K Jongchansitto

P Jongchansitto

I Preechawuttipong

J. -B Le Cam

F Blanchet

M Grédiac

X Balandraud
email: xavier.balandraud@sigma-clermont.fr

Analysis of the Thermomechanical Response of a Rubber-like Granular Material

Keywords: Granular material, Rubber-like material, Infrared thermography, Thermoelastic coupling, Intrinsic dissipation

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

Introduction

Granular materials are omnipresent around us, in many industrial fields and in many natural phenomena. Rice and sugar are used in the food industry and in our daily lives. Sand and rocks are commonly used in civil engineering for the construction of buildings or streets. Granular flows are involved in avalanches and landslides. In the context of engineering, granular materials can be defined as a set of solid particles whose macroscopic mechanical behavior is governed by interparticle forces, i.e., contact forces between particles. Granular media are generally made up of grains having various distributions in terms of size, shape, and base material. This leads to a variety of mechanical phenomena that are not yet clearly understood. Numerical simulations have been widely used to study the influence of parameters such as particle shape, density, polydispersity, elasticity, and friction [START_REF] Radjai | Modeling granular materials: century-long research across scales[END_REF]. Several experimental techniques are also available. For measurements in the volume, we can mention X-ray tomography [START_REF] Khalili | Discrete digital projections correlation: a reconstruction-free method to quantify local kinematics in granular media by X-ray tomography[END_REF]. For surface measurements, particle image velocimetry and digital image correlation are widely used [START_REF] Slominski | Application of particle image velocimetry (PIV) for deformation measurement during granular silo flow[END_REF][START_REF] Hall | Localised deformation patterning in 2D granular materials revealed by digital image correlation[END_REF][START_REF] Richefeu | An experimental assessment of displacement fluctuations in a 2D granular material subjected to shear[END_REF][START_REF] Karanjgaokar | Experimental inference of inter-particle forces in granular systems using digital image correlation[END_REF][START_REF] Karanjgaokar | Study of energy contributions in granular materials during impact[END_REF][START_REF] Hurley | Extracting inter-particle forces in opaque granular materials: beyond photoelasticity[END_REF][START_REF] Hurley | Dynamic inter-particle force inference in granular materials: method and application[END_REF]. Stress fields can be obtained by photoelasticimetry measurement using particles made of birefringent materials [START_REF] Shukla | Experimental investigation of wave velocity and dynamic contact stresses in an assembly of disks[END_REF][START_REF] Roessig | Dynamic stress chain formation in a two-dimensional particle bed[END_REF][START_REF] Mirbagheri | Sensitively photoelastic biocompatible gelatin spheres for investigation of locomotion in granular media[END_REF]. Mechanoluminescent materials have also been used to visualize the intensity of interparticle contacts [START_REF] Jongchansitto | Using mechanoluminescent materials to visualize interparticle contact intensity in granular media[END_REF]. In most of the studies available in the literature, the particles are rigid or hard. Contact stiffness is then the main parameter. A granular system consisting of soft matter is more complex to analyze. Recently, the compaction of highly deformable particle assemblies has been performed numerically in Ref. [START_REF] Cantor | Compaction model for highly deformable particle assemblies[END_REF], opening the possibility of comparison with experimental results for soft granular materials.

Infrared (IR) thermography has also been used to measure the thermal signature of the mechanical response of soils and sands [START_REF] Luong | Characteristic threshold and infrared vibrothermography of sand[END_REF][START_REF] Luong | Infrared Thermography of the Dissipative Behaviour of Sand[END_REF][START_REF] Luong | Introducing infrared thermography in soil dynamics[END_REF]. Some studies have mainly focused on Schneebeli materials (two-dimensional discrete media made with cylinders) in order to analyze the contact zones between the particles, i.e., the stress concentration zones [START_REF] Jongchansitto | Using infrared thermography to study hydrostatic stress networks in granular materials[END_REF][START_REF] Chaiamarit | Stress network analysis of 2D non-cohesive polydisperse granular materials using infrared thermography[END_REF][START_REF] Jongchansitto | Thermoelastic couplings and interparticle friction evidenced by infrared thermography in granular materials[END_REF][START_REF] Jongchansitto | Numerical investigation of the influence of particle size and particle number ratios on texture and force transmission in binary granular composites[END_REF][START_REF] Jongchansitto | Concept of mechanocaloric granular material made from shape memory alloy[END_REF]. In the present study, IR thermography was used to analyze the thermal response of Schneebeli media made of thermoplastic polyurethane (TPU). Temperature changes were measured with an IR camera during cyclic confined compression. The objective was to distinguish the thermoelastic coupling effect (associated with reversible mechanical behavior) and the mechanical dissipation effect (associated with irreversible mechanical behavior).

Experimental Preparation

The experimental setup is presented in Fig. 14.1. A granular sample was prepared by randomly placing cylinders with elliptical cross-section into a rectangular metallic frame: see the schematic view in Fig. 14.1a. The particles were made of TPU manufactured by using an in-house device. Each particle was molded at ambient temperature in a vacuum chamber to avoid bubble formation. One side of the elliptical face of each cylinder was polished to obtain a smooth surface perpendicular to the longitudinal axis. To maximize the thermal emissivity of the surfaces observed by the camera (and thus reduce reflections in the IR range), a matt black paint was sprayed on the particle cross-sections as well as on the frame containing the granular system. Black curtains and cardboards were also placed around the device (not visible in Fig. 14.1b) to minimize parasitic reflections.

A cyclic triangular compressive loading was applied on the top of the granular system by using a Zwick/Roell ZMART PRO testing machine through a pusher (see Fig. 14.1b). The minimum and maximum forces were set to À1200 N and À 12,000 N, respectively. The loading was force-controlled with a force rate equal to 900 N/s, leading to cycle duration of 24 s. Note that some preliminary mechanical cycles were applied in order to compact the granular system. Next, the minimum force was kept constant for about 10 min to ensure that a steady thermal equilibrium of the system was reached before starting the cyclic loading.

A Cedip Jade III-MWIR camera was utilized to capture the temperature fields on the surface of each elliptical particle during the mechanical loading at a recording frequency of 10 Hz. In practice, the base acquisition frequency of the camera was set to 100 Hz with a real-time averaging every ten images in order to improve the thermal measurement resolution. The resulting standard deviation of the thermal noise (measurement resolution) was lower than 0.01 C thanks to this real-time average operation.

Temperature maps were also captured during 5 seconds just before the beginning of the cyclic loading in order to define the reference temperature field. Figure 14.2a shows the field of temperature differences at the beginning of the mechanical test with respect to this reference thermal state in order to reveal the spatial noise during the test. The corresponding distribution of the values within the particles (i.e., excluding the voids between the particles) is displayed in Fig. 14

Thermomechanical Background

Thermomechanical couplings in materials can be separated into two different parts, namely a part associated to reversible processes (elasticity) and a part associated to irreversible processes (e.g., plasticity, viscosity, fatigue damage, friction):

-The first case is called thermoelastic coupling. Two types of coupling between temperature and strain must be considered according to the physics associated with elasticity: isentropic coupling governed by thermal expansion or compression; and entropic coupling governed by the degree of disorder. In rubber-like materials, entropic coupling becomes dominant over isentropic coupling as soon as the level of deformation is greater than 10% [START_REF] Balandraud | Some specific features and consequences of the thermal response of rubber under cyclic mechanical loading[END_REF]. -In the second case, the associated calorific quantity d 1 (in W/m 3 ) is called mechanical dissipation or intrinsic dissipation.It is worth remembering that it is different from the thermal dissipation d 2 , the two types of dissipation being involved in the Clausius-Duhem inequality d 1 + d 2 >0.

Mechanical dissipation can be revealed through the temperature change over integer numbers of mechanical cycles. Indeed, heat quantities due to reversible mechanical phenomena are null over a thermodynamical cycle. More precisely, the heat quantities upon loading and unloading are equal in magnitude but opposite in sign. On the contrary, the mechanical dissipation is positive whatever the loading evolution: d 1 > 0. Thermoelastic coupling is a "strong" coupling. Indeed, the corresponding heat power density is much higher in magnitude than the mechanical dissipation in most cases. Extracting mechanical dissipation effect from the global thermal response of the material is in general possible for a cyclic loading, for which thermoelastic coupling effect vanishes cyclically. Moreover, the heat produced by irreversible phenomena accumulates over the cycles (because d 1 is always positive), which helps to experimentally identify this quantity. In the present experiment, thermoelastic coupling was evidenced by considering half of the first mechanical cycle (assuming that the mechanical dissipation is low over this duration) whereas mechanical dissipation was highlighted by considering ten cycles.

Analysis of the Reversible Mechanical Phenomena

Figure 14.3 shows the temperature change field at the half of the first mechanical cycle. "Hot" zones are clearly evidenced at each contact between the particles. They are also visible at the contacts with the metallic frame. They are logically due to the stress concentrations resulting mainly a priori from the normal interparticle forces. The largest temperature increase is observed in the upper left corner of the granular material. Tangential forces may be also involved in this zone, as revealed by the analysis of the thermal signature of the irreversible mechanical phenomena in the next section. Based on the assumption that the heat quantity due to the thermoelastic coupling is null over the preceding successive mechanical cycles, this map displays a thermal signature of the mechanical dissipation effect, i.e., of the irreversible mechanical phenomena. In granular media, this latter quantity can be mainly associated to friction at the contacts. However, viscosity and damage in the volume can be also involved, especially in the zones subjected to high stress levels. Figure 14.4 clearly shows that the mechanical dissipation effect is not present at all the contacts, which strongly differs from the case of the thermoelastic coupling effect (compare with Fig. 14.3). "Hot" zones are now mainly visible only in the upper two corners of the granular system. This can be explained by the greater movement of the particles in the upper two corners, potentially leading to greater friction. It can also be observed that the size of the "hot" zones is quite large, which can be explained by the heat diffusion over the ten cycles.

Finally, Fig. 14.5 shows the variation in time of the temperature at a given interparticle contact located in the upper left part of the granular material: see point A in the schematic view. As expected, the temperature oscillates at the same frequency as the mechanical loading. It can be seen that the mean temperature change first increases over the cycles and then stabilizes from nearly the seventh cycle: see the red dashed curve. This increase can be attributed to the monotonous production of mechanical dissipation over the cycles. The stabilization results from the equilibrium between the heat produced by the mechanical irreversible phenomena at point A and the heat diffused to the environment of point A.

Conclusion

IR thermography is in principle applicable to analyze thermomechanical phenomena of any types of material. However, it remains difficult to apply to cohesionless granular materials, which explains the small numbers of studies published in the literature (see Refs [START_REF] Luong | Characteristic threshold and infrared vibrothermography of sand[END_REF][START_REF] Luong | Infrared Thermography of the Dissipative Behaviour of Sand[END_REF][START_REF] Luong | Introducing infrared thermography in soil dynamics[END_REF][START_REF] Jongchansitto | Using infrared thermography to study hydrostatic stress networks in granular materials[END_REF][START_REF] Chaiamarit | Stress network analysis of 2D non-cohesive polydisperse granular materials using infrared thermography[END_REF][START_REF] Jongchansitto | Thermoelastic couplings and interparticle friction evidenced by infrared thermography in granular materials[END_REF][START_REF] Jongchansitto | Numerical investigation of the influence of particle size and particle number ratios on texture and force transmission in binary granular composites[END_REF][START_REF] Jongchansitto | Concept of mechanocaloric granular material made from shape memory alloy[END_REF]). The objective of this study was to analyze the thermomechanical response of a two-dimensional granular system made from TPU cylinders with elliptical cross-section. A cyclic compression loading was applied to a granular system while an IR camera measured the resulting temperature changes. The thermoelastic coupling effect and the mechanical dissipation effect were distinguished in the thermal response. The thermoelastic coupling effect is clearly visible in the contact zones between the particles, which can be explained by the stress concentrations occurring there. The mechanical dissipation effect manifests itself in specific contacts, which can be explained by the high friction between certain particles.

  .2b. Values lower than about À0.04 C are due to pixels near the boundary of the particles. The standard deviation of the distribution within the [À0.04 C; 0.04 C] range is equal to 0.012 C.

Fig. 14 . 1

 141 Fig. 14.1 Experimental setup: a) schematic view, b) picture of the experiment

Fig. 14 . 2

 142 Fig. 14.2 Thermal noise: (a) temperature differences at the beginning of the cyclic loading with respect to the reference temperature field, (b) corresponding distribution for the pixels within the particles

Figure 14 .

 14 Figure 14.4 presents the field of temperature change at the end of the tenth mechanical cycle. Based on the assumption that the heat quantity due to the thermoelastic coupling is null over the preceding successive mechanical cycles, this map displays a thermal signature of the mechanical dissipation effect, i.e., of the irreversible mechanical phenomena. In granular media, this latter quantity can be mainly associated to friction at the contacts. However, viscosity and damage in the volume can be also involved, especially in the zones subjected to high stress levels. Figure14.4 clearly shows that the mechanical dissipation effect is not present at all the contacts, which strongly differs from the case of the thermoelastic coupling effect (compare with Fig.14.3). "Hot" zones are now mainly visible only in the upper two corners of the granular system. This can be explained by the greater movement of the particles in the upper two corners, potentially leading to greater friction. It can also be observed that the size of the "hot" zones is quite large, which can be explained by the heat diffusion over the ten cycles.Finally, Fig.14.5 shows the variation in time of the temperature at a given interparticle contact located in the upper left part of the granular material: see point A in the schematic view. As expected, the temperature oscillates at the same frequency as the mechanical loading. It can be seen that the mean temperature change first increases over the cycles and then stabilizes from nearly the seventh cycle: see the red dashed curve. This increase can be attributed to the monotonous production of mechanical dissipation over the cycles. The stabilization results from the equilibrium between the heat produced by the mechanical irreversible phenomena at point A and the heat diffused to the environment of point A.

Fig. 14 . 3

 143 Fig. 14.3 Field of temperature change at the half of the first mechanical cycle, evidencing the thermoelastic coupling effect at the interparticle contacts in the granular system under confined compression

Fig. 14 . 5

 145 Fig. 14.5 Temperature variation at the interparticle contact point A along the cyclic loading (blue curve). The red dashed curve corresponds to the global self-heating

Fig. 14 . 4

 144 Fig. 14.4 Field of temperature change at the end of the tenth mechanical cycles, evidencing the mechanical dissipation effect especially in the two top corners of the granular material

Acknowledgments K. Jongchansitto would like to acknowledge the National Research Council of Thailand (NRCT) through the Royal Golden Jubilee Ph.D. program (grant no. PHD/0100/2561) for the support during this research.


Joe Wiart

Soichi Watanabe

Isabelle Bloch

Jérémie Anquez

Juan Pablo De La

Plata Alcalde

Elsa Angelini

Tamy Boubekeur

Noura Faraj

Christian Person

Yenny Constanza

Pinto Ballesteros

J De La Plata

Y Pinto

N Varsier

Th Kientega

M Jala

A Hadjem

A Gati

M F Wong

E Conil

B Sudret

T Nagaoka

K Wake

O Fujiwara

A Hirata

J Wang

K Saito

M Takahashi

K Ito

Fetus RF exposure analysis. Preliminary results based on three realistic 3D digital models

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

I Introduction

Mobile phones have been increasingly used over the 30 last years. The versatile use of personal Digital Assistant (PDA) is strengthening this tendency. In spite of existing protection limits (ICNIRP, IEEE) there is worldwide a public concern about the exposure to electromagnetic fields (EMF). Several expert groups have pointed out the need of research dedicated to children, pregnant women and fetus exposure. Recently the World Health Organization (WHO) has recommended the study of the EMF dosimetry on fetuses as a high-priority research topic. The estimation of the Radio frequency (RF) fetus exposure induced by wireless communication systems is complex since new technologies can be used in versatile ways and since the exposure depends on many parameters (usage, frequency, posture, age of fetus…). The exposure assessment of fetuses is facing 3 major challenges. The first challenge is the limited number of existing anatomically corrects models of mother and fetus that can be considered reliable for the exposure assessment. The second challenge is the lack of tools allowing deforming the fetus and mother models in a correct anatomical way. The third challenge is the management of the complexity of this problem to assess the statistical distribution of the exposure and consequently the maximum exposure. The FETUS project, granted by ANR in France and JST in Japan, is dealing with these ambitious challenges. In this paper we present the works performed within this project to characterize the RF fetus exposure to far field exposure modeled using plane wave.

II Fetus and pregnant woman models

Prior to our project there were only few fetus models. To characterize the fetus exposure to EMF we developed three types of models. The first one is based on deformation of a non-pregnant woman heterogeneous model (Japanese woman) which was built from Magnetic Resonance Imaging (MRI) data, and in which a heterogeneous fetus model obtained from MRI data was inserted. The second type of model is based on a deformable synthetic woman (DSW) model composed of skin, fat, muscle, bone and a homogeneous tissue representing the other organs. In this DSW heterogeneous Uterus+Fetus models, built from the segmentation of 3D MRI data, were inserted; these models have various ages and postures. The last one is an MRI based model of a pregnant woman. In this case the images are limited to the thorax and abdomen of the pregnant woman.

Model 1:

In this model (see Figure 1) the fetus is a realistic model of a 26 weeks pregnancy fetus. The pregnant woman is based on the non-pregnant Japanese heterogeneous woman model Hanako that has been deformed to insert the fetus model. In a previous project called FEMONUM, antenatal images have been segmented at different stages of pregnancy. First these fetus models have been inserted in a completely homogeneous woman model coming from the software DAZ studio (www.daz3d.com) and called Victoria. To provide more realistic models, we developed in the ANR FETUS project a Deformable Synthetic Woman (DSW). This DSW is based on the initial homogeneous woman model with additional basic tissues such as skin, subcutaneous fat, muscles and bones in a realistic way, using physical properties (see Figure 2). The other organs are represented using a homogeneous tissue. The dielectric property of this tissue is determined using comparison with heterogeneous models. As shown in Figure 2 the deformation of this DSW allows inserting the Uterus+Fetus heterogeneous model.

Model 3:

As explained in the previous section, to compare to real configurations, pregnant woman images have also been segmented (see Figure 3). MRI images of a 19 weeks pregnant woman have been segmented and a 3D model has been created. Since these MRI were performed for medical diagnose there are limited to the fetus area. As a consequence and as shown in Figure 3, the model is truncated. But the distance from the border to the fetus is large enough to avoid spurious reflection if the frequency is above 900 MHz.

III RF exposure analysis

The model 1 has been exposed to a frontal plane wave operating at 900 MHz (Figure 4). To do that a method based on finite difference (FDTD) has been used with plane wave excitation performed with a Huygens box. The whole body absorption is almost the same for the pregnant woman than the non pregnant models as shown in Table 1. But as the pregnant woman is heavier, the whole body SAR of the pregnant woman is lower than for the non-pregnant woman. This result might be different for other incidences because the variations of highlighted surfaces might be more important by side for example than by front. The fetus absorbed about 0,1% of the whole power absorbed by the mother (Table 1). But this result might also change with the direction of arrival of the incident plane wave. The model 2 with homogeneous mother has also been exposed to a frontal plane wave. As shown in Figure 5 and Table 2, the fetus exposure is weak as it is with the previous model.

IV Conclusion

The studies carried on in the FETUS project on various fetus and pregnant women models show that the fetus exposure depends on several parameters such as the fetus posture or the incident angle of the wave. This study also shows that the exposure (whole body averaged SAR) of the fetus is well below the mother one. These preliminary results will be extended in our future work.

Figure 1 .

 1 Figure 1. Model 1 (left : non pregnant, right : pregnant)

Figure 2 .

 2 Figure 2. Fetus inserted in the deformable synthetic woman model

Figure 3 .

 3 Figure 3. Abdomen of a 19 weeks pregnant woman: 3D voxel model and sagittal view of the heterogeneous model

Figure 4

 4 Figure 4 Normalized SAR ( color scaling in dB) induced in pregnant and non pregnant models by a frontal plane wave at 900MHz.

Figure 5 Table 2 :Figure 6 .

 526 Figure 5 Model 2 exposure to frontal plane wave operating at 900 MHz

Table 1 : Results in power and SAR for an incident plane wave at 900MHz with amplitude of 1V/m

 1

Acknowledgments:

This work was partially funded by grants from Fondation RFS, the French National Research Agency (http://www.agence-nationale-recherche.fr/) and the Japan Science and technology Agency (http://www.jst.go.jp). We thank DAZ studio for providing the Victoria model, and Saint Vincent de Paul, Cochin and Beaujon hospitals for the imaging data and medical expertise.


Didier Bresson

François Roubille

Cyril Prieur

Loic Biere

Fabrice Ivanes

Claire Bouleti

Olivier Dubreuil

Gilles Rioufol

Florent Boutitie

Georges Sideris

Colchicine for Left Ventricular Infarct Size Reduction in Acute Myocardial Infarction: A Phase II, Multicenter, Randomized, Double-Blinded, Placebo-Controlled Study Protocol -The COVERT-MI Study

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


domain: spi phys

text:
Guillaume Druart
email: guillaume.druart@onera.fr

Valentin Reux

Laurent Calvez

Xiang-Hua Zhang

Florence De

La Barrière

Jean-Baptiste Volatier

Elodie Tartas

Raphael Proux

Evaluation of the potential of high index Chalcogenide lenses for automotive application

Keywords: Infrared, Microbolometers, Chalcogenide, Automotive Application, Curved Sensor

Infrared cameras could serve automotive applications by delivering breakthrough perception systems for both in-cabin passengers monitoring and car surrounding. However, low-cost and high-throughput manufacturing methods are essential to sustain the growth in thermal imaging markets for automotive applications, and for other close-to-consumer applications, which have a fast growth potential. With the reduction of the pixel pitch of microbolometer detectors, their cost has decreased considerably and now the optical part represents a significant part of the system cost. Fast low cost infrared lenses suitable for microbolometers are already sold by companies like Umicore, Lightpath, FLIR… Chalcogenide glasses are widely used as materials for optics because they have many cost advantages, especially due to the possibility of mass molding the optics. However, with the reduction of the pixel pitch, it is more and more difficult to design high performance lenses with a limited number of optics. The possibility of molding the optics allows us to use many highly aspherical surfaces at affordable costs. However, Chalcogenide glasses have usually a lower refractive index than other more expensive infrared materials such as Germanium. Indeed, high refractive index materials are known to be effective in attenuating the amplitude of many geometric aberrations. In this presentation, we evaluate the interest of high index Chalcogenide lenses, especially TGG and TGS, to design optical systems meeting the needs of the automobile with a limited number of optics. TGG glass has an index of refraction of 3.396 at a wavelength of 10µm, i.e. its index of refraction is close to the Silicon one and was initially studied for space applications. TGS has a lower index of refraction (3.12@10µm) but can be used in a cost effective manufacturing process by using flash spark plasma sintering (SPS) on raw powder. Demonstrators with TGG glass have been made and their performance evaluated.

INTRODUCTION

With the emergence of new forms of personal mobility, the automotive industry is facing a drastic change. Photonic technology, one of the six Key Enabling Technology (KET) recognized by the European Commission, plays a crucial role in meeting automotive needs and expectations. Even if all sensors are combined, limitations in the fields of assistance and autonomous vehicle are still expected. Whether they are using their own vehicle or sharing one, drivers will demand a better driving experience for themselves, their passengers and other road users: quality and safety, simplified driving (i.e. increasingly autonomous and connected cars), air quality, and combating global warming. Innovation and technology are crucial drivers for these changes: today, innovation in the automotive sector must meet higher expectations in terms of consumer and user quality of life. Photonic technologies can play a crucial role in meeting these needs and expectations. Implementation of photonic technologies in the automotive industry aims at integrating technologies in the car as well as at improving optics manufacturing methods. The new ways of driving and using a vehicle as expected in the scope of Smart Mobility ask for reliable, affordable and versatile perception systems. It is now clear that the interaction between the vehicles and environment (in and out of cabin) has to be improved. This need is even more important in the case of autonomous driving for which the four mandatory steps (starting with "hands on" and ending with "hands off", "eyes off" and "minds off") are full of technical hurdles, barriers, obstacles. Depending on the level of automation (from "hands on" to "mind off"), the decisions taken by the human driver or by the autonomous vehicle change. The required reaction time by the human driver to take over the vehicle control increases with the level of automation. In other words, safe machinehuman interaction requires safe perception of the environment and the human driver state inside the vehicle. Traditionally, two major complementary approaches exist to perform perception. Object based approaches relays on the identification of objects on vehicle environment. In complement, map fusion approaches perform perception based on building map models of the environment. Traditionally, these two complementary approaches are conceived and adapted to better fit specific sensors. For instance, visible image sensors are well fitted to perform object perception while map fusion perception work well with LIDAR and RADAR sensors.

Infrared cameras, taking benefits of Long Wave Infra-Red bandwidth (LWIR) in which all object radiates energy depending only on its structure and temperature, could deliver breakthrough perception systems thanks to their unique feature over visible or Near Infra-Red (NIR) cameras. Therefore, they could be a key technology for autonomous vehicles by making them safer and will improve object classification of the automotive sensor suite in all light conditions, provide redundancy and thus extend vehicle autonomy towards level 3 and beyond, operating 24/7. Infrared cameras could be a must-have in the mix of sensing systems since the driver and passenger monitoring needs to be improved as well as the environment surrounding monitoring, in all light and weather conditions:

• The facial thermal imaging, combined to computational psychophysiology, will dramatically improve the monitoring of the driver on vital signs including liveliness, drowsiness, and emotions. The same systems will also contribute to the overall monitoring of the vehicle interior for comfort management. The combination of the two monitoring capabilities enables individualization of the vehicle, with an instantaneously adaptation to all functions and services of such a vehicle to the user and passengers.

• Environment recognition as an out-of cabin application essential feature will also benefit from the addition of the LWIR thermal sensing to existing systems composed of LIDAR, RADAR and other vision systems. In addition to those, thermal perception is the only technology that is accurate and reliable in all light and weather conditions, even in extreme cases.

An IR thermal module is based on an uncooled InfraRed Focal Plane Array (IR FPA) based on a microbolometer technology, an optical system focusing in order to provide a thermal infrared image, an embedded system dedicated to the correction of the raw IR image. However, to meet the cost and performance requirements of automotive industry, the whole system needs to aggregate different cutting-edge technologies, for which technological developments are required. First, the primary cost is the microbolometer whose technologies are developed to reduce the sensor size and pixel pitch like detectors for cell phones. In 2012, DARPA founded three contracts to develop sub $500 thermal imaging camera with 12 µm pixels. At the same time, LYNRED with CEA released IR FPAs with 12µm pixel pitch [START_REF] Becker | Latest pixel size reduction of uncooled IR-FPA at CEA, LETI[END_REF]. Nowadays, IR FPAs with 10µm pixel pitch can be found [2]. Infrared cameras as smartphone add-ons released by FLIR (FLIRONE camera) or SEEKTHERMAL can be considered as the first consumer market for thermal imaging that reaches prices under $250. Indeed this step change in volumes enables a step change in system costs and now thermal imaging can move into automotive applications [START_REF] Vieider | Low-cost far infrared bolometer camera for automotive use[END_REF][4] [START_REF] Valldorf | Far Infrared Low-Cost Uncooled Bolometer for Automotive Use[END_REF]. Both thermal add-ons use 12µm pixel pitch technology. Now the optics represents a non-negligible part of the cost. Chalcogenide glasses represent a cost effective alternative to single-crystalline Germanium or poly-chrystalline ZnSe. Moreover, these IR glasses have good material's thermo-optic properties.

The aim of this paper is to evaluate high refractive index Chalcogenide glass to design a low cost and high performance infrared lens that will detect LWIR light both for in-cabin passengers monitoring and for car surrounding. In a first part, two high refractive index Chalcogenide glass are presented: TGG and TGS. They have an index of refraction greater than 3. In a second part, we study the impact of using TGG for two designs and with field of views of interest for automotive application. A special focus is made on the correction of the field curvature. The study is done with a VGA (640x480 pixels) detector with a pixel pitch of 10µm. Finally, a status on the manufacturing of TGG lenses in the framework of Heliaus project is presented.

STUDY OF HIGH-INDEX CHALCOGENIDE GLASS FOR VGA SENSORS

Chalcogenide glasses are good candidates to make low cost IR optics. The fact that these Chalcogenide glasses can be molded further reduces the cost of the optics. Nowadays, the most common IR lenses available on the market are based on As2Se3 (n=2.81@1.5µm [START_REF] Novikova | Élaboration d'optiques infrarouges par combinaison de la mécanosynthèse et du frittage SPS[END_REF]) and Ge-As-Se glasses (n=2.75@10µm [START_REF] Dantanarayana | Refractive index dispersion of chalcogenide glasses for ultra-high numerical-aperture fiber for mid-infrared supercontinuum generation[END_REF]). Glass compositions free of Germanium such as As2Se3 are low-cost and attract a growing interest even if they present weaker mechanical properties. However, the final cost of IR optics, especially small-size optics, is mainly governed by the synthesis and processing instead of raw materials. This problem particularly concerns the automotive industry which seeks to take advantage of the reduction of the size of the detectors and the reduction of the size of the optics (now around 8mm). Therefore, Chalcogenide glasses with higher index of refraction could be very interesting as long as they lead to a reduction of the number of lenses in a design. Indeed higher index of refraction will lead to high optical power and reduced geometric aberrations. Table 1 lists some glass compositions having high refractive index with their characteristic temperatures (Tg is the Glass-transition temperature and Tx is the crystallization temperature). 3.12@10µm 189 340 [START_REF] Sarrach | Studies of amorphous GeSeTe alloys (I): Preparation and calorimetric observations[END_REF], [START_REF] Peng | Fabrication and characterization of multimaterial Ge25Se10Te64/As2S3 chalcogenide fiber with a high value of the numerical aperture[END_REF] For industrial applications, ideal composition should present a high refractive index, a glass transition temperature ideally above 180°C and a good thermal stability (highest difference of temperature between Tx and Tg) in order to be easily shaped. Within the framework of the Heliaus project, we focus on two types of glass composition: Ga10Ge15Te75 called in the following TGG and Ge25Se10Te65 called in the following TGS.

TGG has a high index of refraction close to that of Silicon, despite having a transition temperature slightly lower than 180°C. It was fabricated by the University of Rennes for space application [START_REF] Zhang | Purification of Te75Ga10Ge15 glass for far infrared transmitting optics for space application[END_REF]. Tellurium based glasses are the only known vitreous materials with good chemical and thermal stability as well as low losses in the 6-20µm spectral range. In the framework of the Heliaus project, we decided to make lenses in TGG by diamond manufacturing technics.

TGS has a lower index of refraction than TGG but still greater than a value of 3. It has however a better transition temperature and a better thermal stability. Moreover, this glass is compatible with spark plasma sintering (SPS) to mold lenses in a potential lower cost than traditional molding technics. Indeed, usually, glass ingots of big diameter (around 20cm) are produced in high volume and discs are obtained by first coring and then cutting. In the next step, glass slices are molded above Tg to final shape for making high precision IR optics. The coring process could induce a material loss higher than 30%, which can only partially be re-used as starting material. In this context, developing a process that allows for making a near-shape or even finished IR optics by using residual glass may be of high interest. In Ref [START_REF] Reux | High refractive index IR lenses based on chalcogenide glasses molded by spark plasma sintering[END_REF], Univ. of Rennes demonstrated that flash SPS sintering gives the possibility to shape lenses from raw powder rapidly and reproducibly.

The refractive index of TGG and TGS are given in Fig. 1.

DESIGN STUDY WITH HIGH-INDEX CHALCOGENIDE GLASS FOR VGA SENSORS

The current trend is to reduce the size of the pixels and therefore the size of the detectors in order to reduce the costs of thermal cameras dedicated to automotive applications. However, when the pixel size decreases, the depth of field of fast optical system also decreases and reduces the tolerance of the system to optical aberrations. A rule of thumb for evaluating depth of field is to take the largest of the two following equations. The first gives the geometric depth of field and the second gives the diffractive depth of field.

ℎ = ± # (1) ℎ = ± # (2)
In the case of a design with a F-number (F#) of 1.2 and a detector with a pixel pitch of 10µm (tpix), we obtain a geometric depth of field of ±12µm and a diffractive depth of field of ±14.4µm. In this configuration, the depth of field may therefore not be sufficient to compensate for the Petzval curvature of the optical system. This is particularly problematic for large field of view or medium field of view systems that rely on reverse lens or Petzval design, i.e. optical systems that contain only positive optical powers and for which the Petzval curvature cannot be corrected. The Petzval curvature is given by the following equation:

= -∑ 1 ⁄ (3)
Cp is the Petzval curvature, Fi is the focal length of lens number i and ni is its corresponding index of refraction. So for designs with only positive optical powers, the only way to reduce the Petzval curvature is to increase the index of refraction. High-index Chalcogenide glasses are therefore of great interest and Univ. of Rennes is currently developing TGG [START_REF] Zhang | Purification of Te75Ga10Ge15 glass for far infrared transmitting optics for space application[END_REF] and TGS glasses [START_REF] Reux | High refractive index IR lenses based on chalcogenide glasses molded by spark plasma sintering[END_REF] that have an index of refraction greater than 3.

We have designed a reverse lens with a focal length of 5.6mm and a HFOV of 68° as well as a two lens design with a focal length of 8.35mm and a HFOV of 44°. Both designs use a VGA detector with a pixel pitch of 10µm. In 2010, during the EU funded FNIR project (Fusing Far-Infrared and Near-Infrared Imaging for Pedestrian Injury Mitigation), it was determined that, for the automotive application, a minimum F/number (F#) of 1.4 was necessary [START_REF] Schweiger | Sensor fusion to enable next generation low cost Night Vision systems[END_REF]. In the following, we consider a F/number of 1.2 to take benefit from the small pixel pitch. To focus on geometric aberrations, the designs have been studied at the wavelength of 10µm. Moreover, for both designs, different configurations have been studied.

First, we studied designs with GASIR1, GASIR5 or TGG Chalcogenide glasses.

Then we explored the possibility of further decreasing the Petzval curvature of a design in TGG by replacing the Silicon window of the microbolometers with a Silicon lens. This lens close to the sensor plays the role of a field lens. To maintain a low cost approach, we imposed a constraint on the sag height of the Silicon lens so that it can be realized by photolithography methods. In a previous work [START_REF] De La Barrière | Compact infrared cryogenic wafer-level camera: design and experimental validation[END_REF], we manage to manufacture a plano-convex Silicon lens with a sag height of 100µm. Another reference reports a sag height of 200µm [START_REF] Logean | High numerical aperture silicon collimating lens for mid-infrared quantum cascade lasers manufactured using wafer-level techniques[END_REF]. In the following, we will consider a maximum sag height of 150µm. We will work as well on plano-concave Silicon lens to ease the lithographic process despite that, in Ref [START_REF] Ovrutsky | TIR imaging lens image capturing system having the same and associated methods US20150109456[END_REF], curvatures on both sides of a Silicon lens can be found. In first approximation, the sag height is linked to the radius of curvature R and the diameter of the lens ϕ by the following equation:

= ! " # $ # % (4)
For a plano-convex lens, the focal length is then given by the equation:

= ! " # $ # &'()*+,- (5)
With a sag height of 150µm, a lens diameter of 8mm (diagonal of a VGA sensor with a pixel pitch of 10µm), the focal length of a Silicon plano-concave lens is equal to -22.6mm.

Finally, we explored the potential gain of using curved detectors on a design with either TGG or GASIR1. The benefit of a curved imaging surface was analyzed for mobile camera lenses [START_REF] Reshidko | Optical analysis of miniature lenses with curved imaging surfaces[END_REF]. The conclusion was that the curved surface allows producing an equivalent lens performing design with faster F-Number than a conventional design. The curved sensor helps achieving uniform image quality over the whole FOV and it increases the effective depth of focus when we consider the full field aberrations. As infrared detectors follow the same trend in terms of decreasing pixel size as cell phone detectors, it is tempting to also evaluate the gain of curved detectors for infrared systems. In a previous work [START_REF] Dumas | Infrared camera based on a curved retina[END_REF], we managed to curve a QVGA detector (320x256 pixels) with a pixel pitch of 25µm. The minimum radius of curvature obtained was equal to 40mm. The sag height obtained is thus equal to 328µm. By reporting this sag height to a VGA sensor with a pixel pitch of 10µm, we could expect a minimum radius of curvature of 24.4mm.

Table 2 analyzes the Petzval curvatures of the reverse lens for different materials based on Eq. 3. With TGG or TGS glasses, the Petzval curvature is lower than with other chalcogenide glasses (GASIR1 and GASIR5). The use of a divergent Silicon lens to replace the window of the IR FPA decreases further the Petzval curvature. The combination of a TGG lens and a Silicon lens gives better results than a Ge lens as shown in the column TGG+Si in Table 2. Figure 2 shows the different configurations for the reverse lens. Figure 3 gives the RMS field maps for these configurations. We notice that the image quality of the optical system is limited by the field curvature and all strategies to reduce it increase the performance of the system: increasing the refractive index of materials, using a field lens or bending the sensor. The best strategy to reduce the Petzval curvature is to bend the sensor. Using a high index of refraction for the lens material reduces the bending of the sensor: the radius of curvature of the sensor with a reverse TGG lens is equal to -45mm whereas the radius of curvature of the sensor with a reverse GASIR1 lens is equal to -14mm. With regard to what has been previously obtained technologically [START_REF] Dumas | Infrared camera based on a curved retina[END_REF], the radius of curvature of the detector with the TGG lens seems to be more easily possible. Nevertheless, the configurations with the TGG lens with or without the Silicon field lens are very efficient solutions with respectively average spot radius RMS values of 7.6µm and 8.4µm, that is to say lower than the pixel size. Finally, we notice that the Petzval curvature of the different reverse lens configurations calculated with the software Zemax Optics Studio (ZOS) are slightly different from the estimated values from Eq. 3. The values calculated with ZOS are given in Table 2. This difference may be explained by the fact that a reverse lens is a thick lens compared to its focal length and that the "divergent" surface is far away from the "convergent" surface allowing to get closer to the properties of a Retrofocus. the material used for the reverse lens is GASIR1. B: the material used for the reverse lens is GASIR5. C: the material used for the reverse lens is TGG. D: the material used for the reverse lens is TGG and we replace the window of the sensor by a divergent Silicon lens. E: the material used for the reverse lens is TGG and the sensor is curved. F: the material used for the reverse lens is GASIR1 and the sensor is curved.

Figure 3. RMS field maps for the different configurations of a reverse lens. A: the material used for the reverse lens is GASIR1. B: the material used for the reverse lens is GASIR5. C: the material used for the reverse lens is TGG. D: the material used for the reverse lens is TGG and we replace the window of the sensor by a divergent Silicon lens. E: the material used for the reverse lens is TGG and the sensor is curved. F: the material used for the reverse lens is GASIR1 and the sensor is curved.

In the case of the two lens design, there exist more configurations. Indeed three types of optical architectures can be designed: Telephoto lens, Petzval lens and Retrofocus lens. Having a divergent optics and a convergent optics, both Telephoto and Retrofocus designs can deal with Petzval curvature which is not the case for the Petzval design which has only convergent optics. For wide field of view system, Petzval design and Retrofocus design are preferred. The advantage of the Petzval design is that the optics can have an aperture smaller than that of the optical system unlike the Retrofocus design where some optics can have an aperture larger than that of the optical system. The choice of one architecture over the other will result from a compromise between the different aberrations. Sometimes it is useful to split an optics into two other optics to reduce their aperture but considering the important cost constraints for automotive applications, we try to do the maximum with only two lenses [START_REF] Bigwood | It's only two lenses in a tube: how complicated can it be?[END_REF]. In this way, all surfaces are aspherical surfaces up to the 8 th order. Like the case of the Reverse lens, we have studied different configurations: lenses in GASIR1, GASIR5 or TGG, the use of a Silicon field lens or a curved sensor. With several options to correct the field curvature and the use of many aspherical surfaces, the merit function has many local minima. We used a global optimizer to find the optimal optical system (Hammer current from ZOS). Finally, we found two families of optical systems according to the allowed footprint.

The first family is a Petzval type design. Figure 4 shows the different configurations of this first family. Figure 5 gives the RMS field maps for these configurations. The gain in performance is not as obvious as in the case of the Reverse lens, but implementing strategies to correct the Petzval curvature can improve the performance of the optical system. The best strategy to reduce the Petzval curvature is to bend the sensor: the design with TGG optics has a sensor with a radius of curvature of -72mm whereas the design with Gasir1 optics has a sensor with a radius of curvature of -28mm. Nevertheless, the configurations with the TGG lens with or without the Silicon field lens are very satisfactory solutions with respectively average spot radius RMS values of 5.0µm and 5.5µm, that is to say lower than the pixel size. Figure 4. Different configurations of the first two lens design family having a HFOV of 44° for a VGA sensor with a pixel pitch of 10µm. A: the material used for the two lens design is GASIR1. B: the material used for the two lens design is GASIR5. C: the material used for the two lens design is TGG. D: the material used for the two lens design is TGG and we replace the window of the sensor by a divergent Silicon lens. E: the material used for the two lens design is TGG and the sensor is curved. F: the material used for the two lens design is GASIR1 and the sensor is curved.

Figure 5. RMS field maps for the different configurations of the first two lens design family. A: the material used for the two lens design is GASIR1. B: the material used for the two lens design is GASIR5. C: the material used for the two lens design is TGG. D: the material used for the two lens design is TGG and we replace the window of the sensor by a divergent Silicon lens. E: the material used for the two lens design is TGG and the sensor is curved. F: the material used for the two lens design is GASIR1 and the sensor is curved.

The second family more compact than the previous one oscillates between a Petzval type design and a Retrofocus type design. Figure 6 shows the different configurations of this second family. Figure 7 gives the RMS field maps for these configurations. Once again, the best strategy to reduce the Petzval curvature is to bend the sensor: the design with TGG optics has a sensor with a radius of curvature of -35mm whereas the design with Gasir1 optics has a sensor with a radius of curvature of -22mm. Nevertheless, the configurations with the TGG lens with or without the silicon field lens are very satisfactory solutions with respectively average spot radius RMS values of 7.7µm and 7.2µm, that is to say lower than the pixel size.

Despite the fact that increasing the refractive index of refraction of the optics improve the performance of the optical system, it is interesting to note that the best results were obtained with GASIR1 optics and a curved sensor. However, the technological feasibility of important curvature of the sensor remains to be demonstrated. Figure 6. Different configurations of the second two lens design family having a HFOV of 44° for a VGA sensor with a pixel pitch of 10µm. A: the material used for the two lens design is GASIR1. B: the material used for the two lens design is GASIR5. C: the material used for the two lens design is TGG. D: the material used for the two lens design is TGG and we replace the window of the sensor by a divergent Silicon lens. E: the material used for the two lens design is TGG and the sensor is curved. F: the material used for the two lens design is GASIR1 and the sensor is curved.

Figure 7. RMS field maps for the different configurations of the second two lens design family. A: the material used for the two lens design is GASIR1. B: the material used for the two lens design is GASIR5. C: the material used for the two lens design is TGG. D: the material used for the two lens design is TGG and we replace the window of the sensor by a divergent Silicon lens. E: the material used for the two lens design is TGG and the sensor is curved. F: the material used for the two lens design is GASIR1 and the sensor is curved.

MANUFACTURING AND TEST OF LENSES MADE OF TGG MATERIAL

Two designs were manufactured based on this work. HELIAUS-OPT-82 is a 46° horizontal field of view lens which is a TGG doublet and HELIAUS-OPT-84 is a 69° horizontal field of view lens made of a single TGG lens. Figure 8 displays photographs of the lens assembly process. The lenses are assembled by hand into an aluminium housing. On the left hand side, one can see the different pieces which constitute the assembly of lens HELIAUS-OPT-84. This lens is a TGG singlet which is simple to assemble with a lens barrel and a clamp ring to secure it in place. On the right hand side, an operator is finishing the assembly of lens HELIAUS-OPT-82, which is another Heliaus prototype lens. The mounting principle is the same for all lenses. On the photograph, the operator is applying thread lock to secure the front lens clamp ring in place. Figure 9 shows the measurement of the Modulation Transfer Function (MTF) for two prototype lenses (HELIAUS-OPT-82, serial number 20 and HELIAUS-OPT-84, serial number 16). The value of the MTF is displayed as a function of the spatial frequency up to 60 cy/mm. The diffraction limit for an f/1.2 aperture is also displayed. One can notice some measurement curves go above the diffraction limit for frequencies higher than 40 cy/mm. This is attributed to measurement bench inaccuracy at these high spatial frequencies. For lens 84-16, the MTF follows the diffraction limit closely, demonstrating exceptional performance. For lens 82-20, on the other hand, the MTF is a bit lower. This can be explained by the fact that lens 82 is a doublet lens that is subject to more tolerance stacking and can be expected to have a slightly lower performance. This being said, the lens behaves exceptionally well by remaining close to the diffraction limit. These measurements validate the use of TGG in lens design as an excellent material. However, managing to produce this glass in large quantities for industrial processes and applications remains a challenge.

CONCLUSION

IR FPA with small pixel pitch seem to be key technologies to meet the cost requirement of automotive industry. However, the reduction of the pixel pitch represents an important challenge for the optical designer to maintain the optical performance with a minimum number of lenses. It is indeed important to limit the number of optics to reduce the cost of the system. Using higher index materials is one way to reconcile simplicity of the optical architecture with performance. For small-size optics, the final cost of IR optics is mainly governed by the synthesis and processing instead of raw materials. We also explored the possibility of replacing the microbolometer window with a divergent field lens or of using a curved detector. Both approaches will however increase the cost of the detector. Finally, we made the choice in this paper to limit the aperture to F/1.2. However, such an aperture associated with small pixels remains to be evaluated experimentally in real driving condition.

Figure 1 .

 1 Figure 1. Refractive index of TGG and TGS.

Figure 2 .

 2 Figure 2. Different configurations of a reverse lens designed for a HFOV of 68° and for a VGA sensor with a pixel pitch of 10µm. A:the material used for the reverse lens is GASIR1. B: the material used for the reverse lens is GASIR5. C: the material used for the reverse lens is TGG. D: the material used for the reverse lens is TGG and we replace the window of the sensor by a divergent Silicon lens. E: the material used for the reverse lens is TGG and the sensor is curved. F: the material used for the reverse lens is GASIR1 and the sensor is curved.

Figure 8 .

 8 Figure 8. Assembly of lenses. Left: pieces to assemble for lens HELIAUS-OPT-84. Right: final assembly of lens HELIAUS-OPT-82.

Figure 9 .

 9 Figure 9. Measurement of MTF on axis for lenses 82-20 and 84-16.

Table 1 .

 1 Composition and properties of some chalcogenide glasses with high refractive index

	Composition	n @wavelength Tg(°C) Tx(°C)	Ref.
	Ga10Ge15Te75	3.39@10µm	172	285	[8]
	Ge20Se2Te78	~3.42@10µm	153	250	[9],[10]
	Ge20Se10Te70	~3.26@10µm	156	236	[9],[10]
	Ge20Se60Te20	~2.55@10µm	188	405	[9],[11]
	Ge20Se70Te10	~2.50@10µm	175	430	[9],[11]
	Ge25Se10Te65

Table 2 .

 2 Evaluation of the Petzval curvature for the reverse lens design

	Material	GASIR1 GASIR5	TGS	TGG	Si	Ge	TGG+Si
	Index @ 10µm	2.494	2.777	3.12	3.396	3.47	4.004
	Cp (mm -1 )	-0.072	-0.064	-0.057	-0.053	-0.051	-0.045	-0.039
	Sag (mm)	0.573	0.514	0.458	0.421	0.421	0.357	0.316
	Cp ZOS (mm -1 )	-0.059	-0.047		-0.028			-0.022

ACKNOWLEDGMENT

This research is supported and funded by the Heliaus European Union Project. The project focused on enabling safe autonomous driving systems. This project has received funding from the ECSEL Joint Undertaking (JU) under grant agreement No 826131. The JU receives support from the European Union's Horizon 2020 research and innovation program and France, Germany, Ireland, Italy.