopologue Abundance Ratios in CO 2 Us-ing Molecular Absorption Spectroscopy: Ap-Chapter 2 2.7. PUBLICATION 1: DIRECT, PRECISE MEASUREMENTS OF plication to ∆ 17 O

Table 2 .

 2 • C and 29.405 • C. A temperature reduction of 109.405 • C, improves the isolation by more than a factor of five. The qf increases about eightfold. There is a trade-off to be made, since the decreased temperature increases the temperature sensitivity of some lines up to 10-fold. Correlated with their total an-4: Best Lines for 627, 628, 636, 638 and 637 found in reach of available diodes at 20 mbar and 302.555 Kelvin.

	Iso.	Freq.	LQNup peak absorption	qf	qf br T. sens.
	627 6279.04125 cm -1	P23e	1.23 x 10 -7 cm -1 900 111	0.50
	627 6284.34666 cm -1	P17e	1.41 x 10 -7 cm -1 650	90	0.63
	627 6285.20846 cm -1	P16e	1.42 x 10 -7 cm -1 238	31	0.65
	628 6272.86709 cm -1	R27e	4.72 x 10 -7 cm -1 6930 431	0.39
	628 6269.93145 cm -1	R22e	2.99 x 10 -8 cm -1 5669 258	0.53
	636 6266.52904 cm -1	R34f	1.02 x 10 -7 cm -1 551	90	0.88
	636 6267.28360 cm -1	R42e	9.86 x 10 -7 cm -1 1258 87	0.23
	638 6718.41520 cm -1	P12e	3.08 x 10 -8 cm -1 590	82	0.72
	638 6713.56354 cm -1	P17e	2.99 x 10 -8 cm -1 132	41	0.65
	638 6708.29510 cm -1	P22e	3.12 x 10 -8 cm -1 332	38	0.54
	637 6717.02370 cm -1	P34e	2.37 x 10 -9 cm -1	31	4	0.16

Table 2 .

 2 5: Best regions for multi-isotope analysis in the reach of available diodes.

	2.8. IDENTIFICATION OF SUITABLE ABSORPTION LINES
	Isotopes	Spectral Region	total qf b
	626, 636, 638	6707.15 -6707.55 cm -1	228
	628, 627	6278.87 cm -6779.47 cm -1	232
	626, 628	6280.95 cm -6281.40 cm -1	1255

  .3, together with a comparison to Hitran transition frequencies in column 2. It becomes obvious, that Hitran values do not match our experimental

	Label Dip	∆Hitran	∆Gopher ∆Comb. Diff
	Position [cm-1]

Table 3 .

 3 4: Lower and upper level constants retrieved by combination difference fitting. H is undefined. combination fit, shown in column 3 of Table 3.3. The observed differences from the experimentally determined transition frequencies are bigger than in the global fit, 3.2. SATURATED ABSORPTION SPECTROSCOPY

  3.4. FIRST DETERMINATION OF16 O 13 C18 O ABUNDANCE examples include a study from Affek et al., who used ∆47 paleo-thermometry to derive the growth temperature from speleothems. They successfully resolved glacial/interglacial variations, well reflecting other available data from the region[START_REF] Hagit | Glacial/interglacial temperature variations in Soreq cave speleothems as recorded by 'clumped isotope'thermometry[END_REF]. Kele et al. applied the proxy to a suite of modern calcitic and aragonitic travertines and tufae to investigate possible differences in fractionation patterns, which were not found[START_REF] Kele | Temperature dependence of oxygen-and clumped isotope fractionation in carbonates: A study of travertines and tufas in the 6-95 C temperature range[END_REF]. Came et al. analyzed Silurian and Carboniferous brachiopods and mollusks to reconstruct sea-surface temperatures[START_REF] Came | Coupling of surface temperatures and atmospheric CO2 concentrations during the Palaeozoic era[END_REF]. Tripati et al. analyzed the clumped isotope composition of coccolithophores and foraminifers to reconstruct growth temperatures. Finnegan et al. as well studied marine calcifying animals to estimate paleo ocean temperatures[START_REF] Finnegan | The magnitude and duration of Late Ordovician-Early Silurian glaciation[END_REF]. Eagle et al. analyzed bio-apatite from teeth of rhinoceros, elephants, crocodiles, alligators and sharks to reconstruct their body temperature. The values they found all where in good agreement with available data, again proving the potential of clumped isotope thermometry.

  et al. explained the origin of this fractionation with the processes during acid digestion below,M CO 3 + 2H 3 P O 4 → M 2+ + 2(H 2 P O 4 ) -+ H 2 CO 3 (3.11)

  et al. proposed the following pathway 12 C 16 O 2 + 13 C 18 O 16 O → 12 C 16 O + 13 C 16 O 16 O + 18 O → 13 C 16 O 2 + 12 C 18 O 16 O (3.13)

Chapter 1

Chapter 2

Univ. Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France

LSCE, Gif-sur-Yvette, France

Acknowledgements

This work was supported by the Agence Nationale de la Recherche (Grant ANR-13-JS060005), INSU-CNRS (LEFE/ChAt) and Labex OSUG@2020 (Grant ANR10 LABX56). We are grateful to the Universite ́ Joseph Fourier and the GRAM Equipex REFIMEVE+ for additional financial support. M.C has received funding from the European Research Council under the European Union's Seventh Framework Programme (Grant FP7/2007-2013)/RC Grant Agreement Number 306045, attributed to A. Landais (LSCE) to whom we are very indebted, since this grant also highly contributed to the experimental developments of the present setup, dedicated to ultra-precise water spectroscopy. We thank A. A. Kyuberis and O. L. Polyansky (Institute of Applied Physics in Nizhny Novgorod) for provided us with unpublished variational position values included in Table 2. We are indebted to S.N. Mikhailenko (Institute of Atmospheric Optics, Tomsk) for valuable discussion and information about the K-type splitting in water.

Acknowledgements

Chapter 4

Bibliography

First Determination of 16 O 13 C 18 O Abundance

The primary target of this thesis was to measure isotopic ratios of CO 2 with high precision. In the following, we will describe the first determinations of 638 abundances and thus the first exciting steps towards laser based clumped isotope measurements.

∆47

"Clumped" Isotope geochemistry deals with deviations of a certain isotopic ratio from that expected from a stochastic composition [START_REF] John | Clumped-isotope" geochemistry-The study of naturallyoccurring, multiply-substituted isotopologues[END_REF]. The formation of isotopic "clumps" of rare isotopes in different materials is dependent on a variety of factors. In the case of CO 2 , the most studied clumped isotope is 16 O 13 C 18 O, used in the ∆47 paleo thermometer as proposed by Ghosh et al. [START_REF] Ghosh | 13 C-18 O bonds in carbonate minerals: A new kind of paleothermometer[END_REF]. ∆47 is defined as

where R 45* , R 16 O is typically computed based on an assumed mass dependent fractionation between 18 O and 17 O species of CO 2 . The ∆47 paleo thermometer is based on the assumption that, at thermodynamic equilibrium, the abundance of 13 C 18 O 16 O 2 -2 anion is defined by

with M being a metal, such as Ca or Mg. The equilibrium constant drives the reaction towards the right for lower temperature and approaches stochastic distributions for high-temperatures. By analyzing all involved isotopologues one can thus constrain the crystallization temperature of a given carbonate using [START_REF] Ghosh | 13 C-18 O bonds in carbonate minerals: A new kind of paleothermometer[END_REF]

The benefits of this paleo-thermometer are simple: Since it is probing a homogeneous equilibrium effect, all necessary information is contained in the mineral itself. Therefore, no assumptions as to the composition of the phase of the original carbonate are necessary. This is different for the classical δ 18 O paleo-thermometer, which strongly depends on a good knowledge of the isotopic composition of both involved phases, that is the sea-water and the carbonate. In fact, ∆47 can be used to reconstruct the δ 18 O values of seawater. Determining the temperature using the clumped isotope paleo-thermometer allows to combine the δ 18 O value of the carbonate with the known temperature fractionation [36,[START_REF] Morden | On the isotopic chemistry of carbonates and a paleotemperature scale[END_REF][START_REF] Kim | Equilibrium and nonequilibrium oxygen isotope effects in synthetic carbonates[END_REF] between water and carbonates and thus reconstruct the δ 18 O value of the parent water. This proxy has been applied to a variety of geoscientific subjects by now. Some In region 1, we used the ratio 638/636 as a test case. In region 2, we used the ratio 638/626 as a test case. In region 1 we needed to fit one strong water absorption line, which translate to a water concentration of 50 ppm. Figure 3.14 shows the performance of this preliminary experiment in the two different regions in terms of an Allan-Variance plot. Dashed lines indicate measurements at 5 mbar, continuous lines indicate measurements at 10 mbar.

In both cases, the measurements were limited in precision by the determination of 638. The precision on the 638 abundance determination at 5 mbar was 420 and 400 ppm for region 1 and region 2, respectively. For region 1, the precision on 636 was 202 ppm. For region 2, the precision on 626 was 203 ppm. The one-spectrum precision on 638/626 and 638/636, respectively, has been evaluated to 280 ppm and 309 ppm for region 1 and region 2, respectively. Thus, the ratio noise is lower than the sum of the noise from the two absorption line measurements. This is because common noise cancels out in ratio computation. For the measurements at 10 mbar the precision was roughly expected to be two-fold better. However, the one spectrum precision was found to be 146 ppm and 206 ppm. While region one is therefore very close to the expectations, region 2 performs significantly worse than expected. In fact, this is due to an uncorrected drift of the measurement cavity. It should be noted, that for all current clumped isotope measurements no temperature correction was applied. For the 10 mbar measurement of region 1, two spectral intervals with strong temperature drifts were therefore omitted. Those regions could be corrected for by applying a suitable temperature correction.

Chapter 4