Yannick Le Cozler
email: yannick.lecozler@agrocampus-ouest.fr

C Allain

Anaïs Caillot

J M Delouard

L Delattre

T Luginbuhl

Philippe Faverdin

High-precision scanning system for complete 3D cow body shape imaging and analysis of morphological traits

Keywords: body measurement, cows, sensors, 3D images

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

Introduction

Body weight (BW), morphological traits and body condition score (BCS) are important parameters traditionally used in dairy cattle production. They are essential for accurately monitoring growth rate or changes in growth and thus for adapting animal nutrition to increase efficiency or maintain productivity. Currently, except for BW, most measurements are performed manually (e.g. measuring tape, ruler) or visually (Heinrichs and Hardgrove, 1987). These measurements are time consuming and could result in injury to livestock farmers. They are also a source of stress for animals and, in many cases, observer-dependent. As a result, such information during the growing period is rare on many commercial farms, and when available in France, is reduced to 4-6 BW measurements during the growing period. Developing accurate and automatic technologies that do not depend on humans could help address these issues. Developing automatic measurement methods to study phenotypic traits, however, is considered a bottleneck in biology, particularly for large live and moving animals such as dairy cows [START_REF] Chéné | On the use of depth camera for 3D phenotyping of entire plants[END_REF].

Techniques based on optical detection devices are interesting alternatives to manual measurements or more costly methods (Pezzuolo et al., 2018). Technologies have been developed to detect lameness in cows [START_REF] Van Hertem | Automatic lameness detection based on consecutive 3D-video recordings[END_REF][START_REF] Zhao | Automatic lameness detection in dairy cattle based on leg swing analysis with an image processing technique[END_REF] and to measure body parameters such as BCS [START_REF] Halachmi | Cow body shape and automation of condition scoring[END_REF][START_REF] Fischer | Rear shape in 3 dimensions summarized by principal component analysis is a good predictor of body condition score in Holstein dairy cows[END_REF]Sploliansky et al., 2016). Two-dimensional (2D) image approaches have been used for pigs with a certain degree of success [START_REF] Marchant | Extending the snake image processing algorithm for outlining pigs in scenes[END_REF]Schofield et al., 1998). Their effectiveness is decreased, however, by the lack of a third dimension, distortion problems, the calibration procedure, and the need for multiple cameras and three-dimensional (3D) reconstruction models. The development and marketing of relatively inexpensive 3D cameras has decreased interest in 2D technology in favor of 3D approaches. Recently, new imaging technologies have been successfully developed and used to analyze body condition in dairy cattle, using either a fixed [START_REF] Fischer | Rear shape in 3 dimensions summarized by principal component analysis is a good predictor of body condition score in Holstein dairy cows[END_REF] or mobile [START_REF] Kuzuhara | A preliminarily study for predicting body weight and milk properties in lactating Holstein cows using a three-dimensional camera system[END_REF] device.

Others [START_REF] Negretti | Determination of live weight and body condition score in lactating Mediterranean buffalo by Visual Image Analysis[END_REF][START_REF] Buranakarl | Estimation of body weight and body surface area in swamp buffaloes using visual image analysis[END_REF][START_REF] Guo | LSSA_CAU: an interactive 3d point clouds analysis software for body measurement of livestock with similar forms of cows and pigs[END_REF]Pezzuolo et al., 2018) have developed and used 3D imaging technologies for a wider variety of livestock. In most cases, animals were measured under laboratory conditions (heavy equipment and landmarks on animals to guide computer measurement), providing either images of the entire body of restrained animals or of part of the body of unrestrained animals. In most cases, equipment can adapt to farm conditions; recent literature describes devices used to estimate weight of pigs in barns (Pezzuolo et al., 2018;[START_REF] Wang | A portable and automatic Xtion-based measurement system for pig body size[END_REF] and broilers in houses [START_REF] Mortensen | Weight prediction of broiler chickens using 3D computer vision[END_REF]. Pezzuolo et al. (2018) used inexpensive and portable equipment based on the Microsoft Kinect® v1 sensor but concluded that the method needed additional technical development to acquire and extract data automatically.

The present study presents a new, more accurate scanner -Morpho3Dthat was developed in an eponymous study to easily capture the full shape of cow bodies and to precisely accurately measure their morphological traits in the 3D imaging space.

Its measurements were compared to direct measurements of the live cows. To validate the method, repeatability and reproducibility, which are important criteria when applying methods, were estimated.

Materials and methods

2.1. Animals: Data were obtained from the INRA-UMR PEGASE experimental dairy station at Mejusseaume, Le Rheu, in western France (48°11'N; 1°71'W; elevation 35 m). Data were collected from May-June 2017. The study involved 30 dairy cows, with a mean (± 1 standard deviation (SD)) age of 3.0 (± 1.2) years and milk production of 25.5 (± 3.6) kg milk per day. After each milking (twice a day), cows were individually and automatically weighed on a static weighing station (DeLaval France, Elancourt, France) at the milking parlor's exit. Their mean (± 1 SD) weight was 674 (± 66) kg.

Mean BCS (± 1 SD), based on the French scoring scale of 0-5 [START_REF] Bazin | Grille de notation de l'état d'engraissement des vaches pie-noires[END_REF], was 2.1 (± 1.2). Data from the 30 cows were used to estimate the accuracy of the measurements extracted from images from the new scanner and calculate correlations between these estimates and manual measurements of the cows.

Morphological acquisition system:

3D images of the cows were acquired automatically using the sliding acquisition system, Morpho3D, located near the weighing station. The system has 5 cameras, each paired with a laser projector. The laser has a wavelength of 650 nm, which is shorter than those of infrared lasers (750-2000 nm), to make it visible to humans and animals. This decreases risks to them, since the visible laser, unlike an infrared laser, triggers a blink reflex in humans. The laser is turned on only when the system's portal is moving. With a power of approximately 80 mW, it is a class 3B laser (CDRH, 2018). Looking directly at the beam is dangerous. The risk was low in the present study, however, because the beams are emitted on the sides of the animal, and looking at diffuse reflections of the laser is not considered dangerous. In addition, full power is distributed over a stripe and not concentrated on a single point. Also, the laser moves at a mean speed of 0.5 m.s -1 , so it spends little time on the eye.

The VGA image resolution of each camera was 640 × 480 pixels. Reconstructing an animal in 3D is a generalization of laser triangulation. Traditionally, triangulation is based on the triangle formed by a camera, a laser and the single point the laser projects on an object. In contrast, each Morpho3D laser generates a vertical plane, whose intersection with the object appears as a stripe in each image yielding more points per image. Knowing the equation of the plane in the camera frame allows the 3D position of the points in each stripe in the camera frame to be determined by intersecting the plane with the radius passing through the origin of the camera and the points observed in the image plane (Fig. 1). Sliding the system's portal horizontally scans the laser plane over the entire object, yielding a cloud of points consisting of several "slices" of 3D points (1 slice = 1 image). These point slices are aggregated based on the location of the system's portal.

Since the cameras are sensitive to light, excessive direct sunshine was avoided in the stable. The cameras were attached to the sliding portal (l = 5.00 m; l = 2.58 m; h = 3.00 m; Fig. 2).

Fig. 2. Design of the Morpho3D scanner

Two cameras were fixed at 0.40 and 1.77 m above ground level, respectively, on each side of the portal. A fifth camera was fixed to the middle of the top of the portal (3.00 m above ground level). The portal moved at a mean speed of 0.5 m.s -1 from back to front (phase 1) and returned to its initial position at a mean speed of 0.3 m.s -1 (phase 2). Each camera took 80 images per second and did so only during phase 1, yielding a total of 2,000 images. Images are used only to extract laser stripes; 90% of each image is not used, like in many triangulation systems that use laser planes.

Four stainless steel cables were used within the Morpho3D Scanner, on both side of cow, to secure the scanner and restrict cow movement. Cows could also be restrained by a self-locking head gate if necessary.

Calibration.

Calibration consisted of finding the position of the laser plane in each camera space and the relative positions of the cameras. The cameras were calibrated in three ways:

1. Calibration of each camera to determine its intrinsic parameters and to correct distortions; 2. Calibration of the laser plane in each camera frame for triangulation and reconstruction of 3D points;

Calibration of all five cameras to place their point clouds in the same frame

The cameras were calibrated using a black-and-white checkerboard placed in different locations in the Morpho3D. Each camera-laser pair was calibrated individually and then two-by-two to calibrate all five cameras collectively.

Calibration determined the relative position of a camera to its corresponding laser plane, which is required to triangulate 3D data. It also determined the positions of the cameras relative to each other in order to merge their clouds. For Morpho3D, a blackand-white checkerboard of known dimensions was used. The technique corresponds to a "model" type of calibration (the model is the target). The camera is calibrated by capturing at least ten images of the target with laser stripes. A program then analyzes these images and determines the required parameters and also provides a confidence value. Calibration was performed twice, first in the laboratory and then after installation on the farm.

Image capture and reconstruction.

When a cow entered the Morpho3D, image capture did not begin until it stopped moving. If the cow moved during recording, the record was deleted and another was started. Two or three attempts were usually required the first time, but since images were recorded once a month for the entire lactation period, cows became accustomed to the process and usually required only one attempt afterwards, though some cows required more.

Images of the laser stripes projected onto the cow were captured by their corresponding camera and sent to a computer to reconstruct the cows' 3D information. First, images from each camera were processed to build separate point clouds using calibration information and the speed of the portal. A 3D reconstruction of the entire cow was generated by recording and merging the multiple 3D point clouds from the five camera-laser pairs. This resulted in a single point cloud representation of the entire cow (Fig. 3). Two camera filters were used during image capture. The first was a physical filter centered on the laser wavelength to reduce ambient light and increase the contrast of laser stripes in each image. The second was a software filter. For this filter, since each camera-laser pair was fixed at a specific height on the structure, the distance between the ground and the camera was known. The depth of field of each camera varied from 0.3-3.5 m. A maximum depth was determined for each individual camera to prevent recording undesirable points that were too far from the camera and did not belong to the cows, such as walls. Other undesired objects (e.g. a cable) were easily deleted (Fig. 4) during a cleaning process, using Metrux2α® software (3DOuest company, Lannion, France). This step ensures that the point cloud is a sampling of a smooth surface on which surface normal vectors can be estimated. An example of using Morpho3D with a live cow is available online (https://vimeo.com/219370900). Finally, surface normals were estimated from the point cloud, and a screened Poisson surface reconstruction algorithm was applied to build a triangulated mesh [START_REF] Kazhdan | Screened Poisson surface reconstruction[END_REF] using Meshlab open-source software [START_REF] Cignoni | MeshLab: an Open-Source Mesh Processing Tool[END_REF]. Image-processing steps are shown in Fig. 4.

1.

2. (3) point cloud after cleaning and (4) final 3D image after Poisson reconstruction.

4.

It took 5 s to record the entire body and 2 minutes to acquire the point cloud automatically, which was then saved. The final mesh used for analysis required 10-12 minutes to generate.

Nomenclature of body traits and measurements:

The two measurement methods were compared for the 30 cows. Six of the 30 cows underwent a series of repeated manual measurements of the same body traits (six times each) to estimate reproducibility (see next section). Since reference measurements for animal development are always measured on live animals, qualified and experienced technicians trained us how to find where to measure cow body traits, using a group of non-experimental live cows. The next step consisted of comparing body traits measured by the trained technicians (hereafter "reference measurements") to those that we measured, using another group of non-experimental cows. Differences between the two sets of measurements were similar among body traits, even for several traits that are usually difficult to detect (e.g. ischial width).

Measurements were then taken of experimental cows. A plastic model cow was used to estimate repeatability (see next section). For manual measurements, we used permanent ink to identify measurement locations on the plastic model. For measurements extracted from 3D images, we first fixed small balls on the plastic model to precisely locate where to perform measurements. We then used a 3D image without the balls to extract reference measurements of the model.

Six measurements were taken of live animals and extracted from images: heart girth (HG), chest depth (CD), wither height (WH), hip width (HW), backside width (BaW)

and ischial width (IW) (Fig. 6). For live animals, a tape measure was used to measure HG, while a height gauge was used for the other measurements. For images, the relevant measuring location was determined visually, and measurements were extracted using Metrux2α® software. six live cows six times each on the same day. Two individuals extracted measurements from each 3D image. In total, each body trait of each live cow was measured six times by each method i.e., a total of 12 times. For repeatability and reproducibility, we estimated the error associated with each body trait for each measurement method independent of that associated with the measurers. Extracting body trait measurements from each 3D image six times (on six cows) meant that the six extraction processes had the same body measurement, and the landmarking was repeated six times. Similarly, scanning cows six times on the same day meant that the error associated with extracting measurements was the same for a given image, but the error associated with image acquisition and processing differed for each scan.

Thus, the reproducibility error included the repeatability error in its variability.

Variability in measurements extracted from 3D images was corrected for the effect of individual cows by extracting residuals from an ANOVA model. Coefficients of variation for repeatability and reproducibility (CVr and CVR, respectively) were estimated from their respective means (µr and µR, respectively) and standard deviations σr and σR, respectively). Likewise, variability in the repeatability and reproducibility of manual measurements was corrected for the effects of individual cows and individual measurers by extracting residuals from two ANOVA models. The first included cow identity as a factor to explain repeatability, while the second included cow identity and measurer identity as factors to explain reproducibility. The more repeatable (or reproducible) the 3D measurement was, the smaller was its CVr (or CVR).

Statistical analysis: Correlations between measurements extracted from 3D

images and reference values of repeatability and reproducibility were calculated using SAS software (SAS institute, 2016).

Results

Comparison of body traits measured manually and with the 3D scanner

Most manual measurements were smaller than those extracted from the 3D images (Table 1). The largest difference between the two sets of measurements (11.2%) was observed for IW, while the smallest difference (1.3%) was observed for WH. The correlation between manual and Morpho3D measurements was also high, ranging from 0.63 for IW to 0.89 for CD (Table 2).

Repeatability and reproducibility

Repeatability and reproducibility were generally similar between methods, but the method with higher value varied among body traits (Table 3). For Morpho3D measurements, σr ranged from 0.34-1.89 cm (CV = 0.26-9.81%) and σR from 0.55-5.87 cm (CV = 0.94-7.34%). For manual measurements, σr ranged from 0.21-1.32 cm (CV = 0.11-10.30%) and σR from 0.49-1.19 cm (CV = 0.42-4.46%).

Discussion

It is unknown why manual measurements were usually smaller than those extracted from the 3D images. With additional effort, the point clouds behind the final mesh were also analyzed; they yielded similar results, indicating that the scanning equipment probably overestimated certain measurements (by 2-7%). In particular, IW (11.2% difference between manual and mesh measurements) is extremely difficult to measure accurately on live animals, even for trained technicians. The prominence of bones used to measure HW explained the small differences observed between manual and Morpho3D measurements, as Pezzuolo et al. (2018) This method can detect and identify anatomical landmarks that could be of interest for further development, but authors concluded that proposed models need to be adapted and calibrated to specific breed.

According to [START_REF] Fischer | Rear shape in 3 dimensions summarized by principal component analysis is a good predictor of body condition score in Holstein dairy cows[END_REF], measurement methods whose repeatability and reproducibility have a CV less than 4%, as in the present study, are considered promising. The difference in measurements between the plastic model and live cows was initially attributed to the latter's movement and long hair. However, 3D images were deleted if cows moved during image acquisition, and the cows' hair had been clipped; thus, these were not the source of the differences.

Research in the field of animal imaging, first 2D and now 3D, is increasing due to improvements in costs, ergonomics, maintenance, etc. This research has identified several objectives for high-speed acquisition of phenotypic traits, such as measurement of morphological traits, body condition traits and, indirectly, BW of animals (to be published). However, [START_REF] Tscharke | Review of methods to determine weight and size of livestock from images[END_REF] identified limits to these approaches and suggested ways to improve them. The first recommendation was to automate measuring and image processing. [START_REF] Brandl | Determination of live weight of pigs from dimensions measured using image analysis[END_REF] and [START_REF] Arias | Estimate of the weight in bovine livestock using digital image processing and neural network[END_REF] identified the need for further research to facilitate complete automation of the often semi-automatic scanners. Two completely automatic systems for weighing and sorting pigs and for measuring body condition of dairy cows have been marketed (Hölscher+Leuschner, Emsbüren, Germany), but they were only moderately accurate [START_REF] Bergfeld | Automatic measurement of the body condition of dairy cows with three-dimensional picture processing[END_REF]. The second recommendation was to maximize repeatability of the measurements. Many authors highlight the strong influence of animal position on measurement variability and the importance of selecting, often manually, the best images in order to decrease undesirable variations [START_REF] Kmet | Application of video image analysis in the slaughter value estimation of live Simmental bulls[END_REF][START_REF] Stajnko | Estimation of bull live weight through thermographically measured body dimensions[END_REF]. [START_REF] Fischer | Rear shape in 3 dimensions summarized by principal component analysis is a good predictor of body condition score in Holstein dairy cows[END_REF] showed that only a few of the studies that estimated BCS from images evaluated their method (e.g. determination of repeatability and reproducibility). Spolianski et al. ( 2016) extracted BCS from images and evaluated the repeatability and accuracy of the method, as did [START_REF] Viazzi | Analysis of individual classification of lameness using automatic measurement of back posture in dairy cattle[END_REF]. Other authors studies have evaluated methods for studying cow problems [START_REF] Beiderman | Automatic solution for detection, identification and biomedical monitoring of a cow using remote sensing for optimised treatment of cattle[END_REF] or measuring BCS [START_REF] Bercovich | Development of an automatic cow body condition scoring using body shape signature and Fourier descriptors[END_REF]) by calculating correlations with measurements from other methods (manual, or those extracted from images) or calculating classification accuracy (Beidermann et al., 2014). All authors, however, emphasized the importance of evaluating each method accurately.

According to [START_REF] Tscharke | Review of methods to determine weight and size of livestock from images[END_REF], controlling the environment is also important. Since most technologies are sensitive to daylight, they are used under controlled light conditions. Similarly, restricting animal movement to obtain usable images is also crucial. Animal color or lack of cleanliness can sometimes cause problems acquiring images. Further studies are needed so that scanners developed under controlled conditions can be used in the "aggressive" environment of a commercial, or at least an experimental, farm. [START_REF] Tscharke | Review of methods to determine weight and size of livestock from images[END_REF] indicated that bias and modeling are also important when working with images. Many potential biases exist when estimating BW or BCS. Optimizing models and equations that consider parameters such as age or sex will increase accuracy.

Conclusion and future studies

This new scanning technology provides new perspectives for assessing animal morphology. The time required to measure all six body traits was estimated as 2.5

and 15 min for the manual and Morpho3D methods, respectively. Image acquisition is rapid for the latter (mean = 6 seconds), but the time required to analyze and obtain the final results was approximately 14 minutes. The prototype was not designed to minimize image processing times, however, so it is possible to reduce them in the future. A valuable advantage of 3D images is that they remain available for additional or new analyses if necessary.

The risk of human injury when acquiring images is reduced to nearly zero, which could be of interest to types of production in which animal measurements are necessary and risky, such as beef production. A major concern, currently under review, is to automate the steps of image analysis: cleaning, reconstruction and extraction of measurements. This is clearly a major point when using this method at a large scale and when developing new technology based on "one-shot" technology, in which animal movement is no longer a problem. In the latter case, image definition will probably decrease, but based on developments in the Morpho3D project, accurate equations and algorithms should be available to optimize analysis. The ability to capture a 3D image of an entire animal will allow for many potential improvements in the near future. Automatic estimation of visual BCS, morphological scoring for selection purposes, BW, surface area and volume will be developed and implemented in Metrux2α® software and compared to manual measurements. Body surface area, for example, has been demonstrated as useful for determining precise doses of medication for large animals. Moreover, it is likely that calibrating carcass characteristics from slaughterhouse data with these animal shapes will help estimate the quality of meat of live animals.

Fig. 1 .

 1 Fig. 1. Diagram of the triangulation process (adapted from[START_REF] Taubin | ENGN 2502 3D Photography / Assignment 2[END_REF]

Fig. 3 .

 3 Fig. 3. The process of reconstructing 3D clouds of cows from the five camera-laser pairs, as a function of the speed of the scanner's portal (to generate a cloud of the entire body)

Fig. 4 .

 4 Fig. 4. Steps from data acquisition to final 3D image: (1) data acquisition; (2) raw point cloud;

Fig. 6 .

 6 Fig. 6. Body traits measured on live animals and extracted from 3D images

Table 1 .

 1 Mean measurements (cm) of body traits of 30 live Holstein cows performed

	Body trait	Manual	Morpho3D	P value
	Heart girth	207.5	221.5	< 0.0001
	Chest depth	79.4	83.8	< 0.0001
	Wither height	146.9	148.8	< 0.003
	Hip width	55.5	54.4	< 0.02
	Backside width	51.9	54.4	< 0.008
	Ischial width	17.4	19.6	< 0.02

manually and extracted from images from a new 3D scanner (Morpho3D) and P values of the difference between them (Student's t-test)

Table 2 .

 2 Correlation coefficients (r) and their P values between mean values of body traits manually measured and those estimated from images from a new 3D scanner (Morpho3D) for 30 live Holstein cows

	Body trait	r	P value
	Heart girth	0.78	< 0.001
	Chest depth	0.89	< 0.001
	Wither height	0.62	< 0.001
	Hip width	0.80	< 0.001
	Backside width	0.76	< 0.01
	Ischial width	0.63	< 0.01

Table 3 .

 3 Mean (µ), standard deviation (σ) and coefficient of variation (CV) of repeatability and reproducibility of manual measurements and those extracted from images from a new 3D scanner (Morpho3D) of body traits of cows. A model cow was used to estimate repeatability, while six live cows were used to estimate reproducibility.

	Body			Repeatability	Reproducibility
	trait	Method	µr (cm) σr (cm)	CVr (%)	µR (cm)	σR (cm)	CVR
	Heart	Manual	194.2	0.21	0.11	204.2	0.86	0.42
	girth	Morpho3D	195.8	1.89	0.97	221.1	5.87	2.63
	Chest	Manual	75.1	0.42	0.56	79.1	0.49	0.62
	depth	Morpho3D	76.5	0.44	0.58	84.4	0.92	1.09
	Wither	Manual	129.1	1.04	0.80	148.9	1.07	0.72
	height	Morpho3D	131.1	0.34	0.26	148.6	2.12	1.42
		Manual	39.8	0.35	0.88	55.5	1.01	1.82
	Hip width
		Morpho3D	39.9	0.67	1.68	58.6	0.55	0.94
	Backside	Manual	50.9	0.36	0.71	50.8	1.19	1.82
	width	Morpho3	52.6	0.34	0.64	55.5	1.82	3.28
	Ischial	Manual	12.8	1.32	10.30	17.3	0.77	4.46
	width	Morpho3D	17.5	1.78	9.81	15.4	1.13	7.34

  observed.Conversely, no prominent bones are available for measuring SW. In addition, HG and CD were overestimated because the cow's front leg often obscured its chest in the image. Correlations between measurements of both methods were generally lower in the present study than those reported byBuranarkal et al. (2012) andPezzuolo et al.

	(2018). Buranarkal et al. (2012) measured animals under laboratory conditions and
	placed landmarks on them, but this approach would be difficult to implement under
	commercial conditions. Pezzuolo et al. (2018) used a method based on a suitable
	low-cost depth camera (Microsoft Kinect v1), which allowed to take measurements
	without contacts on pigs and extract body dimension and calculate then, body weight.

Acknowledgments

The authors wish to thank everyone involved in the Morpho3D project, especially technicians at the Mejusseaume experimental station, who took excellent care of the animals. The Morpho3D project is supported by the National Fund CASDAR, which supports innovation in agriculture (RFP "Recherche Technologique" 2015, no.005), special funds from the INRA Animal Physiology and Livestock Systems division for innovative projects and the collaborative ANR -APIS-GENE project DEFFILAIT.


Manel Mattoussi

M Rey

M Rotger

A V Nikitin

I Chizhmakova

Xavier Thomas

H Aroui

S Tashkun

Vladimir G Tyuterev

Preliminary analysis of the interacting pentad bands ( ν 2 +

Keywords: CF 4, Tensorial formalism, ab initio, Infrared spectrum, Line positions and intensities

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

Introduction

Tetrafluoromethane CF 4 appears to be of vast industrial, environmental and economical interest. For these reasons, the ro-vibrational spectroscopy of this molecule was a subject of several theoretical and experimental studies. CF 4 belongs to the group of perfluorocarbons (PFCs) which designates the chemicals composed of carbon and fluorine only. These species predominantly CF 4 are extremely stable, inoffensive for the stratospheric ozone layer but powerful greenhouse gases (GHGs). This molecule is found among the longest-lived atmospheric trace gases because of its great chemical stability with an estimated lifetime of more than 50,000 years [START_REF] Ravishankara | Atmospheric lifetimes of long-lived halogenated species[END_REF][START_REF] Morris | Effects of electron and ion reactions on atmospheric lifetimes of fully fluorinated compounds[END_REF]. In addition, it seems to be the most abundant PFC in the stratosphere. Infrared high spectral resolution solar occultation spectrometer lead to an abundance of 70.45 ±3.40 ppt [START_REF] Rinsland | Long-term stratospheric carbon tetrafluoride CF 4 increase inferred from 1985-2004 infrared space-based solar occultation measurements[END_REF]. Because of this atmospheric persistence, CF 4 is regulated by the Kyoto Protocol of the United Nations Framework Convention on Climate Change (UNFCCC) [START_REF] Harnisch | Comparison of emissions estimates derived from atmospheric measurements with national estimates of HFCs, PFCs and SF 6[END_REF][START_REF] Harnisch | Halogenated compounds and climate change[END_REF][START_REF] Boudon | Spectroscopic tools for remote sensing of greenhouse CH 4 , CF 4 and SF 6[END_REF] as a substance whose atmospheric concentration should be supervised and reduced. Besides its natural origin [START_REF] Harnisch | Effect of natural tetrafluoromethane[END_REF][START_REF] Harnisch | Tropospheric trends for CF 4 and C 2 F 6 since 1982 derived from SF 6 dated stratospheric air[END_REF][START_REF] Deeds | Evidence for crustal degassing of CF 4 and SF 6 in Mojave Desert groundwaters[END_REF], the second source of CF 4 is linked to aluminium production and to the manufacturing of semiconductor [START_REF] Khalil | Atmospheric perfluorocarbons[END_REF]. The spectroscopic databases like HITRAN [START_REF] Rothman | The HITRAN 2012 molecular spectroscopic database[END_REF][START_REF] Gordon | The HITRAN 2016 molecular spectroscopic database[END_REF] or GEISA [START_REF] Jacquinet-Husson | The 2009 edition of the GEISA spectroscopic database[END_REF][START_REF] Jacquinet-Husson | The 2015 edition of the GEISA spectroscopic database[END_REF] only contain a limited range of data for CF [START_REF] Harnisch | Comparison of emissions estimates derived from atmospheric measurements with national estimates of HFCs, PFCs and SF 6[END_REF] , without intensity analysis. The spectroscopy of CF 4 which is essential for quantitative measurement in the atmosphere still remains relatively poorly studied because of the complexity of analyses. Some detailed high-resolution studies exist, however they mostly concern line positions. This was the case of the analysis of the ν 3 fundamental with the 2ν 3 overtone [START_REF] Gabard | Study of the ν 3 and 2ν 4 interacting states of 12 CF 4[END_REF] and the interaction of this stretching state with the 2ν 4 overtone [START_REF] Boudon | High-resolution spectroscopy and analysis of the ν 3 /2ν 4 dyad of CF 4[END_REF]. Recent work was already dedicated to the analysis of some rovibrational bands of this molecule including some hot bands around 1283 cm -1 [START_REF] Carlos | High-resolution spectroscopy and global analysis of CF 4 rovibrational bands to model its atmospheric absorption[END_REF], the data being included in the Dijon database [START_REF] Ba | MeCaSDa and ECaSDa: Methane and ethene calculated spectroscopic databases for the virtual atomic and molecular data centre[END_REF]. First accurate and complete ab initio based line lists for CF 4 up to 400 K in the range 0-4000 cm -1 have been recently published by the Reims-Tomsk groups [START_REF] Rey | Understanding global infrared opacity and hot bands of greenhouse molecules with low vibrational modes from first-principles calculations: the case of CF 4[END_REF], resulting in 2 billion rovibrational transitions. In Ref. [START_REF] Rey | Understanding global infrared opacity and hot bands of greenhouse molecules with low vibrational modes from first-principles calculations: the case of CF 4[END_REF], although the variationally-predicted were not computed at the spectroscopic accuracy, the error on line intensities was only of few % allowing a correct global description of the overtones and combination bands up to 6 vibrational quanta validated by direct comparisons with experimental PNNL spectra. In this work, we report the analysis of rovibrational interacting pentad bands (ν 2 + 2ν 4 , ν 2 + ν 3 , 4ν 2 , ν 1 +2ν 2 , 2ν 1 ) of this molecule, in order to obtain a reliable simulation of CF 4 'atmospheric absorption in the region between 1600-1800 cm -1 , including the most significant hot bands. The study of this system of bands requires the investigation of various vibrational fundamentals, combinations and harmonics bands. For the first time, high resolution analysis was made by combining spectroscopic effective models and information provided by accurate ab initio potential energy (PES) and dipole moment (DMS) surfaces both for line positions and line intensities.A non-empirical effective Hamiltonian was built from a PES by applying high-order contact-transformations (CT) [START_REF] Vl | High-order contact transformations: general algorithm, computer implementation and triatomic tests[END_REF][START_REF] Vl | Accurate spectroscopic models for methane polyads derived from a potential energy surface using high-order contact transformations[END_REF]. For the line intensities, some effective dipole moment parameters have been adjusted directly on the ab initio intensities [START_REF] Rey | Understanding global infrared opacity and hot bands of greenhouse molecules with low vibrational modes from first-principles calculations: the case of CF 4[END_REF]. Section 2 describes the experimental data used, while Section 3 reviews some basic principles concerning the theoretical model for tetrahedral molecules used for our analysis and presents the obtained results.

Experimental details

Spectra measurements were carried out with the Fourier Transform Spectrometer (FTS) of GSMA laboratory [START_REF] Plateaux | Reims high resolution Fourier transform spectrometer. Data reduction for ozone[END_REF]. The CF 4 spectrum was recorded at room temperature over the range 1600-1800 cm -1 , with a spectral resolution of 0.003 cm -1 (maximum optical path length of 2.99 m). This experimental setup was equipped with a globar source, a CaF 2 beam splitter and a HgCdTe detector. A White-type multi-pass cell with a basis length of 2m was used to provide a path length of 8.262 m. The pressure in the cell was maintained at 9.93 Torr. The spectrum was obtained by co-adding and averaging 289 one-sided interferometer scans in order to achieve a sufficient signal-to-noise ratio. The diaphragm diameter was set to 4.5 mm. Wavenumber calibration was carried out using residual of ten water lines with intensities in the range 2 × 10 -19 -2 × 10 -20 cm/molecule. The detailed experimental conditions are listed in Table 1, and an overview of transmittance spectrum of the (ν 2 + 2ν 4 , ν 2 + ν 3 , 4ν 2 , ν 1 + 2ν 2 , 2ν 1 ) pentad is plotted in Figure 1.

Spectra analysis and modeling

Theoretical methods

The aim of the present work is the detailed analysis of the pentad system composed of five bands, namely ν 2 + 2ν 4 , ν 2 + ν 3 , 4ν 2 , ν 1 + 2ν 2 and 2ν 1 in the spectral range 1600-1800 cm -1 using a specific spectroscopic model (see also section 4.2), t. The absorption in this range is dominated by ν 2 +ν 3 with the band center near 1717 cm -1 . The complexity of CF 4 vibrational states is outlined in Figure 2 where the scale on the right panel represents sublevel with their symmetry type of the pentad split into 14 different components. The ν 2 +2ν 4 vibrational band has 6 vibrational sublevels of A 1 , A 2 , 2E, F 1 and F 2 symmetry types, the ν 2 +ν 3 band has 2 sublevels (F 1 , F 2 ), 4ν 2 has 3 sublevels of symmetry A 1 and 2E, ν 1 + 2ν 2 has 2 sublevels (A 1 , E) and 2ν 1 has one upper state vibrational level of A 1 symmetry. The infrared tetrafluoromethane spectra are known to be very complex due to the high tetrahedral symmetry of CF 4 which causes degeneracies and quasi-degeneracies of the vibration modes and large and complicated resonance interactions because of the inter-modes coupling. Note that such a line-by-line analysis from a judicious combination of effective and ab initio models-both for line positions and line intensities-was not yet available in this spectral interval. In order to extend rovibrational analyses of experimental spectra, we used a tensorial formalism with vibrational extrapolation [START_REF] Champion | Spherical top spectra, Spectroscopy of the Earth's atmosphere and interstellar medium[END_REF][START_REF] Boudon | Symmetryadapted tensorial formalism to model rovibrational and rovibronic spectra of molecules pertaining to various point groups[END_REF] including supplementary information derived from ab initio PES/DMS and first-principles calculations. These ab initio variational line lists are available in the TheoReTS information system [START_REF] Rey | TheoReTS-An information system for theoretical spectra based on variational predictions from molecular potential energy and dipole moment surfaces[END_REF]. Significant recent advance in ab initio PES, DMS and in rotationally resolved variational spectra calculations reported by Rey et al. [START_REF] Rey | Understanding global infrared opacity and hot bands of greenhouse molecules with low vibrational modes from first-principles calculations: the case of CF 4[END_REF] permitted identification of the most important bands in this range. But, many weak transitions remained not yet assigned.

The rovibrational model for line-by-line analysis is built by admitting that the vibrational energy levels of CF 4 can be gathered in a series of polyads. In the framework of this theory, an effective Hamiltonian (EH) for all the considered polyads was constructed from high-order contact transformations (CT) to eliminate inter-polyad interaction terms in the rovibrational Hamiltonian (transform completely the Hamiltonian to a block-diagonal form) [START_REF] Vl | High-order contact transformations: general algorithm, computer implementation and triatomic tests[END_REF][START_REF] Vl | Accurate spectroscopic models for methane polyads derived from a potential energy surface using high-order contact transformations[END_REF]. This approach allows a fairly precise characterization of resonance coupling terms to avoid the ambiguity of purely empirical EH models [START_REF] Vl | Fourth-order invariant parameters for F 2 isolated fundamental states of tetrahedral molecules: The study of the ν 4 band of 12 CH 4[END_REF][START_REF] Perevalov | Ambiguity of spectroscopic parameters in the case of accidental vibration-rotation resonances in tetrahedral molecules. r 2 J and r 2 J 2 terms for E-F 2 interacting states[END_REF]. The effective Hamiltonian operator H adapted to the polyad structure of the CF 4 is constructed as the sum of contributions appropriate to the various polyads designed by P k (k=0, 1, . . . , k, . . . ), P 0 being the ground state (GS). This effective Hamiltonian is expressed as (see Figure 2)

H = H {P k } = H {P 0 } + H {P 1 } + ... + H {P k } + ... (1)
= H {P 0 } + H {ν 2 } + H {ν 4 } + H {Dyad1} + H {ν 2 +ν 4 } + H {T etrad} + H {Dyad2} + H {Pentad}
The terms of this expansion gather operators specific to the successive polyads in the representation of the irreducible tensor operators (ITO) [START_REF] Boudon | Symmetryadapted tensorial formalism to model rovibrational and rovibronic spectra of molecules pertaining to various point groups[END_REF][START_REF] Nikitin | Improved Algorithms for the Modeling of Vibrational Polyads of Polyatomic Molecules: Application to T d , O h , and C 3v Molecules[END_REF][START_REF] Rey | Ab initio ro-vibrational Hamiltonian in irreducible tensor formalism: a method for computing energy levels from potential energy surfaces for symmetric-top molecules[END_REF]. They are written as a linear combination of rovibrational operators

T Ω(K,nΓ r )Γ 1 Γ 2 Γ v {n s }{m s }
as

H {P k } = all indices t Ω(K,nΓ r )Γ 1 Γ 2 Γ v {n s }{m s } T Ω(K,nΓ r )Γ 1 Γ 2 Γ v {n s }{m s } . (2)
In this equation, the t's are the corresponding adjustable parameters to be determined. All the indices represent the intermediate quantum numbers and symmetries. Here T refers to a rovibrational operator expressed as a tensor product between rotational and vibrational operators as

T Ω(K,nΓ r )Γ 1 Γ 2 Γ v {n s }{m s } = β R Ω(K,nΓ r ) ⊗ ε V Γ 1 Γ 2 Γ v {n s }{m s } (A 1 ) . (3)
Rotational operators R Ω(K,nΓ r ) are the usual symmetry-adapted irreducible tensor operators (ITO) for spherical top molecules [START_REF] Champion | Spherical top spectra, Spectroscopy of the Earth's atmosphere and interstellar medium[END_REF][START_REF] Boudon | Symmetryadapted tensorial formalism to model rovibrational and rovibronic spectra of molecules pertaining to various point groups[END_REF][START_REF] Champion | Développement complet de l'Hamiltonien de vibration-rotation adapté à l'étude des interactions dans les molécules toupies sphériques. Application aux bandes ν 2 et ν 4 de 12 CH 4[END_REF][START_REF] Wenger | Spherical top data system STDS software for the simulation of spherical top spectra[END_REF][START_REF] Zhilinskii | The method of irreducible tensor operators in the theory of molecular spectra[END_REF][START_REF] Moret-Bailly | Calculation of the frequencies of the lines in a threefold degenerate fundamental band of a spherical top molecule[END_REF][START_REF] Zhilinskii | Reduction of rotational operators to standard form[END_REF]. The upper index Ω is the rotational degree in the molecular frame components J x , J y and J z ; K is the tensor rank relative to the full rotation group O(3), n is a multiplicity index and Γ r (=A 1 , A 2 , E, F 1 or F 2 ) is the rotational symmetry in the T d point group. The vibrational ITOs are constructed by recursive coupling of elementary creation a + and annihilation a operators for each of the four normal modes. ε is the parity in conjugate momenta with the condition ε = (-1) Ω and Γ 1 and Γ 2 are the symmetries of vibrational operators; n s and m s are the degrees in the a + and a operators. Here, β is a numerical factor, equal to [Γ 1 ] 1/2 (-

√ 3/4) Ω/2 if (K, nΓ r ) = (0, 0A 1 )
, and 1 otherwise. Since the Hamiltonian is totally symmetric, we have necessary Γ r = Γ v . The order of the individual terms in T is defined as s (n s + m s ) + Ω -2. Orientation of the ITOs in the chain O(3) ⊃ T d has been described in details in Ref. [START_REF] Rey | Orientation of O(3) and S U(2) × C I representations in cubic point groups (O h , T d ) for application to molecular spectroscopy[END_REF].

In order to perform intensity calculation, the dipole moment operator is built in the same way as the effective Hamiltonian operator. Its components µ Θ (Θ = X, Y or Z) in the laboratory fixed frame (LFF) are linked to the components µ θ (θ = x, y or z) in the molecule fixed frame (MFF) as

µ Θ = θ λ Θθ µ θ , (4)
where λ Θθ are the direction cosines. The transformed LFF components can be expressed in terms of the MFF transformed components as

µ Θ = 1 2 θ (λ Θθ µ θ + µ θ λ Θθ ), (5)
where the MFF effective dipole moment is of symmetry F 2 with its three components µ θ expanded as a series of rovibrational operators [START_REF] Champion | Spherical top spectra, Spectroscopy of the Earth's atmosphere and interstellar medium[END_REF][START_REF] Papousek | Molecular vibrational-rotational spectra[END_REF]

µ θ (F 2 ) = {i} µ {i},Γ R Ω(K,nΓ r ) ⊗ ε V Γ 1 Γ 2 Γ v {n s }{m s } (F 2 ) θ . (6)
Here µ {i},Γ are the effective dipole moment parameters to be determined. A way to determine these parameters will be described in the section 3.2.2. Note that the order of the individual terms of the dipole moment is s (n s + m s ) + Ω -1.

Analysis and discussion

Line positions

Line-by-line analysis and assignments of experimental spectra are known to be tedious and difficult tasks. They are usually based on empirical models for the polyads of close states where line positions are generated from empirically-fitted effective Hamiltonians (EH). Using a vibrational extrapolation scheme, we simulate the spectrum by considering the polyad P 0 , which contains the GS level and the polyad P 7 containing the ν 2 +2ν 4 , ν 2 +ν 3 , 4ν 2 , ν 1 +2ν 2 and 2ν 1 levels as the upper polyad. To obtain a result with a precision comparable with the experimental accuracy, the effective Hamiltonian was expanded up to the sixth order. As a starting point, we needed a first estimation of the tensorial parameters. That permitted a correct description of the experimental spectrum at a given temperature. Starting with the best possible set of parameters permits to identify a large number of observed line positions. Here as a first guess, the ab initio based EH parameters obtained via the CT method were used and further refined after various iterations by increasing the number of assigned lines. This supplied realistic estimations for the rovibrational coupling parameters between various bands of a given polyad that are responsible for the intensity perturbations due to accidental resonances. This first set of parameters allowed a preliminary simulation. In what follows, parameters for ν 2 , ν 4 , (2ν 2 , ν 1 ) dyad, ν 2 +ν 4 , (2ν 4 , ν 3 , 3ν 2 , ν 1 ) tetrad and (2ν 2 +ν 4 , ν 1 +ν 4 ) dyad states will be fixed to the "ab initio" values derived from CTs. That means that only the parameters for the ground state and (ν 2 +ν 4 , ν 2 +ν 3 , 4ν 2 , ν 1 +2ν 2 , 2ν 1 ) are adjusted. Spectrum simulations, line assignments and the fitting process were carried out using the MIRS [START_REF] Nikitin | The MIRS computer package for modeling the rovibrational spectra of polyatomic molecules[END_REF][START_REF] Nikitin | Extension of the MIRS computer package for the modeling of molecular spectra: from effective to full ab initio ro-vibrational hamiltonians in irreducible tensor form[END_REF] and SpectrAssign softwares based on an iterative semi-automatized comparison of synthetic and experimental spectra. The T d formalism is implemented in MIRS that thus provides all vibrational and rotational quantum numbers. The SpectrAssign program was used for assignments and visualization. It allows a simultaneous display of predicted lines from MIRS output and of an experimental spectrum. A limited number of observed lines were assigned by comparing the positions and intensities of the observed and simulated lines calculated from the initial values of the spectroscopic parameters. Afterwards, new assignments were made leading to a new set of fitted tensorial parameters. This process was performed iteratively until no more lines could be assigned. Finally, among the 618 parameters included in the sixth order effective Hamiltonian, only 48 have been fitted. The root mean square (RMS) deviation of the IR data is very satisfactory. In Figure 3, we present an overview of the pentad region. It compares the observed spectrum with the calculated one at the same experimental conditions by using our final set of parameters in the region 1600-1800 cm -1 dominated by the ν 2 +ν 3 combination band. As shown in this figure, calculated and observed spectra are in very good agreement. As can be seen in Figure 4, different zooms reveal the precision obtained of calculated positions in the R and P-branches though weaker lines belonging to hot bands need to be still improved. Note that the Q-branch has an unresolved structure due to a tremendous number of overlapping lines making assignments very complicated. In order to keep the total number of adjusted parameters reasonable and to make the model "stable" when slightly changing parameters, an important part of the non-diagonal resonance parameters have been kept fixed to their theoretical values generated from the PES [START_REF] Rey | Understanding global infrared opacity and hot bands of greenhouse molecules with low vibrational modes from first-principles calculations: the case of CF 4[END_REF] in a manner similat to that described for the methane molecule [START_REF] Champion | Spherical top spectra, Spectroscopy of the Earth's atmosphere and interstellar medium[END_REF]. Although the ab initio values for non-diagonal parameters are approximations, they describe the resonance couplings in a quite qualitatively correct way. On the other hand, an empirical "blind" fitting of a big set of effective polyad Hamiltonian parameters to rovibrational energies is known as a mathematically poorly defined inverse problem [START_REF] Vl | Fourth-order invariant parameters for F 2 isolated fundamental states of tetrahedral molecules: The study of the ν 4 band of 12 CH 4[END_REF][START_REF] Perevalov | Ambiguity of spectroscopic parameters in the case of accidental vibration-rotation resonances in tetrahedral molecules. r 2 J and r 2 J 2 terms for E-F 2 interacting states[END_REF]. Purely empirical approach could improve a root-mean-square deviation on line positions, but it often results in wrong values of interaction parameters and thus wrong intensity extrapolations. The accurate theoretical calculations of resonance coupling parameters from ab initio PES and of the corresponding intensities are difficult tasks.

According to this preliminary study, we were able to assign 1831 line positions, belonging mainly to the ν 2 +ν 3 combination band, with a root mean square deviation of 1.590×10 -3 cm -1 . Nevertheless, a large part of the transitions remained unassigned. A complete modelling of all bands in this region will require more assignments of both hot and cold transitions. Number of assigned transitions per band depends on the inherent intensity of the band and on the degree of interaction with other states. Figure 5 shows the residual defined by the difference between the observed and calculated wavenumbers versus J. It gives a global idea of the quality of the fit. We note that the data are well distributed on the scale of the J values. It allowed to make sure that the rovibrational energy levels are well sampled and that the results of the fit are reliable. Figure 6 presents the resulting calculated reduced upper state energies vs J showing the mixtures between the vibrational sub-levels.

Line intensities

Tetrafluoromethane has the same tetrahedral geometry as methane but the main difference is that the CF 4 molecule is heavier and consequently has much lower vibrational modes and much higher J-levels are populated. This leads to a considerable number of IR-active transitions belonging to hot bands that make the experimental spectra more complicated to analyse. Rey et al. [START_REF] Rey | Understanding global infrared opacity and hot bands of greenhouse molecules with low vibrational modes from first-principles calculations: the case of CF 4[END_REF] showed that the CF 4 spectra could be described from (i) a set of strong lines responsible for the strongest absorption features and (ii) of a kind of quasi-continuum formed by an accumulation of very week overlapping lines (see figure of [START_REF] Rey | Understanding global infrared opacity and hot bands of greenhouse molecules with low vibrational modes from first-principles calculations: the case of CF 4[END_REF]). This situation is quite similar to that observed in hot methane spectra at ≈ 1000-1200 K [START_REF] Rey | Accurate theoretical methane line lists in the infrared up to 3000 K and quasi-continuum absorption/emission modeling for astrophysical applications[END_REF]. Because the infrared spectra of CF 4 are very congested, no single line intensity measurements were made. Almost all the observed lines result from overlapping of several transitions. To overcome such a difficulty, we have adopted a strategy quite different from "usual" spectroscopic studies. It consists in fitting the effective dipole moment parameters directly on the variationally-determined ab initio intensities. In other words, the variational line list built in Ref. [START_REF] Rey | Understanding global infrared opacity and hot bands of greenhouse molecules with low vibrational modes from first-principles calculations: the case of CF 4[END_REF] was taken as an "observed" line list for the present work. To our knowledge, this procedure has never been applied before for such a complex fiveatomic molecular system. The improvement of hot bands intensity modelling will be necessary to achieve a more detailed assignment in the region between 1600-1800 cm -1 because many other bands belonging to upper polyads e.g. {2ν 2 +2ν 4 -ν 2 , 2ν 2 +ν 3 -ν 2 , ν 2 +3ν 4 -ν 4 , ν 2 +ν 3 +ν 4 -ν 4 } contribute to the absorption. Detailed statistics on this fit are listed in Table 2. The obtained effective dipole moment parameters for each band summarized in Tables 3, 4 and 5 rely on tensorial formalism notations. Figure 7 presents the resulting comparison between experiment and simulation, with a nice agreement.

Conclusion

In this work, we have built a tensorial model that permitted for the first time a detailed analysis of the (ν 2 +2ν 4 , ν 2 +ν 3 , 4ν 2 , ν 1 +2ν 2 , 2ν 1 ) band system of CF 4 by combining non-empirical CT Hamiltonian, ab initio based variational predictions and experimental information. The present analysis supplies a first accurate and complete description of the infrared high-resolution spectrum of CF 4 in the region 1600-1800 cm -1 . The final set of effective Hamiltonian/dipole moment parameters allows to reproduce simultaneously (i) quite accurately the cold bands and (ii) in a qualitative manner the main hot band transitions. The global fit of parameters and calculation of infrared spectrum was carried out with the MIRS and SpectrAssign softwares. Assignments was made up to J max = 70 and a set of 48 tensorial parameters has been adjusted. The accuracy of the final empirically optimized calculated line list is satisfactory. We have obtained a root mean square deviation RMS of about 1.590×10 -3 cm -1 for 1831 cold transitions. The standard deviation for line intensities for the cold bands {ν 2 +2ν 4 , ν 2 +ν 3 , 4ν 2 , ν 1 +2ν 2 , 2ν 1 } is of 1.1%, with respect to the ab initio intensities, while, for the hot bands {2ν 2 +2ν 4 -ν 2 , 2ν 2 +ν 3 -ν 2 } and {ν 2 +3ν 4 -ν 4 , ν 2 +ν 3 +ν 4 -ν 4 }, the standard deviation is of ≈ 8 % and 5 %, respectively. The main objective of this study was to construct a CF 4 line list for various applications. This final list will include new assignments in the forthcoming versions of the spectroscopic HITRAN and GEISA databases. The line list for the assigned transitions is available as supplementary material to this paper. By using cold spectra (<200 K), future works will consist to both improve the present region and extend analysis to other spectral ranges on the basis of the present results.

Figure 1 :

 1 Figure 1: Transmittance spectrum of CF 4 , recorded at 294 K at a pressure of 9.93 Torr in the spectral range between 1600 and 1800 cm -1 .

Figure 2 :

 2 Figure 2: Scheme of vibrational level patterns of the CF 4 polyads (left side) and vibrational sublevels of the part of the pentad system corresponding to ro-vibrational bands analyzed in this work. At the right hand side panel, symmetry type (T d irreducible representations) of vibration sublevels, vibrational ranking numbers within the pentad and the corresponding vibrational bands are given. The first dyad is composed of [2ν 2 , ν 1 ], the tetrad is composed of [2ν 4 , ν 3 , 3ν 2 , ν 1 +ν 4 ] and the second dyad is composed of [ ν 1 +ν 2 , 2ν 2 +ν 4 ].

Figure 3 :

 3 Figure 3: Comparaison between experimental and simulated spectra of CF 4 at 294 K.

Figure 4 :

 4 Figure 4: Detailed comparison of the R, P and Q-branches between the observed spectrum and the simulation.

Figure 5 :{ν 2 {ν 2

 522 Figure 5: Observed minus calculated wavenumbers versus J for the pentad obtained using the tensorial model. We have a lack of assignments between J = 50 and J = 60 because of the complexity of the CF 4 spectrum in this region.

Figure 6 :

 6 Figure 6: Calculated reduced rovibrational energy levels of CF 4 transitions from 1600 to 1800 cm -1 up to J = 70. Various colors correspond to mixing coefficients of normal mode wavefunctions due to resonance interactions.

Figure 7 :

 7 Figure 7: Observed and calculated intensities in (cm -1 /molecule.cm -2 ) vs line positions in (cm -1 ) for the pentad transitions.

Table 1 :

 1 Experimental details.

	Spectral range (cm -1 )	1600-1800
	Resolution (cm -1 )	0.003
	Source	Globar
	Separator	CaF 2
	Detector	HgCdTe
	Cell	White multi-pass
	Optical Path (m)	8.262
	Temperature (K)	294
	Pressure (Torr)	9.93
	Aperture diameter (mm)	4.5

Table 4 :

 4 Effective dipole moment parameters for the {2ν 2 +2ν 4 -ν 2 , 2ν 2 +ν 3 -ν 2 } bands.

		Tensorial nomenclature	Parameter value
		Rotational	Vibrational
	1	R 0( 0, 0A 1 ) 0100 0202 3.9825129095E-04
	2	R 0( 0, 0A 1 ) 0100 0210 8.5008049280E-03
	3	R 0( 0, 0A 1 ) 0100 0202 6.5544003405E-06
	4	R 0( 0, 0A 1 ) 0100 0210 7.9030718238E-05
	5	R 0( 0, 0A 1 ) 0100 0202 -4.4623481744E-04
	6	R 0( 0, 0A 1 ) 0100 0210 1.2930872868E-02