D Ventrillard

A Romanini

Campargue

L Richard

D Mondelain

S Kassi

I Ventrillard

D Romanini

A Campargue
email: alain.campargue@univ-grenoble-alpes.fr

Collision-induced absorption and electric quadrupole transitions of N2 by OF-CEAS near 4.0 µm and CRDS near 2.1 µm

Keywords: Nitrogen, N 2, dinitrogen, Collision Induced Absorption, CIA, electric quadrupolar transitions, CRDS, OF-CEAS

Introduction

The absorption of light by dinitrogen, N 2 , is very weak. Being a homonuclear diatomic molecule, 14 N 2 has no dipole-allowed vibrational bands and its rovibrational infrared spectrum consists of extremely weak quadrupolar bands formed of rotational lines following the ∆J= 0, ±2 selection rules (where J is the rotational quantum number) [START_REF] Goldman | Identification of electric quadrupole O 2 and N 2 lines in the infrared atmospheric absorption spectrum due to the vibration-rotation fundamentals[END_REF][START_REF] Camy-Peyret | Quadrupole transitions of the 1<-0 band of N 2 observed in a high resolution atmospheric spectrum[END_REF][START_REF] Reuter | The n = 1 <-0 quadrupole spectrum of N 2[END_REF][START_REF] Rinsland | The fundamental quadrupole band of 14 N 2 : Line positions from high-resolution stratospheric solar absorption spectra[END_REF][START_REF] Kassi | First detection of transitions in the second quadrupole overtone band of nitrogen near 1.44 µm by CW-CRDS with 6×10 -13 cm -1 sensitivity[END_REF][START_REF] Li | Quadrupole moment function and absolute infrared quadrupolar intensities for N 2[END_REF]. As a consequence of their weakness, the detection of N 2 quadrupole transitions by absorption is difficult and mostly limited to the 1-0 fundamental band centered at 2250 cm -1 [START_REF] Goldman | Identification of electric quadrupole O 2 and N 2 lines in the infrared atmospheric absorption spectrum due to the vibration-rotation fundamentals[END_REF][START_REF] Camy-Peyret | Quadrupole transitions of the 1<-0 band of N 2 observed in a high resolution atmospheric spectrum[END_REF][START_REF] Reuter | The n = 1 <-0 quadrupole spectrum of N 2[END_REF][START_REF] Rinsland | The fundamental quadrupole band of 14 N 2 : Line positions from high-resolution stratospheric solar absorption spectra[END_REF]. This band, firstly reported by Goldman et al. [START_REF] Goldman | Identification of electric quadrupole O 2 and N 2 lines in the infrared atmospheric absorption spectrum due to the vibration-rotation fundamentals[END_REF] and Camy-Peyret et al. [START_REF] Camy-Peyret | Quadrupole transitions of the 1<-0 band of N 2 observed in a high resolution atmospheric spectrum[END_REF] from long path atmospheric spectra, is now routinely observed and modeled in the atmospheric spectra recorded by Fourier Transform Spectroscopy (FTS) in the frame of the Total Carbon Column Observing Network (TCCON) [START_REF]Total Carbon Column Observing Network[END_REF].

Fig. 1 Overview of the N 2 room temperature absorption between 2000 and 5000 cm -1 as provided by the HITRAN2016 database [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF][START_REF] Richard | New section of the HITRAN database: Collision-induced absorption (CIA)[END_REF].

Upper panel: Quadrupolar electric transitions of the fundamental and first overtone bands of 14 N 2 [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF].

The 2-0 S [START_REF] Richard | New section of the HITRAN database: Collision-induced absorption (CIA)[END_REF] and S [START_REF] Čermák | First detection of an absorption line of the first overtone electric quadrupolar band of N 2 by CRDS near 2.2µm[END_REF] electric quadrupole transitions measured in this work are highlighted (red circles) together with the 2-0 O [START_REF] Shapiro | The collision-induced fundamental and first overtone bands of oxygen and nitrogen[END_REF] transitions measured by CRDS in Ref. [START_REF] Čermák | First detection of an absorption line of the first overtone electric quadrupolar band of N 2 by CRDS near 2.2µm[END_REF] (green circle).

Lower panel: Collision Induced Absorption bands as provided in the HITRAN database [START_REF] Richard | New section of the HITRAN database: Collision-induced absorption (CIA)[END_REF]. The HITRAN data are derived from the experimental results by Baranov and Lafferty for the fundamental band [START_REF] Baranov | Investigation of collisioninduced absorption in the vibrational fundamental bands of O 2 and N 2 at elevated temperatures[END_REF] and from results of classical molecular dynamics simulations (CMDS) for the first overtone [START_REF] Hartmann | Collision-induced absorption by N 2 near 2.16 µm: Calculations, model, and consequences for atmospheric remote sensing[END_REF]. The dashed lines indicate the spectral points of the measurements reported in this work.

In fact, in the atmosphere of Earth and of other bodies in the Solar System (e.g. Titan or Triton), most of the N 2 absorption is not due to quadrupolar bands but to the collision-induced absorption (CIA) bands. The CIA bands result from the transient dipole moment induced by collisions of N 2 molecules with N 2 (and O 2 , in our atmosphere) and thus scale as the product of the densities of N 2 and of the collisional partner [START_REF] Frommhold | Collision-Induced Absorption in Gases[END_REF]. Fig. 1 shows an overview of the fundamental and first overtone quadrupolar bands of N 2 together with their corresponding N 2 -N 2 CIA bands, as provided by the HITRAN spectroscopic database [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF][START_REF] Richard | New section of the HITRAN database: Collision-induced absorption (CIA)[END_REF].

The laboratory measurement of the very weak nitrogen CIA bands is made difficult because of the weakness of the signal to be detected as a small and spectrally broad depletion of the light intensity transmitted through an absorption cell containing the gas The maximum of absorption for the fundamental and first overtone CIA are on the order of 10 -6 and 10 -8 cm -1 /amagat 2 , respectively. A few previous works have been devoted to the N 2 -N 2 CIA bands [START_REF] Baranov | Investigation of collisioninduced absorption in the vibrational fundamental bands of O 2 and N 2 at elevated temperatures[END_REF][START_REF] Shapiro | The collision-induced fundamental and first overtone bands of oxygen and nitrogen[END_REF][START_REF] Menoux | Collision-induced absorption in the fundamental band of N2: temperature dependence of the absorption for N 2 -N 2 and N 2 -O 2 pairs[END_REF][START_REF] Lafferty | Infrared collision-induced absorption by N 2 near 4.3 µm for atmospheric applications: measurements and empirical modeling[END_REF][START_REF] Mckellar | Low-temperature infrared absorption of gaseous N 2 and N 2 + H 2 in the 2.0-2.5 µm region: Application to the atmospheres of Titan and Triton[END_REF] (see Table 1). Spectra were recorded with grating spectrographs or by FTS associated with high pressure multipass cells. Pressure values up to 90 atm [START_REF] Shapiro | The collision-induced fundamental and first overtone bands of oxygen and nitrogen[END_REF] were used to enhance the CIA signal (proportional to the pressure-squared).

In support of planetary studies, the temperature dependence of the CIAs was also investigated at 97.5 K [START_REF] Mckellar | Low-temperature infrared absorption of gaseous N 2 and N 2 + H 2 in the 2.0-2.5 µm region: Application to the atmospheres of Titan and Triton[END_REF].

In the present contribution, we use highly sensitive laser techniques to measure N 2 -N 2 CIA around two spectral points of the fundamental and first overtone bands. The measurement points located near 2492 and 4720 cm -1 are indicated on the bottom of Fig. 1. The used laser absorption techniques, namely, Optical Feedback Cavity Enhanced Absorption Spectroscopy (OF-CEAS) and Cavity Ring Down Spectroscopy (CRDS), are based on the coupling of laser sources and high finesse optical cavities containing the gas. Although much more limited than FTS in terms of spectral coverage, these techniques are inherently much more sensitive. Our recent accurate characterization of the water vapor absorption continuum by OF-CEAS and CRDS in the 4.0, 2.3, 1.6 and 1.25 µm windows [START_REF] Ventrillard | Accurate measurements and temperature dependence of the water vapor self-continuum absorption in the 2.1 µm atmospheric window[END_REF][START_REF] Campargue | Accurate laboratory determination of the near infrared water vapor self-continuum: A test of the MT_CKD model[END_REF][START_REF] Richard | Water vapor self-continuum absorption measurements in the 4.0 and 2.1 µm transparency windows[END_REF][START_REF] Lechevallier | The water vapour self-continuum absorption in the infrared atmospheric windows: new laser measurements near 3.3 and 2.0 µm[END_REF] and of the O 2 CIA near 1.27 µm [START_REF] Mondelain | Accurate laboratory measurement of the O 2 collision-induced absorption band near 1.27 µm[END_REF], have shown that the performances in terms of sensitivity and spectra baseline stability make these techniques ideal to study weak broad band continua. In the following, the first measurements of the N 2 CIA at sub-atmospheric pressures are presented. In the two next sections, the spectra acquisition, the continuum retrieval and a comparison to previous experimental and theoretical results are presented for each of the two spectral points. In Section 4, the detection of the 2-0 S [START_REF] Richard | New section of the HITRAN database: Collision-induced absorption (CIA)[END_REF] and S [START_REF] Čermák | First detection of an absorption line of the first overtone electric quadrupolar band of N 2 by CRDS near 2.2µm[END_REF] electric quadrupole transitions is reported and the derived line parameters are compared to the values provided by the HITRAN database.

OF-CEAS of the CIA fundamental band at 2491 cm -1

OF-CEAS is a quantitative and highly sensitive laser absorption technique, alternative to CRDS, routinely applied to trace gas measurements [START_REF] Morville | Two schemes for trace detection using cavity ringdown spectroscopy[END_REF][START_REF] Morville | Cavity Enhanced Absorption Spectroscopy with Optical Feedback[END_REF]. OF-CEAS has specific advantages which make it particularly suitable for the measurement of absorption continua. OF-CEAS exploits optical feedback toward the diode laser source selectively produced only at cavity resonances allowing optimized cavity injection by the laser radiation. This is possible thanks to the adopted V-geometry of the high-finesse optical cavity. OF-CEAS is able to generate several spectral scans per second of a narrow spectral region (~1 cm -1 ). The acquired spectra have an intrinsically linear frequency scale with equally spaced spectral points separated by the cavity Free Spectral Range FSR=c/2nL, where c is the speed of light, L the effective cavity length, and n the refractive index of the intra-cavity sample.

The OF-CEAS setup used in this work is similar to that used for water vapor self-continuum measurements [START_REF] Ventrillard | Accurate measurements and temperature dependence of the water vapor self-continuum absorption in the 2.1 µm atmospheric window[END_REF][START_REF] Richard | Water vapor self-continuum absorption measurements in the 4.0 and 2.1 µm transparency windows[END_REF]. The reader is referred to Ref. [START_REF] Ventrillard | Accurate measurements and temperature dependence of the water vapor self-continuum absorption in the 2.1 µm atmospheric window[END_REF] (in particular, its Fig. 1) for a detailed description of the experimental setup. Here, an Interband Cascade Laser (ICL) emitting around 2491 cm -1 , designed by Nanoplus GmbH, is used as the light source. The V-shaped cavity with 6 mm apex diameter cavity is made in a thick stainless steel block drilled from side to side. Each arm of the Vcavity has a length of about 399.6+/-0.4 mm resulting in an effective length of ~800 mm and a FSR= 187.56+/-0.10 MHz. At the laser wavelength, the reflectivity of the cavity mirrors (from LohnStar Optics) is 99.981 %, as deduced from a ring-down time of 6.95 µs measured with evacuated cavity (filled with Ar). Scans over ~1.5 cm -1 (~45 GHz) were produced by modulation of the laser current.

The duration of one spectral scan corresponding to about 240 cavity modes (FSR) was about 200 ms.

By using heating tapes along the cavity and platinum thermistors, the cavity temperature can be controlled between room temperature and about 325 K. Two series of measurements were performed at 295.8 and 315.5 K (22.7°C and 42.4 °C, respectively).

Let us recall that in OF-CEAS, the transmission spectra is converted to loss rate spectra from a measurement of the ring down time (τ) at the last mode of the laser scan [START_REF] Morville | Cavity Enhanced Absorption Spectroscopy with Optical Feedback[END_REF]. In order to average the scan-to-scan fluctuation of the τ values, an averaged value was determined with an accuracy of 0.2 % from about 800 measurements at fixed pressure value.

A series of about 15000 spectra was recorded during a pressure ramp with total duration between 10 and 12 minutes. The N 2 flow was injected inside the cavity through a needle valve. A pressure controller (IQ+Flow, from Bronkhorst) was placed between the cavity's outlet and the pump to generate pressure ramps between 80 and 1000 mbar. The pressure was monitored at the cavity center by a pressure gauge (CPG2500, from Mensor, 0-1000 mbar) with an accuracy better than 0.5 mbar. Fig. 2 illustrates the increase of the baseline level of the OF-CEAS spectra during pressure ramps recorded at temperature of 295.8 and 315.5 K. A pure pressure-squared dependence is obtained at the two temperatures. As a test of the mechanical stability of the OF-CEAS setup, N 2 was replaced by Ar and spectra were recorded in the same experimental conditions. As shown in Fig. 2, no significant variation of the baseline level was obtained with argon up to 1 atm.

If we consider the general case of an N 2 /O 2 mixture, total losses, ( )

T tot , ν α
, are the sum of the cavity losses and of the N 2 CIA:

( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 , , , , , , 2 N O O N N N N cav CIA cav tot T B T B T T T T ρ ρ ν ρ ν ν α ν α ν α ν α - - + + = + = (1)
Where:

-

( ) T cav , ν α
corresponds to the losses of the cavity evacuated (or filled with Ar), ρ i are N 2 and O 2 densities (in amagat) proportional to the partial pressure versus P 2 (Fig. 2). The corresponding values are given in Table 2 for the measurements at 22.7°C and 42.4 °C.

Table 2.

Binary coefficients of the 1-0 and 2-0 CIA bands of N 2 derived by OF-CEAS and CRDS near the 2491 and 4720 cm -1 spectral points.

Measurement point (cm -1 ) The temperature dependence of the CIA is needed for applications to the Earth and planetary atmospheres. As discussed in Richard et al. [START_REF] Richard | New section of the HITRAN database: Collision-induced absorption (CIA)[END_REF] and summarized in Table 1, Lafferty et al. [START_REF] Lafferty | Infrared collision-induced absorption by N 2 near 4.3 µm for atmospheric applications: measurements and empirical modeling[END_REF] and Baranov et al. [START_REF] Baranov | Investigation of collisioninduced absorption in the vibrational fundamental bands of O 2 and N 2 at elevated temperatures[END_REF] reported FTS measurements of the 1-0 CIA in the 230-300 K and 300-360 K temperature ranges, respectively. Fig. 3 shows the obtained variation of the 2 2 N N B -coefficient at 2491 cm -1 together with our values at 295.8 and 315.5 K. Due to the high pressure of the recordings (up to 8 atm), the FTS values were reported with small error bars on the order of 1%. This is significantly better than the uncertainty of our OF-CEAS values which is estimated to be on the order of 5%. The agreement within a few % between the FTS and OF-CEAS results provide a mutual validation of CIA measurements performed in very different pressure conditions.

2 2 N N B -(cm -1 amagat -2 ) 2 2 O N B -(cm -1 amagat -2 ) T(K)
As part of their analysis of the temperature dependence the 1-0 CIA, Lafferty et al. provided an empirical modeling of their CIA measurements between 230 and 300 K [START_REF] Lafferty | Infrared collision-induced absorption by N 2 near 4.3 µm for atmospheric applications: measurements and empirical modeling[END_REF]. The wavenumber and temperature dependences of the 2 2 N N B -binary coefficient was modeled by using a simple empirical law:

( ) )] / 1 / 1 )( ( exp[ ) ( , 0 0 0 2 2 T T B T B N N - = - ν β ν ν (2)
where T 0 = 296 K is the reference temperature and B 0 and β 0 are frequency dependent parameters which were provided with a 5 cm -1 step between 2125 and 2600 cm -1 [START_REF] Lafferty | Infrared collision-induced absorption by N 2 near 4.3 µm for atmospheric applications: measurements and empirical modeling[END_REF]. The corresponding curves have been included in Fig. 3 for our measurement point at 2491 cm -1 and for the 2300, 2400 and 2450 cm -1 wavenumbers. For the experimental values of the B -values in the 300-390 K range as reported by Baranov et al [START_REF] Baranov | Investigation of collisioninduced absorption in the vibrational fundamental bands of O 2 and N 2 at elevated temperatures[END_REF] (and included in the HITRAN database) are also plotted in Fig. 3 while they were not considered in the fit of B 0 and β 0 . On the basis of Fig. 3, it appears that the empirical law with the B 0 and β 0 values taken in Table 1 of Ref. [START_REF] Lafferty | Infrared collision-induced absorption by N 2 near 4.3 µm for atmospheric applications: measurements and empirical modeling[END_REF] does not correspond to the best fit of the experimental data of Lafferty et al. [START_REF] Lafferty | Infrared collision-induced absorption by N 2 near 4.3 µm for atmospheric applications: measurements and empirical modeling[END_REF] (as provided by the HITRAN database). This is particularly clear at 2300 cm -1 and at our spectral point near 2491 cm -1 . We do not have any explanation for this situation. As expected the extrapolation of the empirical law to the high temperature range studied by Baranov [START_REF] Lafferty | Infrared collision-induced absorption by N 2 near 4.3 µm for atmospheric applications: measurements and empirical modeling[END_REF] below 300 K and Baranov et al. [START_REF] Baranov | Investigation of collisioninduced absorption in the vibrational fundamental bands of O 2 and N 2 at elevated temperatures[END_REF] above 300 K (filled and open symbols, respectively) are displayed together with our two measurements points (295.8 and 315.5 K) at 2491 cm -1 (red stars). The curves correspond to an empirical law with fitted parameters from Lafferty et al. [START_REF] Lafferty | Infrared collision-induced absorption by N 2 near 4.3 µm for atmospheric applications: measurements and empirical modeling[END_REF] and Sioris et al. [START_REF] Sioris | Retrieval of carbon dioxide vertical proles from solar occultation observations and associated error budgets for ACE-FTS and CASS-FTS[END_REF] (solid and dashed lines, respectively).

Finally, let us mention that a series of spectra was recorded using a 1:1 mixture of O 2 and N 2 .

The continuum absorption coefficient varies linearly with the total pressure and is about half than for pure nitrogen (see Fig. 3), indicating that the value of the [START_REF] Ventrillard | Accurate measurements and temperature dependence of the water vapor self-continuum absorption in the 2.1 µm atmospheric window[END_REF]. From their spectra recorded using high pressure samples (N 2 density of 5.5 and 9.5 amagat), Menoux et al. found that the relative efficiency of the colliding partners O 2 and N 2 is practically independent of the wavenumber over the 2150-2500 cm -1 region and derived a 0.83(2) value for the ratio of the binary coefficients [START_REF] Menoux | Collision-induced absorption in the fundamental band of N2: temperature dependence of the absorption for N 2 -N 2 and N 2 -O 2 pairs[END_REF]. Although obtained with larger error bar, our low pressure measurement confirms the results of Ref. [START_REF] Menoux | Collision-induced absorption in the fundamental band of N2: temperature dependence of the absorption for N 2 -N 2 and N 2 -O 2 pairs[END_REF].

CRDS of the CIA first overtone near 4720 cm -1

Measurements

The CRDS technique is based on the measurement of the decay time (ring down) of the light intensity leaking from a high finesse cavity [START_REF] Morville | Cavity Enhanced Absorption Spectroscopy with Optical Feedback[END_REF][START_REF] Romanini | CW cavity ring down spectroscopy[END_REF][START_REF] Kassi | Cavity ring-down spectroscopy with 5×10 -13 cm -1 sensitivity[END_REF]. Under vacuum, the ring down time,τ 0 , is determined by the reflectivity of the high reflectivity mirrors (e.g. R≈1-10 -5 ) and can reach several hundred µs (about 150 µs in the present work). In presence of an intracavity gas, additional losses shorten the ring down time,τ, i.e. increase the loss rate, 1/cτ. The absorption coefficient at the wavenumber,ν, is therefore obtained from the variation of the loss rate:

( ) ( ) ( ) ν τ ν τ ν α 0 1 c c n - = (3)
where 1/cτ 0 is the loss rate of the empty cavity related to the mirrors reflectivity. The broadband CIA absorption is deduced from a weak increase of the CRDS spectrum baseline. Because an optical misalignment may affect the ring down time, we paid a particular attention to the long term mechanical stability of the assembly under pressure variations and gas handling. Our recent characterizations of the weak water vapor absorption continuum by CRDS in three infrared transparency windows [START_REF] Campargue | Accurate laboratory determination of the near infrared water vapor self-continuum: A test of the MT_CKD model[END_REF][START_REF] Richard | Water vapor self-continuum absorption measurements in the 4.0 and 2.1 µm transparency windows[END_REF][START_REF] Lechevallier | The water vapour self-continuum absorption in the infrared atmospheric windows: new laser measurements near 3.3 and 2.0 µm[END_REF] have illustrated the performances of the present method with distributed feedback (DFB) laser diodes and an external cavity diode laser (ECDL).

The reader is referred to Refs. [START_REF] Čermák | First detection of an absorption line of the first overtone electric quadrupolar band of N 2 by CRDS near 2.2µm[END_REF][START_REF] Mondelain | The self-and foreignabsorption continua of water vapor by cavity ring-down spectroscopy near 2.35 µm[END_REF][START_REF] Cermák | CRDS with a VECSEL for broad-band high sensitivity spectroscopy in the 2.3 µm window[END_REF] for a description of the CRDS spectrometer dedicated to atmospheric species studies in the 2.3 µm region. A DFB diode laser (8 mW maximum power from Eblana Photonics) is used as light source. Its emission line width is narrowed by applying an optical feedback from an external cavity, as described in [START_REF] Lin | Long-external-cavity distributed Bragg reflector laser with sub-kilohertz intrinsic linewidth[END_REF]. This improves the coupling of the laser to the CRD high finesse cavity and therefore enhances the ring down signal quality. An acoustooptic modulator (AOM), used on first diffraction order, is used to interrupt the injection and initiate the ring-down events. The frequency of the DFB laser diode is continuously monitored with a wavelength meter (model 621-A IR from Bristol, 8 MHz accuracy).

The CRDS cell was filled with either pure Ar (Air Liquide, 99.999% purity), pure N 2 (Air Liquide, 99.9999% purity) or with a reference mixture of O 2 +N 2 with an O 2 relative concentration of 20.965±0.022% (1σ) (Air Liquide; O 2 +N 2 >99.9999%). Pressure was continuously monitored with a 1000 mbar pressure gauge (ATM.1ST from STS, accuracy of ±0.1% of the full scale). The cell temperature was monitored with a TSic 501 sensor (from IST-AG; 0.1 K accuracy) fixed on the cell surface, covered by an external blanket of thermal insulation foam.

Similarly to the OF-CEAS experiments described above for the 1-0 CIA band, our water vapor continuum measurements by CRDS were mostly based on ring-down times measured at fixed optical frequency, during upward and downward pressure ramps [START_REF] Campargue | Accurate laboratory determination of the near infrared water vapor self-continuum: A test of the MT_CKD model[END_REF][START_REF] Richard | Water vapor self-continuum absorption measurements in the 4.0 and 2.1 µm transparency windows[END_REF][START_REF] Lechevallier | The water vapour self-continuum absorption in the infrared atmospheric windows: new laser measurements near 3.3 and 2.0 µm[END_REF]. This was possible because the amplitude of the pressure ramp was at most 20 mbar but, in the present case, N 2 CIA measurements require a pressure range of 1 atm which may modify the optical alignment of the experimental setup.

Therefore, an alternative approach, similar to the one adopted for the CIA of O 2 at 1.27 µm [START_REF] Mondelain | Accurate laboratory measurement of the O 2 collision-induced absorption band near 1.27 µm[END_REF], was preferred. The CRDS spectra were recorded over the 4715-4726 cm -1 spectral interval accessible with the DFB laser diode at disposal. The duration of spectra recording being limited to a few minutes, desorption of water from the CRDS cell is limited and spectra could be acquired in static regime at 500, 700 and 750 Torr for pure N 2 and at 750 Torr for the N 2 -O 2 mixture. To obtain the baseline and to minimize possible changes of mirrors alignment, spectra were also recorded with argon at the same pressures. For each pressure step the same sequence was adopted: recordings of two N 2 spectra followed by two argon spectra and then again by two N 2 spectra. Between the N 2 and argon spectra the cavity was evacuated. The four N 2 spectra series allowed assessing the baseline stability over time and pumping/filling cycle.

An overview of the N 2 recordings is presented in Fig. 4. together with the corresponding Ar recordings. The spectra at pressures of 500 and 750 Torr, shown in Fig. 4, reveal a quasi-doubling of the continuum amplitude. Due to relatively strong water vapor transitions in the region (intensities on the order of 10 -24 cm/molecule), a number of absorption lines are detected in the spectra. The water vapor relative concentration was estimated to be around 25 ppm and 80 ppm in the N 2 spectra and Ar spectra, respectively. Note the smaller pressure broadening of the water lines in Ar compared to N 2 .

Fig. 4.

Frequency dependence of the loss rates measured by CRDS between 4716 and 4726 cm -1 for pure N 2 at 500 and 750 Torr and argon (at 500 Torr). Absorption lines due to water vapor present as an impurity at the 25 ppm and 80 ppm level for N 2 and Ar, respectively, are observed. The solid curves (red and blue for N 2 and Ar, respectively) correspond to the fit of the water line contribution which was subtracted to get the spectra baseline.

To obtain the spectra baseline, the contribution of the water vapor lines was first reproduced using a multiline fitting program and a Voigt function for the line profile. After subtraction of the lines contribution, small losses due to the Rayleigh scattering were considered. Rayleigh scattering crosssections of Ar and N 2 are close [START_REF] Thalman | Rayleigh scattering cross-section measurements of nitrogen, argon, oxygen and air[END_REF] leading to a difference (proportional to pressure) on the order of 6.8×10 -11 cm -1 at 750 Torr. This small effect -the CIA amplitude at 700 Torr is about 7×10 -9 cm -1 -was taken into account in the subtraction of the Ar baselines from the N 2 baselines at the same pressure.

The resulting difference is the CIA absorption coefficient, B -binary coefficients is due to the baseline stability of the spectra which is uncertainty, the overall uncertainty on is estimated to be 1.4×10 -9 cm -1 amagat -2 (i.e. ~30 % relative error).

( ) ( ) 2 2 2 2 , , N N N CIA T B T ρ ν ν α - = . The

Fig. 6

Comparison of the room temperature binary coefficients of the 2-0 CIA of N 2 obtained by classical molecular dynamics simulations (CMDS) (blue line) [START_REF] Hartmann | Collision-induced absorption by N 2 near 2.16 µm: Calculations, model, and consequences for atmospheric remote sensing[END_REF] to the CRDS measurements between 4715 and 4726 cm -1 . The cyan dots correspond to the measured spectra corrected from the contribution of the lines and of the N 2 -N 2 CIA. The red segment corresponds to the linear fit of the measured values. The binary coefficients as predicted by CMDS (grey line) are plotted for comparison.

Comparison to literature

We have gathered in Fig. 5 the few literature results available for the 2-0 CIA of N 2 . As indicated in Table 1, the only previous experimental investigation was performed in 1966 by Shapiro and Gush who used a high pressure cell associated with a grating spectrograph [START_REF] Shapiro | The collision-induced fundamental and first overtone bands of oxygen and nitrogen[END_REF]. Pressure values as high as 90 atm were used, enhancing the CIA absorption by about four orders of magnitude compared to our sub-atmospheric measurements. Our CIA values reported with 3 % error bar are about 20 % higher than these pioneering results. Although this difference is not considerable, it exceeds by a factor of 2 the 10% error bar given by Shapiro and Gush on the integrated intensity of the 2-0 CIA band.

The results of classical molecular dynamics simulations (CMDS) recently performed by

Hartmann et al. [START_REF] Hartmann | Collision-induced absorption by N 2 near 2.16 µm: Calculations, model, and consequences for atmospheric remote sensing[END_REF] are also included in Fig. 5. These calculations consider an ensemble of 10 6 N 2 molecules in interactions described by the force field taken from Ref. [START_REF] Bouanich | Site-site Lennard-Jones potential parameters for N 2 , O 2 , H 2 , CO and CO 2[END_REF]. In this approach, the absorption spectrum is obtained from a Fourier-Laplace transform of the auto-correlation function of the transition dipole moment. As illustrated in Fig. 5, a convincing agreement is achieved between CMDS results and measurements of Shapiro and Gush. In view of atmospheric applications, Hartmann et al. applied some corrections to their CMDS results in order to match the CIA measured by Shapiro and Gush at room temperature and by McKellar at 97.5 K [START_REF] Mckellar | Low-temperature infrared absorption of gaseous N 2 and N 2 + H 2 in the 2.0-2.5 µm region: Application to the atmospheres of Titan and Triton[END_REF]. A 5 cm -1 spectral shift and a linear function with temperature, 0.9 -0.00125 296 -, was applied, leading to a 10% decrease on the CDMS amplitude at 296 K. The empirically corrected CMDS CIA, very close to the results of Shapiro and Gush, is that recently recommended by the HITRAN database (see Fig. 5). We note that the application of the 0.9 empirical correction factor to the CMDS CIA leads to 20 % deviation between the HITRAN CIA and our CRDS results near 4720 cm -1 while the deviation with the original CMDS values was limited to 8 %.

In the case of the N 2 -O 2 CIA, to our knowledge, no other experimental data are available for comparison. Our mean !, coefficients show a clear decrease in the range of the studied spectral interval, in good agreement with the CMDS frequency dependence. Nevertheless, our values near 4720 cm -1 are larger by about 14 %. This deviation is similar to that obtained for the self-CIA but smaller than our estimated error bar on . Note that, in agreement with our measurements, the self-coefficients predicted by CMDS are larger than the coefficients (see Fig. 6). At our measurement point, the / ratio is about 1.59 and 1.43 for CMDS and CRDS, respectively.

The 2-0 S(10) and S(11) electric quadrupolar transitions

As illustrated in Fig. 1, the transitions of the 2-0 quadrupolar band of N 2 are extremely weak (maximum intensity around 6×10 -30 cm/molecule). They are observed with a small S/N ratio in some of the FTS atmospheric spectra recorded at high zenith angle in the frame of the TCCON [START_REF]Total Carbon Column Observing Network[END_REF][START_REF] Hartmann | Collision-induced absorption by N 2 near 2.16 µm: Calculations, model, and consequences for atmospheric remote sensing[END_REF]. To our knowledge, the only laboratory detection of a 2-0 transition is that of the O( 14) line by CRDS near 4518 cm -1 [START_REF] Čermák | First detection of an absorption line of the first overtone electric quadrupolar band of N 2 by CRDS near 2.2µm[END_REF]. By combining a feedback narrowed DFB laser diode with a passive cell tracking technique, a limit of detection of α min ~ 1.2×10 -11 cm -1 was achieved after one day of spectra averaging, allowing for the evaluation of the intensity of this line, on the order of 1.5×10 -30 cm/molecule. In the present work, we used a similar approach to measure the 2-0 S [START_REF] Richard | New section of the HITRAN database: Collision-induced absorption (CIA)[END_REF] and S( 11) transitions. Three series of spectra were recorded, at 100 Torr (68 spectra) and 200 Torr (194 spectra) around the S [START_REF] Richard | New section of the HITRAN database: Collision-induced absorption (CIA)[END_REF] transition and at 200 Torr (151 spectra) around the S(11) transition. About 16 minutes were needed to acquire each spectrum, about 2 cm -1 wide. In all cases, the spectra were recorded in flow regime to contain water vapor desorption from the cell over the long measurement period (up to 64 hours in total). The gas flow was regulated with a proportional electrovalve controlled by a software basedproportional-integral loop. The high finesse cell was filled with pure N 2 either from a tank (Air Liquide, 99.9999% purity) for the series of spectra at 200 Torr around the S(10) transition or from nitrogen evaporating of a liquid nitrogen tank in the case of the two other spectra series. The latter nitrogen source was preferred for frequency calibration of the spectra as it contains higher water vapour concentration (~350 ppm compared to a few ppm) allowing for a better calibration of the spectra.

For each spectrum the minimum detectable absorption coefficient (corresponding to the baseline noise) was typically 1.2×10 -10 cm -1 , mostly limited by interference fringes. The wavenumber scale of the spectrum, obtained from the wavelength meter (model 621-A IR from Bristol, 8 MHz accuracy), was refined by fitting water transitions in every single spectrum. The 5 2 3 -6 1 6 and 3 0 3 -2 1 2 transitions of the 3ν 2 band of H 2 16 O at 4716.7788 and 4725.4166 cm -1 , respectively, were selected as reference position for the calibration of the S [START_REF] Richard | New section of the HITRAN database: Collision-induced absorption (CIA)[END_REF] and S( 11) spectra, respectively. The former is given in HITRAN 2016 with an uncertainty better than 1×10 -4 cm -1 and an air pressure shift of -0.0018 cm -1 atm -1 . The position of the latter has a uncertainty of 1×10 -3 cm -1 and a pressure shift of -0.0035 cm -1 atm -1 . For each recorded spectrum, the centers of the H 2 16 O and N 2 lines were determined using a multiline fit with a Voigt profile as line shape having Gaussian width fixed according to molecular mass and cell temperature. The differences between the HITRAN and fitted positions of the reference line, including pressure shift, were subsequently fitted against spectrum rank number -i.e. relative to time -by a second order polynomial smoothing the noisy and slow wavemeter calibration drift. This polynomial was used to recalibrate the individual spectra. To improve the signal to noise, the calibrated spectra series was then averaged. The procedure consisted in binning data points falling within a determined slice of the spectrum. The mean wavenumber and mean absorption coefficient were computed for every spectral bin. Bin widths of 2×10 -3 cm -1 were adopted. In an individual spectrum, the number of ring down measurements corresponding to a given spectral bin was around 50. As a result, for example, each bin of the averaged spectrum around the S(11) transition corresponds to the statistical averaging of about 7500 ring down measurements. Figs. 7 and8 illustrate the gain achieved by averaging. Minimum detectable absorption coefficients, α min , down to 8×10 -12 cm -1 and 1.1×10 -11 cm -1 were achieved around the S [START_REF] Richard | New section of the HITRAN database: Collision-induced absorption (CIA)[END_REF] and S [START_REF] Čermák | First detection of an absorption line of the first overtone electric quadrupolar band of N 2 by CRDS near 2.2µm[END_REF] lines at 200 Torr, leading to signal to noise ratios of 110 and 40, respectively.

Positions and intensities of the S [START_REF] Richard | New section of the HITRAN database: Collision-induced absorption (CIA)[END_REF] and S [START_REF] Čermák | First detection of an absorption line of the first overtone electric quadrupolar band of N 2 by CRDS near 2.2µm[END_REF] transitions, retrieved from a multiline fit of the final calibrated and averaged spectra, are reported in Table 3. The line profile fit of the S(10) line at 200 Torr is included in Fig. 7.

The uncertainties on the fitted positions, reported in Table 3, are mainly due to the very large uncertainty on the pressure shifts (±0.01 cm -1 atm -1 ) provided in the HITRAN database for the two water reference lines. Note that for the S(10) 2-0 transition for which spectra recorded at 100 Torr and 200 Torr are at our disposal, the extrapolation at zero pressure of the position difference between N 2 and water reference line centers is not affected by the uncertainty on the pressure shifts (see Ref. [START_REF] Čermák | First detection of an absorption line of the first overtone electric quadrupolar band of N 2 by CRDS near 2.2µm[END_REF]).

The S(10) 2-0 line center extrapolated at zero pressure is given as a note of Table 3. Finally, as a validation of the obtained calibration, let us mention that the water lines near 4716.131 cm -1 and 4717.474 cm -1 located near the S( 10) transition (Fig. 7), have their fitted positions within 0.001 cm -1 from the HITRAN positions (known at ±0.001 cm -1 ) even though they were not used for calibration of the spectra.

During the recording of a series of spectra, the temperature can vary over 0.8 K, nevertheless the impact on the intensity is limited due to the very low sensitivity of these N 2 lines to the temperature: 0.02% and 0.09% per Kelvin for the S [START_REF] Richard | New section of the HITRAN database: Collision-induced absorption (CIA)[END_REF] and S( 11) line, respectively. Even if pressure is stabilized, fluctuations on the order of 0.6% are observed during the tens of hours of the recordings, impacting the intensity determination at the same level. Taking into account the signal to noise ratios, uncertainties on the integrated intensities are estimated to be in the 6-10 % range for the two transitions depending of the pressure (see Table 3). The CRDS measurement points were gathered within 2×10 -3 cm -1 wide bins (see Text). The line at 4716.7788 cm -1 due to water (present as an impurity) was used as reference for the frequency calibration of the CRDS spectra.

Lower panel: Line profile fit of the N 2 line using a Voigt profile. The residuals of the fit reach the noise level corresponding to a minimum detectable absorption of 8×10 -12 cm -1 . Fig. 8. Spectra around the S(11) 2-0 transition of N 2 averaged from 151 single spectra with 2×10 -3 cm -1 bins. The H 2 16 O line near 4725.4166 cm -1 (3 0 3 -2 1 2 of the 3ν 2 band) was used as reference for the absolute calibration of the frequency axis. A minimum detectable absorption of 1.1×10 -11 cm -1 is achieved for the averaged spectrum. Note. a Extrapolation at zero pressure gives a value of 4717.1866(10) cm -1 (see Text). b Zero-pressure values. No air pressure-shift on the line position is provised in the HITRAN database [START_REF] Richard | New section of the HITRAN database: Collision-induced absorption (CIA)[END_REF] Compared to HITRAN values, the S(10) and S(11) line positions differ by -1.5×10 -3 cm -1 and -0.9×10 -3 cm -1 , respectively. A similar shift of -1.3×10 -3 cm -1 was reported in Ref. [START_REF] Morville | Two schemes for trace detection using cavity ringdown spectroscopy[END_REF] for the O( 14)

transition. The HITRAN line positions were derived from the semi-empirical potential energy function of Le Roy et al. [START_REF] Roy | An accurate analytic potential function for ground-state N 2 from a direct-potential-fit analysis of spectroscopic data[END_REF]. The observed shifts are largely within the error bars of the line positions given in HITRAN (0.01 cm -1 ). Our (scarce) dataset seems to evidence a systematic shift on the order of 1×10 -3 cm -1 , close to our accuracy on the line center determinations. HITRAN intensities of the N 2 electric quadrupolar lines were derived from the ab initio quadrupole moment function of Li and Le Roy [START_REF] Li | Quadrupole moment function and absolute infrared quadrupolar intensities for N 2[END_REF] and are given in HITRAN with a 20% uncertainty. Compared to HITRAN values, the CRDS intensities show relative differences of -7.5%, +12.0%, -10% for the S [START_REF] Richard | New section of the HITRAN database: Collision-induced absorption (CIA)[END_REF], S [START_REF] Čermák | First detection of an absorption line of the first overtone electric quadrupolar band of N 2 by CRDS near 2.2µm[END_REF] and O [START_REF] Shapiro | The collision-induced fundamental and first overtone bands of oxygen and nitrogen[END_REF] transitions, respectively. No regular trend is observed for the three measured transitions, indicating that these deviations have probably an experimental origin and that the theoretical intensities are fully validated by the present measurements.

Concluding remarks

On the basis of highly sensitivity spectra recorded by OF-CEAS and CRDS, literature data about the collision induced absorption (CIA) and very weak electric quadrupolar transitions have been tested at two spectral points of the fundamental and first overtone bands of nitrogen. Although very limited in terms of spectral coverage, these new data are found to be valuable:

(i)
The considered CIA measurements were performed for the first time at sub-atmospheric pressure allowing to check the agreement with previous high pressure measurements up to 8 atm [START_REF] Baranov | Investigation of collisioninduced absorption in the vibrational fundamental bands of O 2 and N 2 at elevated temperatures[END_REF][START_REF] Shapiro | The collision-induced fundamental and first overtone bands of oxygen and nitrogen[END_REF][START_REF] Lafferty | Infrared collision-induced absorption by N 2 near 4.3 µm for atmospheric applications: measurements and empirical modeling[END_REF] and 90 atm [START_REF] Shapiro | The collision-induced fundamental and first overtone bands of oxygen and nitrogen[END_REF] for the 1-0 and 2-0 bands, respectively. The pure quadratic dependence of the CIA amplitude was carefully checked during pressure ramps up to 1 atm and from series of spectra recorded at different pressures, for the 1-0 and 2-0 measurement points, respectively.

(ii) A good agreement with the results of Lafferty et al. [START_REF] Lafferty | Infrared collision-induced absorption by N 2 near 4.3 µm for atmospheric applications: measurements and empirical modeling[END_REF] and Baranov et al. [START_REF] Baranov | Investigation of collisioninduced absorption in the vibrational fundamental bands of O 2 and N 2 at elevated temperatures[END_REF] are obtained for the 1-0 band. In the case of the 2-0 CIA band, our CRDS determination near 4720 cm -1 exceeds by 20% the high pressure value of Shapiro and Gush [START_REF] Shapiro | The collision-induced fundamental and first overtone bands of oxygen and nitrogen[END_REF]. Our CIA binary coefficients retrieved at 4720 cm -1 are supported by an agreement at the 3% level for determinations from CRDS spectra recorded at 700 and 750 Torr. The CMDS 2-0 CIA calculated by Hartmann et al. [START_REF] Hartmann | Collision-induced absorption by N 2 near 2.16 µm: Calculations, model, and consequences for atmospheric remote sensing[END_REF] was empirically adjusted to the high pressure measurements while they were originally closer to our value (difference of about 8%).

(iii) Although being extremely weak (line intensity on the order of a few 10 -30 cm/molecule), the position and intensity of the 2-0 S [START_REF] Richard | New section of the HITRAN database: Collision-induced absorption (CIA)[END_REF] and S [START_REF] Čermák | First detection of an absorption line of the first overtone electric quadrupolar band of N 2 by CRDS near 2.2µm[END_REF] electric quadrupolar transitions could be measured for the first time. Although more accurate, the obtained values fully validate the theoretical line list provided by the HITRAN database on the basis of Refs. [START_REF] Roy | An accurate analytic potential function for ground-state N 2 from a direct-potential-fit analysis of spectroscopic data[END_REF][START_REF] Li | Quadrupole moment function and absolute infrared quadrupolar intensities for N 2[END_REF]. A systematic shift on the line position on the order of 1×10 -3 cm -1 is tentatively evidenced.

The present study performed by OF-CEAS and CRDS has provided a further illustration of the performances of these two highly sensitive cavity enhanced techniques. While a high sensitivity is required to detect the very weak quadrupolar electric transitions of N 2 , the baseline stability is the main criterion for reliable measurements of the CIA.

B

  -are binary collision absorption coefficients (or density normalized absorption) in cm -1 amagat -2 .The above expression omits losses due to Rayleigh scattering which are negligible near 4 µm.

Fig. 2 .

 2 Fig. 2.Variation of the CIA absorption coefficient near 2491 cm -1 as a function of the pressuresquared. Measurements were performed with pure N 2 at 295.8 and 315.5 K and with a 50/50 O 2 /N 2 mixture at 295.8 K. The solid lines correspond to the fit of the absorption coefficients by a linear function. Note that the plotted data correspond to the superposition of two or three pressure ramps. The constant term due to the cavity losses, obtained from the fit was subtracted. The measurements performed by using argon instead of N 2 are also plotted and confirm the stability of OF-CEAS baseline against pressure variations up to 1 atm.

  NoteError bars are given in parenthesis in the unit of the last quoted digit

B

  -binary coefficients, we used the values of Lafferty et al. as reproduced by the HITRAN database. The 2 2 N N

  et al. is not satisfactory. In a recent work devoted to the retrieval of carbon dioxide vertical profiles from solar occultation observations, Sioris et al. [25] reconsidered the original data from Lafferty et al. and found necessary to correct the values of the β 0 parameter. The temperature dependence obtained with these new β 0 values (and B 0 from Ref. [16]) are also plotted in Fig. 7. An improvement is noted but the situation is not yet satisfactory. Let us note that better fits can be obtained by using as input data both the measurements of Lafferty et al. and of Baranov et al. covering the 230-390 K temperature range.

Fig. 3 .

 3 Fig. 3. Variation of the

B

  -binary coefficient is close to that of 2 2 N N B -(see Eq. 1). The derived value, 2 2 O N B -= 3.8(8)×10 -7 cm -1 amagat -2 , leads to a

  from the 700 and 750 Torr spectra are presented on Fig. 5. Their excellent coincidence (within about 1 %) reflects the pressure-squared dependence of the CIA absorption coefficient. We give in Table 2, the 2 2 N N Bvalues recommended at 4715 and 4725 cm -1 as obtained from a linear fit of the measured values over the 4715.55-4726.09 cm -1 interval. In our case the main uncertainty for the 2 2 N N

Fig. 7 .

 7 Fig. 7. Spectra around the S(10) 2-0 transition of N 2 recorded at 200 Torr. Upper panel: An example of an individual spectrum (grey circles) and spectrum obtained by averaging 194 such individual spectra (solid red).The CRDS measurement points were gathered within 2×10 -3 cm -1 wide bins (see Text). The line at 4716.7788 cm -1 due to water (present as an impurity) was used as reference for the frequency calibration of the CRDS spectra.Lower panel: Line profile fit of the N 2 line using a Voigt profile. The residuals of the fit reach the noise level corresponding to a minimum detectable absorption of 8×10 -12 cm -1 .

Table 1 .

 1 Review of the measurements of the 1-0 and 2-0 CIA bands of N 2 and corresponding experimental conditions and techniques.

	Band	Ref	Technique Pathlength (m)	Pressure (atm)	T (K)
	1-0	Shapiro and Gush, 1966 [14]	grating	40	4-18.4	room
		Menoux et al. 1993 [15]	grating	8-120	10-90	193-300
		Lafferty et al. 1996 [16]	FTS	84.05	up to 8	230-300
		Baranov et al. 2005 [12]	FTS	84.05 or 116.05	3.5-8	300-360
		This work (2491 cm -1 )	OF-CEAS	NR a	0-1	295.8 and 315.5
	2-0	Shapiro and Gush, 1966 [14]	Grating	80	45-90	room
		Mc Kellar, 1989 [17]	FTS	154	3.12 (i.e. 9.3 amagats)	97.5
		This work (4715-4725 cm -1 )	CRDS	NR a	0.66 and 0.99	297.1 (pure N 2 )
					0.99	299.3 (N 2 -O 2 )

a NR:not relevant

Table 3 .

 3 Positions and intensities derived for transitions of the (2-0) band of N 2 and comparison to HITRAN2016.

	Transition	Pressure (Torr)	Meas.	Position (cm -1 ) HITRAN2016 b	Line intensity (cm/molecule) Meas. HITRAN2016
	O(14) 2-0		4518.4115±0.0030 [23]	4518.4128 ±0.01	1.26×10 -30 ±20% [23]	1.405×10 -30 ±20%
	S(10) 2-0	100	4717.1866±0.0014	a	4717.1882 ±0.01	5.55×10 -30 ±10%	6.02×10 -30 ±20%
		200	4717.1869±0.0027 a		5.57×10 -30 ±6%
	S(11) 2-0	200	4724.2177±0.0036		4724.2218±0.01	3.03×10 -30 ±10%	2.71×10 -30 ±20%

Acknowledgements

This project is supported by the Labex OSUG@2020 (ANR10 LABX56 ), the LEFE-ChAt program from CNRS -INSU and the Breath-Diag project (ANR-15-CE18-0 0 06-01). The authors thank K. Jaulin (AP2E company) for lending us the 4 µm ICL laser. We would like to thank JM Hartmann (LMD, Paris) for providing us the original data of classical molecular dynamics simulations (CMDS) relative to the N 2 -O 2 CIA presented in Ref. [13].

estimated to be on the order of 8×10 -11 cm -1 . Uncertainty on density, related to errors on temperature and pressure determinations, can be neglected. We estimate the error bar on the [START_REF] Hartmann | Collision-induced absorption by N 2 near 2.16 µm: Calculations, model, and consequences for atmospheric remote sensing[END_REF] and (iii) recommended by a recent update of the HITRAN database (red line) [START_REF] Richard | New section of the HITRAN database: Collision-induced absorption (CIA)[END_REF].

The same treatment is applied to the four N 2 -O 2 spectra recorded at 750 Torr. The different Rayleigh cross-sections of Ar and air leads to a 5.4×10 -11 cm -1 difference on the Rayleigh contribution to the extinction coefficient at 750 Torr. Taking into account this small contribution, the retrieved CIA of the N 2 -O 2 mixture is the sum of two terms: , , , .

After subtraction of the self-CIA contribution using our experimental determination of (Table 2), the , coefficient was determined by division by . The , values retrieved from the four recorded spectra are presented in Fig. 6 together with a linear fit of their frequency dependence. In spite of the dispersion of the measured values, a clear decrease is evidenced over the 10 cm -1 spectral interval of the recordings. The N 2 -O 2 contribution to the measured N 2 CIA is on the order of the 20% relative abundance of O 2 in air. Thus the 3% error bar on


A,B , Dany Azar C,E , André Nel D,E , Didier Malvina Lak

Paul Tafforeau

The oldest representative of the Trichomyiinae (Diptera: Psychodidae) from the Lower Cenomanian French amber studied with phase contrast synchrotron X-ray imaging

Keywords: Diptera, Psychodidae, Trichomyiinae, Cretaceous amber, Charente, SW France, synchrotron, phase contrast

Trichomyia lengleti sp. nov., is described from the Lower Cenomanian amber of La Buzinie, Charente (SW France) from a piece of fully opaque amber. The Upper Albian Trichomyia swinhoei Cockerell, 1917 is transferred from the Trichomyiinae to the Sycoracinae incertae sedis stat. nov. T. lengleti is the oldest representative of the subfamily Trichomyiinae, supporting at least a Cretaceous diversification for the Psychodidae. The discovery of this fossil fly and its study thanks to propagation phase contrast synchrotron X-ray imaging improves our knowledge of the biodiversity and the historical evolution of psychodoid flies. A check list of fossil trichomyiine species is given.

Introduction

Psychodid flies are relatively well represented in the fossil record [START_REF] Evenhuis | Catalogue of the fossil flies of the World (Insecta: Diptera)[END_REF][START_REF] Azar | New genera and species of phlebotomid and psychodid flies from the Lower Cretaceous amber of Lebanon (Insecta: Diptera: Phlebotomidae, Psychodidae)[END_REF]2003;2007a;2007b;[START_REF] Azar | New Cretaceous psychodid flies from Lebanese amber and Santana Formation (Chapada do Araripe, Brazil). (Diptera)[END_REF]2003;[START_REF] Azar | Xenopsychoda harbi, a new psychodoid fly from the Lower Cretaceous amber of Lebanon (Diptera; Psychodoidea)[END_REF][START_REF] Nel | The oldest representative of the Trichomyiinae from the Lowermost Eocene amber of the Paris Basin (France) (Diptera: Psychodidae)[END_REF][START_REF] Ansorge | Tanyderidae and Psychodidae (Diptera) from the Lower Jurassic of Northeastern Germany[END_REF][START_REF] Ansorge | Eotonisca tertiaria Meunier, 1905 (Psychodidae) aus dem Sachsischer Bernstein[END_REF][START_REF] Wagner | A remarkable new species and genus of moth-flies (Diptera, Psychodidae, Psychodinae) from Dominican amber. [Eine bemerkenswerte neue Schmetterlingsmückenart und gattung (Diptera, Psychodidae, Psychodinae) aus dem Dominikanischen Bernstein[END_REF][START_REF] Wagner | Amber Bruchomyiinae -descriptions of already known and new species, and the position of the 'subfamily' within Psychodidae (s. l.) (Diptera)[END_REF]. Their oldest definitive known fossil is from the Liassic [START_REF] Ansorge | Tanyderidae and Psychodidae (Diptera) from the Lower Jurassic of Northeastern Germany[END_REF] but their occurrence could be as old as Triassic with Triassopsychoda olseni Blagoderov & Grimaldi, 2007 (tentatively included in ?Psychodidae), [START_REF] Fraser | A Triassic Lagerstätte from eastern North America[END_REF][START_REF] Blagoderov | How time flies for flies: diverse Diptera from the Triassic of Virginia and early radiation of the order[END_REF].

Trichomyiinae Tonnoir, 1922 is a subfamily of short-legged psychodid having the wing radial sector with only one vein between radial and medial forks. The monospecific Cenozoic genus Eatonisca Meunier, 1905 is characterized by a very particular wing venation. The other Cenozoic genus Eotrichomyia [START_REF] Nel | The oldest representative of the Trichomyiinae from the Lowermost Eocene amber of the Paris Basin (France) (Diptera: Psychodidae)[END_REF] has the same wing venation as Trichomyia, but is characterized by male genitalia with stylus bearing a sharp spine as in Sycorax (Sycoracinae). Recent representatives and remaining fossils are all included in Trichomyia Haliday, 1839. As a whole this genus embraces a wide range of structures that imposed the creation of different subgenera [START_REF] Duckhouse | Psychodidae of Southern Australia, subfamilies Bruchomyiinae and Trichomyiinae[END_REF][START_REF] Duckhouse | Taxonomy, phylogeny and distribution of the genus Trichomyia (Diptera: Psychodidae) in Australia and New Guinea[END_REF][START_REF] Duckhouse | Trichomyia species (Diptera: Psychodidae) from Southern Africa and New Zealand, with a discussion of their affinities and of the concept of monophyly in southern hemisphere biogeography[END_REF][START_REF] Bravo | Septemtrichomyia, subgenero novo de Trichomyiinae neotropical (Diptera: Psychodidae)[END_REF]Bravo , 2001, etc.), etc.). Several other extant genera were created within Trichomyiinae like Diplonema Loew, 1845, Lepria Enderlein, 1936, and Eubonetia Vargas & Najera, 1953[START_REF] Satchell | On the genus Trichomyia (Psychodidae) with descriptions of four new species[END_REF] sank them in Trichomyia. The genus Phalaenomyia Loew, 1844 originally proposed without included species is considered by all the workers as a nomen nudum. [START_REF] Duckhouse | Psychodidae of Southern Australia, subfamilies Bruchomyiinae and Trichomyiinae[END_REF] concluded that two or more groups are at present intermingled under Trichomyia, but he considered that it would be premature to form new genera.

Nevertheless he subdivided the Trichomyiinae into two groups A and B based on antenna and palp structures.

3

Sycoracinae were first classified within the subfamily Trichomyiinae but [START_REF] Edwards | A note on the amber moth-fly Eophlebotomus connectens Cockerell[END_REF] recognized the difference between Sycorax and Trichomyia and suggested that Sycorax should be classified in a separate tribe of the Trichomyiinae or preferably as a separate subfamily. [START_REF] Jung | Einige neue mitteleuropäische Psychodiden (Diptera)[END_REF][START_REF] Jung | Beiträge zur Biologie, Morphologie und Systematik der europäischen Psychodiden (Diptera)[END_REF]) recognized a separate subfamily for Sycorax, but thereafter [START_REF] Jung | Psychodidae-Trichomyiinae[END_REF] and [START_REF] Hennig | Insektenfossilien aus der unteren Kreide. IV. Psychodidae (Phlebotominae), mit einer kritischen Übersicht über das phylogenetische System der familie und die bisher beschriebenen Fossilien (Diptera)[END_REF] reverted to the single subfamily Trichomyiinae.

For [START_REF] Duckhouse | Psychodidae (Diptera, Nematocera) of South Chile, subfamilies Sycoracinae and Trichomyiinae[END_REF], [START_REF] Vaillant | Contribution à l'étude des Sycorax [Dipt. Psychodidae] de la France[END_REF] and [START_REF] Wagner | Family Psychodidae. In: Contributions to a Manual of Palaearctic Diptera. Volume 2: Nematocera and Lower Brachycera[END_REF], Sycoracinae is considered as a separate subfamily.

The oldest fossil described in the subfamily Trichomyiinae is Trichomyia swinhoei [START_REF] Cockerell | Fossil insects. Appendix[END_REF] from the Myanmar Lower Cretaceous (Upper Albian) amber, but this specimen was badly drawn and Cockrell's (1917) description was very succinct and insufficient for an accurate attribution of this fossil. We transfer below Trichomyia swinhoei [START_REF] Cockerell | Fossil insects. Appendix[END_REF] from the Trichomyiinae to the Sycoracinae. Thus the current oldest published representative of the subfamily Trichomyiinae (Eotrichomyia electronica [START_REF] Nel | The oldest representative of the Trichomyiinae from the Lowermost Eocene amber of the Paris Basin (France) (Diptera: Psychodidae)[END_REF] is from the Lower Eocene amber of the Paris Basin, Oise, France [START_REF] Nel | The oldest representative of the Trichomyiinae from the Lowermost Eocene amber of the Paris Basin (France) (Diptera: Psychodidae)[END_REF], but this subfamily occurs in the Turonian amber of New Jersey and the Upper Cretaceous amber of Myanmar (Azar pers. obs.). We describe herein a new Trichomyia species, from the Lower Cenomanian amber discovered at La Buzinie, in Charente, south-western France (Perrichot et al. 2007a(Perrichot et al. , 2007b) ) and assess its age in relation to other Trichomyiinae. We used new Synchrotron X-ray imaging techniques [START_REF] Tafforeau | Applications of Xray synchrotron microtomography for non-destructive 3D studies of paleontological specimens[END_REF][START_REF] Lak | Phase contrast X-ray Synchrotron Imaging: opening access to fossil inclusions in opaque amber[END_REF]) that have enabled the discovery, imaging and 'virtual' extraction of the specimen from a totally opaque piece of amber

Material and methods

The amber containing the Trichomyiinae has been collected in the mid part of the Lower Cenomanian series of La Buzinie road works (Angoulême area, Charente, SW France) (Perrichot et al. 2007b), in the B2 lithological subunit sensu [START_REF] Néraudeau | Variations of echinoids biodiversity during the Cenomanian-Early Turonian transgressive episode in Charentes (France)[END_REF]. The amber pieces collected in this subunit are more or less opaque, so the specimen has been detected and 3D-reconstructed using phase contrast X-ray synchrotron imaging according to the protocol published in [START_REF] Lak | Phase contrast X-ray Synchrotron Imaging: opening access to fossil inclusions in opaque amber[END_REF]. All the experiments were performed at the ESRF -Grenoble (France) on the Beamline ID19. The microradiograph of the fossil fly 4 being not sufficiently accurate to describe the specimen precisely; therefore the following description is based on a 3D-reconstruction, obtained by local propagation phase contrast microtomography [START_REF] Tafforeau | Applications of Xray synchrotron microtomography for non-destructive 3D studies of paleontological specimens[END_REF][START_REF] Lak | Phase contrast X-ray Synchrotron Imaging: opening access to fossil inclusions in opaque amber[END_REF]. The parameters of the scan were the following: monochromatic beam set at an energy of 20.5 keV using a multilayer monochromator, 100 mm of propagation distance between the sample and the detector, 25 µm thick YAG scintillator screen, isotropic voxel size of 1.4 µm, 1500 projections of 0.2 s each taken over 180 degrees. After tomographic reconstruction and 8 bits conversion, the volume was segmented in 3D using the software VGStudioMax 1.2.1 (Volume Graphics, Heidelberg, Germany), in order to virtually extract the specimen from the opaque amber. We could have a vision of the rotating fossil in order to examine very minute structures, such as the apical flagellomeres, the pattern of the dorsal setae, and the genitalia.

We follow the wing venational nomenclature of [START_REF] Mcalpine | Morphology and terminology -adult. pp. 9-63[END_REF], with the following abbreviations: h, humeral vein; Sc, subcosta; R1, R2, R3, R4+5, radial veins; M1, M2, M3, median veins; CuA1, CuA2, cubital veins; A1, anal vein; r-m, radialmedian cross-vein. Etymology. The species name is dedicated to Mr. Thierry Lenglet, who discovered the type specimen and donated it to the MNHN.

Systematic palaeontology

Family

Type locality and horizon. Lower Cenomanian (subunit B2 sensu [START_REF] Néraudeau | Variations of echinoids biodiversity during the Cenomanian-Early Turonian transgressive episode in Charentes (France)[END_REF] of La Buzinie, Charente, SW France (Perrichot et al. 2007b). Thorax nearly 358 µm long, 260 µm wide and 377 µm high; vestiture indicated by the insertion holes of setae, grouped into three anterior longitudinal zones and two posterior zones on scutum, and two zones on scutellum (Pl. 1, Fig. 3A).

Diagnosis

Legs short, shorter than whole body.

Abdomen 828 µm long excluding genital appendages, 379 µm wide; dorsal surfaces of all abdominal segments bearing few setae, indicated by insertion holes; female genital appendages: two elongated subgenital plates (Sub), 95 µm long and 77 µm wide; cerci (Cer) 132 µm long and 77 µm wide (Fig. 3B,3C).

Discussion

As Trichomyia lengleti sp. nov. is a psychodid that has a typical trichomyiinewing structure characterized by the radial sector with only one vein between radial and medial forks, and CuA2 vein well-developed, we assign it to the Trichomyiinae.

Trichomyia lengleti differs from all the recent and fossil species belonging to Trichomyiinae in its antenna with 15 flagellomeres, while Trichomyiinae have usually antenna with 16 antennomeres, the sixteenth being very diminutive or occasionally fused to fifteenth [START_REF] Duckhouse | Psychodidae of Southern Australia, subfamilies Bruchomyiinae and Trichomyiinae[END_REF]. T. lengleti has flagellomeres 12 to 15 gradually reduced comparing to the more basal ones, a character inexistent in all known Trichomyiinae. Such a reduction in the terminal three or more flagellomeres is known in some Psychodinae.

Even if the antennal structures of T. lengleti are unique within the Trichomyiinae, we prefer to assign it to Trichomyia sensu lato, as the male genital appendages are not available (Eotrichomyia differs from Trichomyia in the male genital appendages), and the palps are not visible. There are not enough arguments to create a new genus. T. lengleti would fall in the group A of [START_REF] Duckhouse | Psychodidae of Southern Australia, subfamilies Bruchomyiinae and Trichomyiinae[END_REF] after its head with well-developed vertex, first flagellomere almost 1.5 times as long as other flagellomeres, elongate-pyriform flagellomeres, and in addition to very reduced and drop-like last flagellomere.

Nevertheless T. lengleti shares with the group B of [START_REF] Duckhouse | Psychodidae of Southern Australia, subfamilies Bruchomyiinae and Trichomyiinae[END_REF] the well-developed digitate ascoids.

8

T. lengleti is in a piece of amber which contains at least 15 well-preserved arthropods (among which Diptera notably represented by Dolichopodidae [Microphorites Hennig, 1971] and Psychodidae, Hymenoptera: Diapriidae [Lengletia chanieraudi [START_REF] Lak | Phase contrast X-ray Synchrotron Imaging: opening access to fossil inclusions in opaque amber[END_REF], Blattodea, and decapod Tanaidacea), and five plant remains and microinclusions (mainly freshwater testate amoebae) (Girard pers. com.). The sedimentological characteristics of the amber deposit and the arthropod species found in other amber pieces allow interpreting the palaeoenvironement of T. lengleti as an estuarine forest, located at the boundary between marine and freshwater influences (Perrichot et al. 2007a(Perrichot et al. , 2007b)).

Although the piece of amber is translucent enough to see some of the macro-inclusions, phase contrast X-ray imaging is necessary for most of them and remains preferable as a non-destructive technique.

Two other psychodoid flies, Eophlebotomus carentonensis Azar et al., 2003, andSycorax neli Azar et al., 2007, were hitherto described from the Albian amber of Charentes, SW France (Perrichot et al. 2007a) and Lebanon respectively (Azar et al. 2003(Azar et al. , 2007b)). These discoveries confirm those from the study of the Lower Cretaceous Lebanese psychodoids about the very high diversity of this group in the Mesozoic.

  PSYCHODIDAE Newman, 1834 Subfamily TRICHOMYIINAE Tonnoir, 1922 Genus Trichomyia Haliday (in Curtis 1839) Type species. Trichomyia urbica Haliday, 1939 by monotypy. Trichomyia swinhoei Cockerell, 1917 Material. Holotype In.19101, Natural History Museum, London, UK. Type locality and horizon. Late Albian, Burmese amber, Myanmar. 5 Discussion The reexamination of this fossil material in the Natural History Museum (London) by one of us (DA) and by Derek A. Duckhouse, indicates that this specimen is definitely not a Trichomyiinae but a Sycoracinae as its CuA2 is rather short as in all known sycoracine flies (pers. obs.; and Duckhouse pers. comm. to DA). We transfer Trichomyia swinhoei Cockerell, 1917 from the Trichomyiinae to the Sycoracinae incertae sedis stat. nov. Its detailed redescription will be done in another paper. ?Trichomyia lengleti, sp. nov. (Plate 1, Figs 1-3) Material. Holotype BUZ 2.7 (female), from the collection of T. Lenglet, deposited in the Muséum National d'Histoire Naturelle, Département Histoire de la Terre, Paris, France. All the tomographic data as well as a surface model of the specimen are available upon request to the first author, and will be deposited in the public palaeontological database project of the ESRF when available. Reference 3D prints of the extracted specimens are deposited in the Muséum National d'Histoire Naturelle (Paris, France), in the Géosciences laboratory (Rennes, France), and at the ESRF (Grenoble, France).

  Head with well-developed vertex puffed out behind antenna; antenna with 15 flagellomeres bearing well-developed digitiform and sigmoid ascoids, flagellomeres 12 to 15 gradually reduced with the last one extremely reduced and drop-like; wing venation of 6 Trichomyia-type with CuA2 elongated and Rs separated from R1 at the same level where Sc meets with R1, and beyond fork of M into M1+2 and M3.DescriptionHead with well-developed vertex puffed out behind antenna; eyes elliptical, 148 µm of large diameter and 107.5µm of small diameter; antenna 617 µm long, with 15 flagellomeres, viz. 13 of normal size, the 14 th reduced and the 15 th (apiculus) very reduced and drop-like (Pl. 1, Fig. 1A); first flagellomere the longest, 42.5 µm, nearly 1.5 times as long as each of following ten flagellomeres; flagellomeres 2 to 11 pyriform and of nearly same length 38 µm long; flagellomeres 12 and 13 of equal length and slightly shorter than the preceding, 30 µm long each; flagellomere 14 well reduced and shorter than half of flagellomere 12 or 13, 17 µm long, bearing the terminal flagellomere apiculus which is much reduced and drop-like; scape subspherical, nearly 34 µm long and 34 µm wide; pedicel subspherical, about 46.8 µm long and 38.3 µm wide; flagellomeres 1-6 with well-developed, digitate, and sigmoid ascoids in their ventral sides (Fig. 1B, 1C); maxillary and labial palps not visible. Wing 1011 µm long, 393 µm wide (Pl. 1, Fig. 2); humeral vein (h) reaching costal margin at 129 µm from wing base; subcostal vein Sc distally fused with R1 in a strong angle, 337 µm from wing base, and a possible cross-vein reaching costal margin, but rather unclear character; R1 reaching costal margin 747 µm from wing base; Rs separated from R1 337 µm from wing base, at same level where Sc meets with R1, and beyond fork of M into M1+2 and M3; Rs three-branched; R2 and R3 separated 708 µm distally, slightly before level where R1 meets with costal margin; R2 sigmoid-shaped reaching costal margin at 921 µm from wing base; R3 slightly curved at base and reaching costal margin at 989 µm from wing base; R4 and R5 fused forming R4+5, 612 µm long, slightly curved at its middle toward posterior side; cross-vein r-m 421 µm distal of wing base; fork of M into M1+2 and M3 112 µm distal of arculus; fork of M1+2 into M1 and M2 269 µm distal of base of M1+2; M1 slightly curved; M2 slightly shorter than M1; M3 reaching wing margin at 803 µm from wing base; CuA1 separating from CuA 309 µm distal of wing base; CuA2 rather long, 444 µm long; A1 hardly visible on right wing but reaching posterior wing margin. 7 Halteres 191 µm long; knob 101 µm long; stem 90 µm long.

  Figure captionsPl. 1: Trichomyia lengleti sp. nov., General habitus, 3D-reconstruction using local phase contrast microtomography. A, dorsal view; B, left-side view; C, dorsal view. Scale bar = 500 µm, pixel size = 1.4 µm.

Fig. 1 :

 1 Fig. 1: Trichomyia lengleti sp. nov. A, detail of head, 15 flagellomeres visible on left antenna. Pixel size = 1.4 µm, scale bar = 200 µm; B, detail of antennae, white arrows: sigmoidal ascoids. Pixel size = 1.4 µm, scale bar = 200 µm; C, drawing of sigmoid ascoids on a: inner view; b: outer view; c: ventro-lateral view. Scale bar = 50 µm.

Fig. 2 :

 2 Fig. 2: Trichomyia lengleti sp. nov. A, left wing, missing parts of veins appear in grey dotted lines. Pixel size = 1.4 µm; B, drawing of wing. Scale bar = 500 µm.

Fig. 3 :

 3 Fig. 3: Trichomyia lengleti sp. nov. A, thorax in latero-dorsal view. Scale bar = 500 µm, pixel size = 1.4 µm; B-C, details of female genitalia, respectively 3D-reconstruction and drawing, subgenital plates Sub, cerci Cer. Pixel size = 1.4 µm, scale bars = 200 µm.

  Trichomyia swinhoei[START_REF] Cockerell | Fossil insects. Appendix[END_REF] has been omitted from the list as this species undoubtedly belongs to the subfamily Sycoracinae.

			13
	Appendix: List of fossil Trichomyiinae:
	Fossil taxa	Age	Deposit
	Trichomyia buceras Loew, 1845	Holocene	Copal of "Ostindische"= eastern
			India or the Indonesian
			Archipelago
	Trichomyia antiquaria Quate, 1961	Oligocene/Miocene Mexican Amber
	Trichomyia declivivena Quate, 1963
	Trichomyia discalis Quate, 1963
	Trichomyia glomerosa Quate, 1963
	Trichomyia mecocerca Quate, 1963
	Trichomyia smithi Quate, 1963
	Eatonisca tertiaria Meunier, 1905	Eocene	Baltic and Saxonian ambers
	Trichomyia brevicornis Loew, 1850		Baltic amber
	Trichomyia concinna Meunier, 1905
	Trichomyia crassicornis Meunier, 1905
	Trichomyia decora Meunier, 1905
	Trichomyia distincta Meunier, 1905
	Trichomyia formosula Meunier, 1905
	Trichomyia longicornis Loew, 1850
	Trichomyia nova Meunier, 1905
	Trichomyia procera Meunier, 1905
	Trichomyia pulchra Meunier, 1905
	Trichomyia tenera Meunier, 1905
	Eotrichomyia electronica Nel et al., 2002 Lower Eocene	Oise French Amber
	Trichomyia lengleti sp. nov.	Lower Cenomanian Charente French amber
	N.B. 13

Acknowledgments

We are grateful to Alain Couillard, who has discovered the amber deposit of La Buzinie and to Thierry Lenglet who collected the amber piece containing the Psychodidae. We are also grateful to the ESRF and the ID19 staff for thier help in synchrotron imaging.

Lastly we thank two anonymous reviewers for their helpful criticism on the first version of the manuscript. This work is supported by the French Research Agency (ANR), project "AMBRACE" n° BLAN07-1-184190. This paper is a contribution to the project 'The Study of the Fossil Insects and their Outcrops: Geology of the Outcrops -Historical and Biodiversity Evolution' accorded by the Lebanese University to DA.


MD, PhD Thomas Neri
email: thomas.neri@chu-st-etienne.fr

PhD Rodolphe Testa

MD Loic Laurendon

Margaux Dehon

MD Sven Putnis

PhD Samuel Grasso

MD David A Parker

Frédéric Farizon

Rémi Philippot

MD Frederic Farizon

MD, PhD Remi Philippot

Determining the change in length of the anterolateral ligament during knee motion: A three-dimensional optoelectronic analysis

Keywords: knee, Anterolateral ligament, kinematic, length, optoelectronic system

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Good control of rotational stability after intra-articular anterior cruciate ligament (ACL) reconstruction is not always achieved and there has been a renewed interest in the role of extra-articular structures, among them the anterolateral ligament (ALL) [START_REF] Claes | Anatomy of the anterolateral ligament of the knee[END_REF]Neri et al., 2018a). Combined ACL and ALL reconstructions in ACL deficient knee have been suggested to offer clinical and biomechanical advantages in controlling anterolateral rotational laxity more than an isolated ACL reconstruction in ACL-deficient knee (Geeslin et al., 2018b;[START_REF] Sonnery-Cottet | Outcome of a Combined Anterior Cruciate Ligament and Anterolateral Ligament Reconstruction Technique With a Minimum 2-Year Follow-up[END_REF]. During ALL reconstruction it is necessary to fix the graft in a position close to its maximum length, corresponding to its range of action, in order to restore normal biomechanics, and avoid insufficient tension or overconstraint. To date there is no consensus on this point and different surgical techniques have subsequently appeared, fixing the graft either with the knee in full extension [START_REF] Sonnery-Cottet | Outcome of a Combined Anterior Cruciate Ligament and Anterolateral Ligament Reconstruction Technique With a Minimum 2-Year Follow-up[END_REF], at 30°of flexion [START_REF] Chahla | Anterolateral Ligament Reconstruction Technique: An Anatomic-Based Approach[END_REF], or at 90° of flexion [START_REF] Helito | Combined Intra-and Extra-articular Reconstruction of the Anterior Cruciate Ligament: The Reconstruction of the Knee Anterolateral Ligament[END_REF]. A detailed understanding of the biomechanical behaviour of the ALL is therefore required to facilitate an optimal reconstruction technique.

The first studies undertaken to evaluate the variation of the ALL length were static analyses using digital calipers measurements at predetermined flexion and rotational values [START_REF] Claes | Anatomy of the anterolateral ligament of the knee[END_REF][START_REF] Neri | The anterolateral ligament: Anatomic implications for its reconstruction[END_REF][START_REF] Runer | The anterolateral ligament of the knee: A dissection study[END_REF]. Three-dimensional imaging analyses have also been used [START_REF] Helito | MRI evaluation of the anterolateral ligament of the knee: assessment in routine 1.5-T scans[END_REF][START_REF] Kernkamp | In Vivo Anterolateral Ligament Length Change in the Healthy Knee During Functional Activities-A Combined Magnetic Resonance and Dual Fluoroscopic Imaging Analysis[END_REF][START_REF] Van De Velde | In Vivo Length Changes of the Anterolateral Ligament and Related Extraarticular Reconstructions[END_REF][START_REF] Wieser | Assessment of the Isometry of the Anterolateral Ligament in a 3-Dimensional Weight-Bearing Computed Tomography Simulation[END_REF]. Although having the advantage to be performed on in vivo subjects, these models were created from theoretical insertions points, which are difficult to identify on MRI and subject to significant inter-individual variability [START_REF] Daggett | Femoral Origin of the Anterolateral Ligament: An Anatomic Analysis[END_REF]Neri et al., 2018b;[START_REF] Parker | Anatomical variation in the anterolateral ligament of the knee and a new dissection technique for embalmed cadaveric specimens[END_REF]. Other studies used freedom robotic systems or knee rig systems [START_REF] Dodds | The anterolateral ligament: Anatomy, length changes and association with the Segond fracture[END_REF][START_REF] Drews | Function and strain of the anterolateral ligament part I: biomechanical analysis[END_REF]Geeslin et al., 2018a;[START_REF] Kittl | Length change patterns in the lateral extra-articular structures of the knee and related reconstructions[END_REF][START_REF] Parsons | The biomechanical function of the anterolateral ligament of the knee[END_REF]. These systems have excellent reliability and optimal precision by dispensing with manipulation by a human operator. Yet all these studies used isolated knees, with sectioning of the musculotendinous structures around the knee, such as the biceps femoris tendon and Iliotibial Band (ITB) subsequently losing their contribution to the rotational stability of the knee and potentially affecting the ALL function [START_REF] Laprade | Mechanical properties of the posterolateral structures of the knee[END_REF][START_REF] Rahnemai-Azar | Structural Properties of the Anterolateral Capsule and Iliotibial Band of the Knee[END_REF]. Surgical navigation systems designed for prosthetic knee surgery have also been used with the advantage of conserving the full leg and the ITB [START_REF] Bonanzinga | Kinematics of ACL and anterolateral ligament. Part I: Combined lesion[END_REF][START_REF] Imbert | Isometric Characteristics of the Anterolateral Ligament of the Knee: A Cadaveric Navigation Study[END_REF]. However, these studies assessed the ALL length without combining both continuous flexion and rotation kinematics. Internal rotation was applied only for some target flexion values (20 and 90° for Imbert,and 30 and 90° for Bonanzinga). In addition, these systems use few cameras with lower data acquisition frequencies, making it difficult to assess the biomechanical behaviour of the ALL [START_REF] Güler | Quantitative error analysis for computer assisted navigation: a feasibility study[END_REF].

Consequently, there are contradictions in current biomechanical results when describing the variation in ALL length during motion leading to inconstancies about the position of the knee at which the ALL is at maximum length. We hypothesised that the use of another measurement device, a three-dimensional optoelectronic system, such as the Motion analysis®, would allow the assessment of combined continuous flexion and rotation kinematics and lead to an accurate and reliable measurement of the ALL length. The objective of this study was therefore to determine the variation of the ALL length during knee motion.

METHODS

Specimen preparation

Twenty-two intact knees from 11 fresh frozen cadaveric specimens were used. The specimens were thawed out at room temperature for 24 hours and showed no signs of degeneration.

Exclusion criteria were examination signs of knee instability (anterior tibial drawer and positive pivot-shift test), evidence of prior knee surgery or ACL reconstruction, severe deformities or severe knee osteoarthritis. An anteromedial knee arthroscopy was performed to confirm the Anterior Cruciate Ligament (ACL) status. A total of two knees were subsequently excluded and 20 intact knees without ACL and ALL injuries were included. There were 5 men and 5 women with a mean age of 68.9 years (range, 57 to 85). We used the full leg and pelvis in order to preserve the entire length of the ITB and all other synergistic bi-articular structures crossing the hip and/or the knee. The dissection protocol used to define the ALL was described in a previous anatomical study [START_REF] Neri | The anterolateral ligament: Anatomic implications for its reconstruction[END_REF]. The number of incisions was kept to the strict minimum in order to limit their effects, and they were always made in line with the tendinous fibres. No lateral structures were removed. The femoral origin of the ALL was always posterior and proximal to the lateral femoral epicondyle and its tibial insertion was posterior to Gerdy's tubercle, anterior to the fibular head and distal to the articular cartilage of the lateral tibial plateau. At the end of the dissection, once the insertions were recorded and the acquisitions made, the ITB was anatomically closed.

Experimental set-up

Superior acetabular screws fixed the pelvis to the table and the cadavers were positioned to allow free range of motion of the knee over the edge of the table (Figures 1B and1C).

Kinematic analysis was performed using a Motion Analysis® (Motion Analysis corp., Santa Rosa, CA, USA) stereophotogrammetry system. The system consisted of 8 high-definition Raptor-E® cameras operating at 100 Hz (Figure 1A). After installation and calibration around the working area the system followed retro-reflective sensors (Targets). A pelvic marker was defined from 3 targets fixed on the ipsilateral anterior superior iliac spine. The femur and the tibia were equipped with 4 targets each: F1 to F4 and T1 to T4 (Figure 2). These targets were fixed using bi-cortical pins placed in such a way as to leave free the muscles and ligaments.

Three points are sufficient to reconstruct the movements of a solid in space, and the use of the fourth provided a backup in the event of disengagement of a target or temporary masking.

Using a navigation probe, points of interest were next identified. The epicondyles and malleoli were then calculated (Figure 2, purple stars) from these palpated points (Figure 2, purple circles). The centre of the hip was calculated kinematically via circumduction [START_REF] Gamage | New least squares solutions for estimating the average centre of rotation and the axis of rotation[END_REF] to overcome the hip movement during knee motion (Figure 2, purple star). The centre of Inter Condylar Eminences (ICE) was located arthroscopically. The set of points determines the axes and the femoral and tibial references as defined in ISB conventions and the work of Grood and Suntay [START_REF] Grood | A joint coordinate system for the clinical description of three-dimensional motions: application to the knee[END_REF][START_REF] Wu | ISB recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion--part I: ankle, hip, and spine[END_REF]. The centre of the tibial and femoral insertion points of the ALL were identified by internally rotating the tibia and determining the course of the central ligamentous fibres coming under the most tension; the position for the optimal surgical reconstruction.

Determining the Change in Length of the ALL

The study was divided into two separate sessions of 10 knees each, separated by one month and performed by two different operators in order to appreciate the reliability of the experimental process. The knees were different between the two sessions.

We studied the knee flexion kinematics in three different test conditions: Forced internal rotation (IR) Forced external rotation (ER) and neutral rotation (NR. For NR, the foot was placed in neutral rotation and the tibia in its reduced position with respect to the femur with unconstrained tibial rotation. A dynamometric torque rig triggering at 5nm, placed above the ankle at the axis of rotation joint and fixed by 2 pins, provided rotation (Figure 3).

The knee was flexed manually by moving the tibia relative to the femur from complete extension to 90° of flexion while controlling the rotation with the dynamometric torque rig. In every test condition, this movement was repeated five times and performed with a very slow speed of 5 seconds per movement corresponding to an average speed of PI / 10 = 0.3 Rad.s -1 .

After processing the kinematics using Cortex® software, the data was filtered (Butterworth filter of order 4 with a cut off frequency of 6 Hz) according to Winter and Pezzack [START_REF] Pezzack | An assessment of derivative determining techniques used for motion analysis[END_REF][START_REF] Winter | Measurement and reduction of noise in kinematics of locomotion[END_REF]. The recorded data was interpolated to obtain values from full extension to 90° of flexion at each degree of flexion. Therefore, we could determine the internal-external rotation angle (ROT) and the distance between the femoral and tibial insertions of the ALL (ALL length) during the full range of knee motion (Figure 4).

Statistical analysis

All statistical analyses were performed using SPSS® software (IBM, Armonk, New York, United States).

Initial statistical analysis was for reliability of the five cycles during the kinematic acquisitions for the three conditions of rotation (IR, ER and NR) and for both variables of interest (ROT, ALLlength). This analysis included all the knees (n=20 knees). A statistical test of the intraclass correlation coefficient (ICC) was used for each measured variable (ROT, ALLlength). According to Smith-Crowe et al., ICC was considered good if it was ≥ 0.75 and excellent if it was ≥ 0.85 [START_REF] Smith-Crowe | Assessing Interrater Agreement via the Average Deviation Index Given a Variety of Theoretical and Methodological Problems[END_REF]. For accepting data without modification, a threshold of 0.85 was required. Two-way mixed ICC calculations with an absolute agreement search were performed. A second statistical analysis was performed to evaluate the reliability of our protocol between the two separate measurement sessions (for each session, n=10 knees). Using the statistical method described above, we calculated the mean curves of the measurements (ROT, ALLlength) during the two sessions for the three test conditions (IR, ER and NR). The ICC of these average curves was then calculated from the data from these two sessions (two-way randomized ICC). In order to compare the lengths of ALL between the IR, NR and ER, a variance analysis study (ANOVA) was performed on repeated measurements. P values less than 0.05 were considered statistically significant.

RESULTS

Accuracy and Reliability

The average error of target positioning was consistently less than 0.15 mm and the measurement error of the angles was less than 0.2 degrees.

In the first analysis on the reliability of the five cycles, ICCs were performed for 120 measurements. 82% of these values had an ICC > 0.85 and did not require curve suppression.

15% required the removal of one curve to obtain an ICC ≥ 0.85. 3% required the removal of 2 curves. In one case, the worst, the ICC after removal of 2 curves was 0.76. Figure 5 illustrates the variability of the measurements (acquisitions) for a knee.

The second analysis showed either good or excellent reproducibility between the two sessions with different operators and different knees. For the ROT measurement, the ICC was 0.93 in IR and 0.83 in ER. For the ALL length measurement, the ICCs were 0.86 in IR, 0.99 in ER, and 0.98 in NR.

Determining the Change in Length of the ALL

After determination of the femoral and tibial insertion points of the ALL, it was then possible to measure the length of the ALL throughout the full range of motion. This length was studied for the 3 rotational conditions in order to determine the flexion and rotation conditions for which the ALL was overtight (maximum length). There was a significant difference for ALL length between the IR and the NR rotation (p<0.001), whatever the knee flexion (Figure 6). In contrast, there was no significant difference between NR and ER (p>0.05). The ALL length was maximum in IR at 25 ° of knee flexion. It should be noted that there is considerable variation in ALL length between individual knee specimens, which is indicated in figure 6 as the extended error bars for the ALL length at different degrees of knee flexion.

DISCUSSION

By using an accurate and reliable three-dimensional optoelectronic system, we were able to analyse the variation in length of the ALL during motion in an intact knee. We demonstrated that its maximum length was in IR at 25° of knee flexion.

Compared to other experimental tools, such as robotic, 3D scan model and traditional navigation systems, our protocol was the first to use a stereophotogrammetry system such as Motion analysis®, recognized as the current gold standard for an instrument evaluating kinematics in three-dimensions. This measurement tool allowed us to obtain continuous knee kinematics combining flexion and rotation in a full lower limb with all the bi-articular structures conserved. By determining the change in length of the ALL during knee motion, the aim of this study has been fulfilled with the required accuracy to analyse the small change in this variable and with good reproducibility of the kinematic assessments.

Experimental accuracy depends on the type of sensor fixation used, the number and configuration of the cameras used and the size of the work volume. To reduce the incidence of experimental errors, we used a large number of cameras (8 HD cameras), a volume restricted to the maximum (0.8 m / 1.2 m / 1.5 m), stable bone fixation, and a wide inter-distance between two targets. The mean error was always less than 0.15 mm and the angle measurement error was less than 0.2 degrees. This protocol therefore has optimal precision for acquisition of data and far greater than when determining the centre of the anatomical insertions; the ALL insertion points cover areas over 5 mm 2 and it is difficult to precisely evaluate the centre. In order to minimize this bias, all dissections were made by an experienced operator who observed the position of the ALL during internal tibial rotation.

Regarding the reproducibility, this protocol demonstrated a good intra-rater reliability between measurements with 82% of ICCs superior to 0.85. In addition, this protocol demonstrated either good or excellent inter-sessional reliability when compared with a second session with new cadaveric set-ups and operator. This makes it possible to validate its use in multisession biomechanical studies.

The protocol described in this study will have many clinical applications. In vitro, it will allow the in-depth study of healthy knee kinematics, or after injury of the ACL and anterolateral complex (ALC). The individual functions of structures composing the ALC (ALL, anterolateral capsule, and iliotibial band Kaplan fibres) are still controversial and unclear. Their individual contribution to the anterolateral rotational laxity require an accurate experimental assessment. It can also be applied to the post-operative knee providing a greater understanding of the role of the ALL reconstruction in providing additional rotational control, and how it may alter knee kinematics.

In vivo, this study provides a useful information to guide ALL reconstruction that may be required in primary surgery for patients with a combined ACL and ALC injury as well as those requiring revision surgery after a first failed ACL reconstruction [START_REF] Sonnery-Cottet | Anterolateral Ligament Expert Group consensus paper on the management of internal rotation and instability of the anterior cruciate ligament -deficient knee[END_REF], 2015). Although this additional procedure has shown clinical and biomechanical benefits (Geeslin et al., 2018b;[START_REF] Sonnery-Cottet | Outcome of a Combined Anterior Cruciate Ligament and Anterolateral Ligament Reconstruction Technique With a Minimum 2-Year Follow-up[END_REF], there are still inconsistencies in graft fixation. In order to ensure efficient and physiological biomechanical behaviour, the graft has to be fixed close to the range of flexion where the ALL operates, i.e when it is tensioned. To date, there is no clear consensus on this point. Regardless of measurement and instrumentation factors, the literature suggests that the other main factor influencing the length is the location of the ALL femoral origin [START_REF] Monaco | Anterolateral ligament reconstruction with autologous grafting: A biomechanical study[END_REF]. Helito et al., recommends that the graft is fixed with the knee flexed between 60 and 90° [START_REF] Helito | Combined Intra-and Extra-articular Reconstruction of the Anterior Cruciate Ligament: The Reconstruction of the Knee Anterolateral Ligament[END_REF][START_REF] Helito | Anatomy and Histology of the Knee Anterolateral Ligament[END_REF] with the ALL femoral footprint identified either anterior or on the lateral femoral epicondyle. Sonnery-Cottet et al., recommend graft fixation close to extension and neutral rotation to avoid overtightening in external rotation [START_REF] Sonnery-Cottet | Outcome of a Combined Anterior Cruciate Ligament and Anterolateral Ligament Reconstruction Technique With a Minimum 2-Year Follow-up[END_REF]. They located the ALL femoral origin posterior to the epicondyle. In another study, the same team demonstrated that the ALL is tight when the knee is at 20° of flexion with internal rotation of the tibia [START_REF] Imbert | Isometric Characteristics of the Anterolateral Ligament of the Knee: A Cadaveric Navigation Study[END_REF]. This is similar to Chahla et al. who recommend graft fixation at 30° of flexion [START_REF] Chahla | Anterolateral Ligament Reconstruction Technique: An Anatomic-Based Approach[END_REF]. We also found the ALL femoral origin to be in a posterior and proximal position [START_REF] Neri | The anterolateral ligament: Anatomic implications for its reconstruction[END_REF], and proved it is at its longest with the knee at 25° of flexion, suggesting that this is the most appropriate position to have the knee in when tensioning a reconstruction.

Several limitations should be noted. Firstly, the small sample size and the variations between the individual knees and specimens has contributed to the large range in ALL length seen.

With 20 knees studied, our sample size is however larger than the majority of ALL biomechanical studies with an average of 10 knees. Secondly, we did not use a rig to bend the knee with the knee range of motion performed manually. Nonetheless, the intra-rater reliability was good to excellent and the movement was performed with a low speed. This slow motion allowed to overcome the effects of speed and therefore recalculation of the angles and positions in a static model by interpolating them at each degree of flexion without using angular velocities.

CONCLUSION

This three-dimensional optoelectronic protocol allowed us to analyse the variation of the ALL length during knee motion with good reliability and the required accuracy to analyse this variable. This makes it a valuable protocol that can be used when carrying out future biomechanical analyses necessary to optimise ALL reconstruction techniques. The maximal length and highest tension of the ALL was reported at 25° of knee flexion in internal rotation, suggesting this as the optimal position for the knee joint when tensioning an ALL reconstruction.

FIGURES

Figure 1 .

 1 Figure 1. Installation of Motion analysis® system with 8 High definition cameras (1a), around the specimen. Front (1b) and lateral (1c) pictures of the set-up showing pelvis, femoral and tibia reflective sensors.

Figure 2 .Figure 3 .Figure 4 .Figure 5 .Figure 6 .

 23456 Figure 2. Definition of bone landmarks and bone axis -Femur: F1, F2, F3, F4, FHC* (Femoral Head Center), Lateral Epicondyle (LE), Medial Epicondyle (ME), KC* (Knee center) -Tibia: T1, T2, T3, T4, center of Inter Condylar Eminences (ICE) -Ankle: Medial malleolar (MM), Lateral malleolar (LM), Ankle Center* (AC) -Purple circle= palpated landmarks -Purple star = calculated landmarks -Femoral axis: XF (in red), YF (in green), ZF (in blue) -Tibial axis: XT (in red), YT (in green), ZT (in blue)

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.