Adrien Broué

Thibeaut Fourcade

Jérémie Dhennin

Frédéric Courtade

Pierre-Louis Charvet

Patrick Pons

Xavier Lafontan

Robert Plana

Adrien Broue
email: adrien.broue@novamems.com

Thibaut Fourcade

Validation of bending test by nanoindentation for micro-contact analysis of MEMS switches

Keywords: MEMS, reliability, micro-contact, contact temperature, nanoindenter, Au contact, contact physics

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

Introduction

The bandwidth of RF MEMS switch specifications is spreading more and more, from DC up to tens of giga hertz. But is the challenge reachable for a reliable MEMS switches? Metal contact RF MEMS switches have demonstrated excellent performance in term of low-power consumption, low on-state impedance, high off-state impedance, and excellent linearity [START_REF] Rebeiz | RF MEMS switches and switch circuits[END_REF]. Some successful companies now propose some of these breakthrough-told technologies, but the gap is still large between the low TRL (Technology Readiness Level) academic demonstrations and the commercially available switches. Several reasons can be exposed to account for this, and one of them is probably the lack of adapted tools to investigate the physics occurring at such a tiny scale. In addition, design of MEMS switches is widely diversified and few comprehensive investigations of micro-contact physics have been reported on a single type of contact. For ohmic contact switches, the main issue is to control precisely the contact pressure and the corresponding temperature. These two parameters are interdependent as soon as some DC or RF signal is flowing through the contact. Furthermore, more complete data for electrical and mechanical properties of contacts made with thin-film metallization are also required to support the miniaturization of electrical contacts in multichip systems, three-dimensional (3-D) systems [START_REF] Kataoka | Contact properties of Ni micro-springs for MEMS probe card[END_REF] and wafer-level testing probe cards [START_REF] Pruitt | Measurement system for low force and small displacement contacts[END_REF] [START_REF] Wang | Micro-cantilever probe cards with silicon and nickel composite micromachining technique for wafer-level burn-in testing[END_REF]. As a consequence, new characterization techniques have been recently developed in order to measure the contact resistance as a function of the applied load and of the contact deformation. Moreover, a precise monitoring of the current intensity and of the associated potential drop is useful to get rid of any parasitic resistance using cross rod configuration. Experimental characterizations using nanoindenter [START_REF] Gilbert | A Nanoindenter Based Method for Studying MEMS Contact Switch Microcontacts[END_REF], piezo actuator [START_REF] Kwon | Investigation of the electrical contact behaviours in Au-to-Au thin-film contacts for RF MEMS switches[END_REF] and atomic force microscope (AFM) [START_REF] Yang | A new test facility for efficient evaluation of MEMS contact materials[END_REF] were published by several researchers, to investigate the behaviour of Au and Au-Ni alloys as contact materials for example. To our knowledge, the micro-scale heating effects on the contact material are not fully understood. However these phenomena are key issues for the designers to understand the capability of the contact to sustain the current before reaching critical temperature values [START_REF] Solazzi | Contact Modelling of RF MEMS Switches Based On FEM Simulations[END_REF]. The presented tests are performed using the dynamic control module (DCM) of the nanoindenter, which allows a higher resolution testing. This apparatus is also coupled with an environmental chamber to control both temperature and humidity. Nevertheless, as these characterization tools are still under development, it is mandatory to assess the results obtained through dedicated validation tests and modeling. The objective of this paper is then to present a so-called validation process of micro bending tests by nanoindentation. This will allow one to rely on the results provided by this methodology.

Micro contact theory

The electromechanical behaviour of the contacting surfaces during switching depends on several mechanical and operating parameters such as thermal ( t ) and electrical ( e ) conductivity of contact materials, mechanical properties of the contact spots (E and H), roughness (Ra), adhesion energy of contact surfaces (, mechanical stiffness (k), humidity (Rh), contact voltage (V C ), contact force (F C ) and contact current (I C ) (cf. Figure 1). The key issue is the stability of the contact surfaces through cycling: the electrical, topological and mechanical properties have to be maintained the longest time.

Analytic models

First, the micro-contact physically differs from the macro-contact due to the roughness of the contact surface. Only high points on each surface come in contact. Thereby the effective contact area, named asperities or a-spots, is largely smaller than the apparent one. At a microscopic scale, contact surfaces have a rugged relief constituted by picks at the extremity of the asperities. Thus the electrical current can only flow through culminating spots at the contact interface. Moreover, the slightest presence of insulating films on the extreme surface will reduce the effective electrical contact even more. To simplify the model, the contact resistance is assumed to be mainly governed by the constriction resistance as the current flow is constricted through the small asperities leading to the electrical contact, ie. the electrical contact is considered strictly ohmic. This electrical resistance is directly linked to the constriction of current lines between both contacts. This constriction of current causes a local increase of the current density and tends to increase the electrical potential drop between the two sides of the contact. Thus the expression of this constriction resistance, so called Maxwell resistance R Maxwell , can be written for a single circular contact spot, named "a-spot", with a contact area radius a as [START_REF] Holm | Electrical Contacts-Theory and Applications[END_REF]:

a R Maxwell 2   (1)
Where  is the resistivity of the contact material. When the two contact surfaces collide with each other, the asperities of each contact could have three deformation modes: elastic, elastic-plastic and plastic, depending on the level of applied stress on the materials. Any time-dependent effects will not be taken into account here by always considering durations long enough to have stabilized deformations. If considering just one actuation, without knowledge about the history of the actuations (maximal loads and time duration), the distinction between perfect-elastic, perfect-plastic and a domain of elastic-plastic transition is difficult to establish [START_REF] Seguineau | Mechanical Cycling for electrical performances of materials used in MEMS: Application to gold micro-switches[END_REF]. However, during the first contact establishment between the two surfaces, the load applied is generally higher than the yield stress of the contact material. Thus the deformation of the contact asperities is considered to be predominantly plastic. The contact area and the contact load can be linked to the radius of the contact spot a using Abbott and Firestone's plastic contact model [START_REF] Holm | Electrical Contacts-Theory and Applications[END_REF].

  H F A a C C   (2)
Where Ac is the contact area, F C the contact force and H the Meyer hardness of the softer material. Assuming that the surfaces have not already be subjected to actuations, one can suppose that the deformation of the asperities undergone during our tests are under plastic solicitations and are part of the burn-in regime. This leads the stress to reduce towards the Yield point after several actuations, where the behaviour becomes closer to a domain of perfect-elastic or elastic-plastic transition. Thus, only perfect-plastic behaviour will be first considerate, by applying Abbott and Firestone's plastic contact model. Secondly, it's necessary to keep in mind that, generally, the current flows by multiple asperities due to the surface roughness. The easier approach consists in considering that the whole conductance is the sum of conductances of the multiple contact spots with varying sizes. The effective contact resistance can be obtained as a first approximation by summing all the contact radii of all the individual asperities as the effective contact radius a eff of the effective contact area A eff . This effective contact radius can be substituted into ( 1) and ( 2) to take into account the multiple asperity features of the micro contact. Because of tiny contact spot size due to small contact force available in micro-switches, mechanical, electrical and thermal properties shift from bulk to a specific physics of thin films lead by the geometry of the asperities. For example, heating of the contact spots is extremely localized when the current flows through the contact, whereas the device level remains at room temperature [START_REF] Jensen | Effect of nanoscale heating on electrical transport in RF MEMS switch contacts[END_REF]. The highest contact spot temperature T c called supertemperature T Θ has already been expressed by Holm as a function of the contact voltage V c [START_REF] Holm | Electrical Contacts-Theory and Applications[END_REF]. By considering that electrical contact is strictly ohmic, this equation becomes:

0 4 T L V T c    (3)
Where L=2.45 x 10 -8 W.Ω/K² is the Lorentz constant and T 0 the ambient temperature. Eq. ( 3) is obtained from the Wiedemann-Franz law for a conductor heated by the current produced by the voltage V C between two arbitrary isotherms with the temperature T 0 : the assumption is made that the thermal and electric currents obey similar laws thus with symmetric contacts the generated heat flows in the same path as the electric current.

Reliability of micro-contact

The second important point to be addressed is the reproducibility of the contact resistance over the actuations, and thus along its whole lifetime (cf. Figure 2). The reliability of the switch depends on its ability to withstand some degradations occurring at the contact interface. Three types of phenomena can be studied: the mechanical (cold welding, strain hardening), electrical (arcing, hot welding, annealing) and chemical ones (formation of insulating films at the extreme surface), all inducing modifications of the topological, mechanical and electrical properties of the contact. As the experimental set-up developed here can be used for studying the fundamental physics of the micro-contact, the understanding of potential failure mechanisms can be made easier if the effort is put upon the identification of the key parameters for each mechanism. In addition, the contact temperature (Tc) of contact a-spots could be linked with the contact force depending on the contact voltage [START_REF] Kwon | Investigation of the electrical contact behaviours in Au-to-Au thin-film contacts for RF MEMS switches[END_REF]. Indeed the plastic deformation of the asperities during the contact formation proceeds more rapidly when the softening temperature is reached [START_REF] Fortini | Asperity contacts at the nanoscale: comparaison of Ru and Au[END_REF]. Thus the effective contact area increases inducing a drop of the contact resistance. However the softening of the metal at the asperities of contact reduces the strain hardening of the a-spots and could accelerate the wear of the contact by the activation of thermal failure mechanisms. Therefore the softening temperature of contact metals is probably one of the most important critical parameter and it has to be studied for reaching a stable and low contact resistance.

Experimental techniques

Description of the experimental set-up

The test described in this paper is based on methods combining a nanoindenter and a high resolution source meter for the determination of the electrical contact resistance versus the contact force and the displacement of the free standing part of the contact. Nanoindentation is firstly designed for material characterization, which is based on the "displacement vs. load" curve obtained by driving a tip into the test material and by monitoring the applied load and the resulting displacement [START_REF] Oliver | An Improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments[END_REF]. In our test bench, the nanoindenter's spherical tip is used as a mechanical actuator. The actuation load is thus reproducible and known with a good accuracy, two points which remain hard to achieve with the actual actuations (for example, electrostatic actuation forces often drift due to dielectric charging [START_REF] Melle | Modeling of the dielectric charging kinetic for capacitive RF-MEMS[END_REF]).

Built-up of insulating films, topological modifications of the contact surfaces or structural fatigue

Cycle number (log scale)

Elastic stress of the contact asperities

Stiction

Stable contact

Burn-in of the contact

Activation of critical failure mechanisms

PART I PART II PART III

R C

Wear of initial contact Once the bridge is correctly located under the column of nanoindentation, the tip is brought in contact with the surface of the mobile electrode, and then lowered until mechanical and electrical contact between the bridge and the line. The stiffness of the membrane can be measured in this step [START_REF] Seguineau | MEMS Reliability : Accurate Measurements of beam stiffness using nanoindentation techniques[END_REF]. From this moment on, the applied load corresponds to the actuation load of the contact. A schematic view of the set-up can be seen on Figure 3.

The main difficulty for applying a load on test vehicles remains the accurate location of the tip above the contact. This issue has been here overcome by the use of a nanopositionning table achieving a 20nm X-Y resolution in a defined 100μm-side square. Thus, a pseudo-AFM scan is performed by probing the surface with a fixed stiffness of contact between the tip and the surface. The coordinates of the bridge and the line are measured in order to locate the tip just above the contact, that is to say in the middle of the bridge and half-width of the line. An accurate location can then be reached on the scan (cf. Figure 4).

Contact line

Bridge

Location of the tip The electrical measurements are performed by the use of a four-wires probe: a current flow I C is applied and the potential drop V C is independently measured. This method for measuring contact resistance is the same method used in crossed rod contact resistance measurements of Holm [START_REF] Holm | Electrical Contacts-Theory and Applications[END_REF]: only the contact resistance is measured independently of the voltage drop in the supply wires and access paths. Moreover the environmental chamber allows the control of the temperature of the DUT and of the relative humidity Rh.

Test vehicle description

Specific test vehicles have been designed for contact analysis, enhancing the extraction of characteristic curves and making possible the comparison between different contact shapes or materials. As illustrated in Figure 5, the tested device is composed of a bridge suspended over a contact line. A 5µmx5µm square bump is processed underneath. The stiffness of the bridge is about 480 N/m. The contact material is Au-to-Au because gold is the most popular material for electrical contact due to its high conductivity, its high resistance to oxidation and its low propensity to form alien surface films [START_REF] Patton | Fundamental studies of Au contacts in MEMS RF switches[END_REF]. 2D FEM simulations were performed using ANSYS® in order to validate the substitution of the distributed pressure by the point load. This is an important point to be assessed because we tend to mimic the actuation of a real micro switch for easier interpretations of our results. Thus we have to compare the repartition of the vertical stress at contact interface bridge-to-bump. It can be seen on the Figure 6 that the stress repartition is barely similar between the both but the level of stress is higher with the point one. The contact force between the bump and the bridge has been calculated in both cases and is 60 % higher using the point force for a same applied load. It can be assumed that the force dissipated in the anchor is lowered using the point actuation principle. Thanks to these simulations, the point load actuation with the nano indentation tip is validated for this methodology.

Requirements concerning the tip used

This part will be focused on the comparison between two types of tip: the Berkovitch one (0.320 µm of radius of curvature due to the tip defect) and the spherical one (5.9 µm of radius of curvature). It can be seen on Figure 7.a that the strain of the bridge close to the contact with the Berkovitch tip is higher than the bridge strain at the bump interface.

The stress induced by the Berkovitch tip is 74 % higher and is more localized under the tip than the stress induced by the spherical one. For a same tip displacement, the contact area between the bump and the bridge is 11 % higher using the spherical tip than with the Berkovitch one. The use of a spherical tip allows a better repartition of strain and decreases the stress concentration and plastic deformations under the tip. However the Figure 7.b shows that the deformation of the bridge under the spherical tip cannot be neglected. For that reason, a preliminary test has to be done on the anchors to measure the deformation of the asperities. In that way, the deformation of the bridge can be subtracted to the total deformation.

Validation tests

Metal contacting switches have a large and complex set of failure mechanisms driven by the current level. And current is also known to have a primary influence on contact lifetime in macroswitches, with lifetime decreasing at higher current [13][16]. The campaign of tests has been performed on the test vehicles described in the previous part. The obtained results give us the opportunity to regain the behaviour predicted by the previous models. These studies are focused on the self-heating of the contact with increasing level of current flowing through the contact which is a key issue of contact reliability.

The measurements are performed by sweeping the contact current from 1 mA to 100 mA by measuring the contact voltage in a cold-switching way (actuating the switch while the DC power is off). The impact of current at low-to medium-power levels is investigated to improve understanding of power dissipation at the contact site and more precisely the topological modifications induced. The following results are based on the same 11 successive tests.

Impact of current at low to medium-levels

Figure 8 shows typical "contact force vs contact resistance" curves for a test structure with a 5 µm² square dimple at 11 different levels of contact current for Au/Au contact. This curves point out the relationship between the contact resistance and the force applied on the contact. These measurements are done with the same bridge-bump pair. The first measurement is performed at 1 mA and then the other ones are done by increasing the current level. When contact is made between the metallic electrodes, the contact force is very low at first and the resistance is high and unstable. At a certain minimum force, depending on the material under investigation, a significant reduction of the resistance occurs. At higher forces the contact is stable and the resistance decreases slightly with further increasing force until reaching saturated regime. The contact resistances decrease with the increasing contact force as a function of the contact current and can be described by the equation

0, 5 1,5 2,5 3,5 4,5 5,5 6,5
x C C AF R  
where A and x are constant parameters for each current level. The parameter x decreases from 0.46 to 0.06 when the contact current rises. These values don't match with equation ( 1) and (2) because it does not take into account the roughness of the microcontact surface (cf. Figure 9). The second observation is that the higher the current is, the lower is the dependence of the contact resistance to the load applied. The initial contact resistance remains lower for subsequent cycle at each increasing step of current. The deformations of the contact asperities at the contact closure produce a certain degree of strain hardening of the a-spots. When the softening temperature of the contact material is reached by increasing the level of current, strain hardening disappears in and around the contact interface and the contact area increases. In the same way, the contact area increase can be due to the remove or the breakdown of insulating film on the electrodes because of heating. The presence of alien thin insulating film on the contact surface indeed seems very likely, probably composed of hydrocarbons [START_REF] Tringe | A single asperity study of Au/Au electrical contacts[END_REF], carbon or sulphur contaminants adsorbed onto the surface [START_REF] Ma | Metal contact reliability of RF MEMS switches[END_REF]. In addition, one cannot exclude the possibility that the contact is not fully metallic and some fraction of the contact is acting as a tunnel conductor. The decrease of the contact resistance with increased current can be also explained if quantum mechanical tunnelling through alien film is the charge transfer mechanism [START_REF] Patton | Fundamental studies of Au contacts in MEMS RF switches[END_REF]. Indeed the current increase yield to the voltage increase across the contact by Ohms law. Voltage shits the Fermi level up on one side of the film barrier, which allows a net tunnelling current to flow [START_REF] Holm | Electrical Contacts-Theory and Applications[END_REF]. In the end, assuming the presence of thin insulating layer on the contact surface, more current level increases voltage across the contact, allowing a higher tunnel effect conduction and the breakdown of the insulating film, making easier a higher current flow [START_REF] Jackson | Electrical contact resistance theory for anisotropic conductive films considering electron tunnelling and particle flattening[END_REF].

To further examine the heating effect on contact resistance, the study is focused on the contact temperature when the maximum contact load is reached. The methodology consists in measuring the contact voltage to deduce the contact temperature using equation 3. The series of tests performed previously will be used to compare the impact of increased contact temperature on the test vehicle. We introduce for this result the power level P c to make easier the parallel with RF concepts. The power through the contact is calculated by using the equation The contact resistance continues to decrease keeping the contact temperature roughly constant after reaching the published softening temperature for gold ~100°C [START_REF] Jensen | Effect of nanoscale heating on electrical transport in RF MEMS switch contacts[END_REF] (ie. the contact softening) corresponding to a contact voltage of 70-80 mV for contact near room temperature. After reaching the softening temperature from 3 mW, the contact resistance continues to decrease keeping the contact temperature roughly constant. At this point the contact temperature stops to increase and fluctuates between 80°C and 120°C (65 mV to 75 mV). The temperature seems to be stabilized while the power within the contact rises. with the contact current. Thus the effective contact area increases inducing a drop of the contact resistance. However, we cannot assume that the initial number of asperities is one, that the reason why the real number of asperities in contact cannot be calculated. Nevertheless, any indication of these increases of the contact asperity number is observed in Figure 8, which is the same experiment. The lake of steps in Figure 8 can be explained because mechanical contact does not mean electrical contact. The transition from a mechanical contact to an electrical contact for asperities is a gradual change which is more progressive and thus hard to observe. Another point is considering a constant contact load, the apparent stiffness decreases when the electrical current increases. (cf. Figure 11). Such a behaviour indicates insofar as K = F C /d, that the displacement of the tip is greater at higher current. Softening temperature is indeed reached and the rise of the electrical current implies then a softening of the contact material. When considering a constant contact force, the resulting deformation of the asperities is higher, and the number of "aspots" grows up. Finally, this decrease in the contact stiffness indicates that structural fatigues of the contact asperities has occurred with repeated actuations.

Topological modification of the contact surface

Conclusions

The presented tests and models bring to light the relevance and the validity of this methodology to investigate the micro-contact physics. The origin of this contact resistance reduction is thermally induced with the increase of the contact temperature with the current until reaching the softening temperature. Thus the annealing of the contact leads to a reduction of the contact hardness and the roughness of the contact is lowered after softening of the surfaces. Thereby, the deformation of the contact asperities is higher with increased current making easier the breakdown of residual insulating films, and enlarging the total contact area. At the same time, increased tunneling through an alien film may be in part responsible for these trends. However, the variation of the contact resistance is determined by a competition between asperities flattening, which lowers the contact resistance and heating, which can affect the topography of the contact surface by the activation of thermal failure mechanisms.

The presented test vehicles could be manufactured for future work with several contact materials, which mainly govern the robustness of the contact. The knowledge gained will be the identification of the specific failure mechanisms for each contact design in order to bring recommendations for further improvements of the contact reliability.

Figure 1 :

 1 Figure 1 : Complexity of micro-contact failure mechanisms

Figure 2 :

 2 Figure 2 :Typical lifetime of micro switches leading to contact failure

Figure 3 :

 3 Figure 3 : Principle of the electrical test performed with a nanoindentation tip

Figure 4 :

 4 Figure 4 : Picture of the scan performed with the nanoindenter on the test structure

Figure 5 :Figure 6 -

 56 Figure 5 : Scheme of the test structures 4. FEM modeling of the mechanical actuation4.1. Point load versus distributed loadElectrostatic actuation is the most widespread actuation modes to deflect a bridge until mechanical and electrical contact with the contact line. This actual actuation principle acts as a distributed pressure on the whole bridge which attracted toward the line by an electrostatic force. During our experiments, this distributed pressure is replaced by a point load applied with the tip of the nanoindenter on the bridge center just above the top of the contact bump.

Figure 7 :

 7 Figure 7: Vertical stress induced by a) a Berkovitch tip actuation; b) a spherical tip actuation in the bridge and in the bump. The color bar shows the vertical stress (SY) in MPa.

Figure 8 :

 8 Figure 8 : Contact resistance versus contact force as a function of the contact current

Figure 9 :

 9 Figure 9 : Evolution of the x parameter versus the contact current for Au/Au contact

.Figure 10 :

 10 Figure 10 : Contact temperature versus the power through the contact

Figure 11 :

 11 Figure 11 : Evaluation of the number of asperitiesA specific method has been developed to estimate the increase n of the asperities number, based on the mechanical measurements provided by the micro-bending test. When the force is high enough, new asperities come into contact, involving a sudden modification of the loading configuration, that is to say a discontinuity in the stiffness K. The parameter n is then evaluated by counting the number of steps in the "K vs. F C " curve. As shown on the Figure11, the number of asperities in contact increases


Julien Colmars

Bertrand Marcon

Emmanuel Maurin

Romain Remond

Morestin Fabrice

Paola Mazzanti

Joseph Gril

Hygromechanical response of a panel painting in a church: monitoring and computer modeling

Wooden panel paintings are commonly displayed in traditional churches, where they play to some degree a religious function in addition to their cultural value. They are subject to uncontrolled microclimatic variations that include weekly heating periods. The actual amount of these variations, as well as the consequence on the panel deformations, are insufficiently known. Such information is particularly required when a painted panel needs to be transported, either to be displayed in a different place like a museum or to a workshop for restoration, in order to assess the risk resulting from the change of ambient conditions and make the appropriate decision for their preventive conservation.

The panel called "Le Couronnement d'Epines", about 500 years old, is made of 3 horizontal boards assembled through a pair of vertical crossbars. It is on display in the choir of Saint Didier church, Avignon, south of France, and presents a satisfactory conservation state. Our study focused on the upper board.

In this paper we give details about the in-situ monitoring of the board deflection, together with results about surrounding environment over a 2 year period. We also introduce optical method based on 3D image correlation that we used for external shape measurements. The analysis of the shape, together with the observation of anatomical orientation of two wood samples, allowed estimating the board position in the stem. The deflection was simulated numerically using a 1D version of the code TransPore, which models the heat and mass transfer through the panel and the hygromechanical response of the wood.

The hygrothermal variations followed very slowly those of the external climate, and little perturbation resulted from the occasional heating. After adjustment of the permeability of the painted face, the observed deflection history was well predicted by the model, which could be used to predict the reaction of the panel to a different hygrothermal environment.

Introduction

Wooden panel paintings are commonly displayed in traditional churches, where they play to some degree a religious function in addition to their cultural value. They are subject to uncontrolled microclimatic variations that include weekly heating periods. The actual amount of these variations, as well as the consequence on the panel deformations, are insufficiently known. Such information is particularly required when a painted panel needs to be transported, either to be displayed in a different place like a museum or to a workshop for restoration, in order to assess the risk resulting from the change of ambient conditions and make the appropriate decision for their preventive conservation.

This paper presents a case study for a painted panel located in a French church. Experimental procedures and numerical tools will be explained, as well general features of the hygromechanical response of painted panels.

Geometry and material orientation:

This panel consists in 4 poplar planks, including one small piece in the lower part. Figure 1 shows the front and back faces of the panel; white dotted lines are added to make a clear distinction between the main boards (numbered 1, 2 and 3). The planks are assembled by two vertical cross beams with dovetail joint (see Figure 1b). The panel is floating in its frame; the frame is fixed to the wall through three angle brackets. All three boards show a general cupping deformation, assumingly the result of many years of humidity variations. This visual assessment has been supported by optical measurement with stereo correlation technique; the deformed shape of the painted side is shown with amplification in Figure 2. The condition of boards 2 and 3 led us to study exclusively the mechanical state of board 1. Two micro samples have been cut from the back of the panel; their localization is schematically indicated in Figure 3. Anatomical images (Figure 3b,c) allowed to estimate the position of the corresponding cross section within the transverse plane (Figure 3d). Optical measurements can also provide with valuable information on the material orientation. By plotting only the upper board (Figure 4), we note a general twist of the plank, which we assume to be due to the grain orientation relative to the length of the board. Plotting the maximum cupping along the length suggested a grain tilted by 5° to the horizontal. General discussion about panel painting deformations.

From a mechanical point of view, deformations commonly observed by curators or restorers are of two types: wooden boards free to deform under climatic variations, and boards under constraint. Completely free deformation is rare: in certain cases, like in the present situation, we will neglect the influence of structural assemblies like cross-beams, or joints between two boards. This paper does not deal with the second type of mechanical problem: an example of panel painting with French "parquetage" is described in this conference [Baldit, et al.].

In the case of free deformation, panel paintings exhibit a permanent cupping oriented toward the paint layer, whatever the material orientation. When a board supposed to be initially flat deforms under wetting or drying, it will gain in transient stages either a negative or positive curvature (Figure 6) due to of reduced permeability on the painted side. When the contraction or the expansion of the back face of the panel is partly prevented by the other parts, it is subjected to tension set or compression set, respectively. However, the transverse behavior of wood is very different in tension and compression: while extensions are limited, leading easily to micro cracks, cellular buckling allows high levels of permanent compression. Consequently, in the long term the compression set always dominate over tension set, resulting in the permanent contraction of the back face of the panel. For a 500 year panel painting, we assume that the permanent cupping has already occurred, but dimensional changes still occur under climatic variations. In this second stage, the material orientation becomes of great importance. We distinguish two different effects:

• Moisture gradient effect (described before as the effect of painted layer)

• Orientation effect (the equilibrium of orthotropic material under homogeneous moisture field in the plank). The solution for a moisture gradient can be approximated through the use of computational models. The solution for the second effect is the analytic solution of: div(σ) = 0 and σ = C.ε with ε = α.h where α is the shrinkage/swelling tensor and h the homogeneous moisture content field. Figure 7 shows the combined influence of painted layer and cross-section orientation of the board. In this diagram, we note that the two effects (gradient and orientation) are sometimes opposite and sometimes consistent. We will discuss later the different orders of magnitude of each effect. In the following part we describe the monitoring of our panel.

Apparatus for deformations monitoring.

Optical measurements provide satisfactory information on the whole panel, but are also a time-consuming technique that cannot be used in situ for continuous measurements. Therefore we designed a device for in-situ monitoring of dimensional variations. This equipment provides continuous data on climatic-induced deformation of the panel. Our dedicated apparatus was set up behind the panel to measure the cupping of board number 1; the method could be extended to the other boards in further experimentations. The global system consists in one apparatus for the cupping measurement and one data logger (the data logger used here is distributed by HOBO ® firm). In this particular case, the data logger records both the cupping signal and the environmental conditions, temperature (T [°C] and air relative humidity (RH) [%]. All power supply needed for these three measurements are given by a 3V battery, so that a receptacle is not required. This should be considered a great advantage for panel monitoring, for instance in exhibition conditions. As mentioned before, we assumed that each plank of its panel is free to deform under climatic environment, i.e. the presence of the two cross-beams is not generating large constraints by limiting the cupping. This first assumption is not as restrictive as it could seem. Both in-situ observations and optical measurements showed that the board deformation is not disrupted in the proximity of the crossbars.

For in-situ monitoring, the complex three dimensions deformation of the board had to be simplified into a single variable; here we chose the bending deflection, proportional to the curvature. By measuring the distance variation between two sidelong points and a central third one (Figure 8), we obtain an image of the panel deformation. Panel paintings are generally exhibited in very close position to the supporting wall. Such an apparatus is so designed to fit the reduced space behind the panel. In this case the back face of the panel is around 10 cm from the wall. In agreement with the restorers the apparatus was fixed on the two cross beams, thanks to a light tubular structure. Mechanically speaking, it was ensured that this fixation does not induce additional constraints.

Measurement Results.

Figure 9 shows the measurement of relative humidity in air (RH) and temperature (T) behind the panel, together with deflection of the board (in mm) over a two years period (07/05/03 to 09/09/15); the period between October and December 2008 is unfortunately missing. For a better view of the correlation between relative humidity variations and deflection, the deflection curve is plotted after multiplication by (-1). Correlation between relative humidity and deflection is evident, so as the smoothing effect of the diffusion in the wood plank. The temperature curve gives evidence of temporary heating during Sunday masses and other religious events.

Aim of the simulation: formulation of the problem.

For a practical, conservational point of view, it would be ideal to determine whether an ambient condition is "good or not" for a panel painting. On the other hand, wood mechanics allow predicting the reaction of a wood plank under given climatic conditions. For predicting the moisture content and the consequent deformation of the board, we used a computational code Transpore developed by P. Perré []. This code is based on heat and mass transfer formulation, and coupled with a 1D mechanical formulation. This allows predicting the cupping of a unidirectional board (radial or tangential direction along the thickness) with given boundary conditions (mainly relative humidity, temperature and convection coefficient on the two faces of the panel). Details on the formulation of Transpore can be found in [START_REF] Perre | TransPore: A generic heat and mass transfer computational model for understanding and visualizing the drying of porous media[END_REF] and [START_REF] Rémond | Approche déterministe du séchage des avivés de résineux de forte épaisseur pour proposer des conduites industrielles adaptées[END_REF].

Diffusion parameters.

Diffusion parameters for poplar were estimated from various experiments on spruce or poplar; some parameters are in consequence not fully representative of poplar. Formulation of diffusion in Transpore depends on many parameters: gaseous permeability, liquid permeability and diffusion coefficients with their dependence to temperature. It means that various experiments are needed for their determination. We only had at our disposal simple drying data on poplar samples, i.e. measurement of mass variation under climatic changes. The reliability of the "spruce" parameters for describing poplar was verified by comparing the simulation with the diffusion data on poplar. The simulations were performed on four different thicknesses (5, 10, 15 and 20 mm) for radial and tangential orientation, as conditions in experiments. Results are reported in Figure 10. Regarding the thickness of our panel (20mm) and delays of sorption, we conclude that the diffusion parameters used in the following are fully acceptable.

Drying step

Radial response Tangential response

Figure 10: experimental diffusion data on poplar and simulations for radial and tangential thicknesses.

Mechanical parameters.

Until now Transpore has been used for short-term simulation: be it in drying applications [START_REF] Rémond | Approche déterministe du séchage des avivés de résineux de forte épaisseur pour proposer des conduites industrielles adaptées[END_REF]) or panel paintings ones [START_REF] Allegretti | A New Experimental Device for Non-Symmetrical Drying Tests -Experimental and Numerical Results for Free and Constrained Samples[END_REF]), the experimental window was always shorter than one day. In our study we initiate parameter identification over a long term period (1 year for example); our final aim is to determine the precision of the prediction on another 1 year long period. Some part of mechanical parameters is estimated from the literature. Indeed some others have to be estimated for our experiments: mainly parameters for time-dependant behavior in our experimental windows (1 year) which is not so common for identification. The 1D rheological model used for the mechanical formulation is schematized in Figure 11. It consists in one swelling element, one elastic element, 4 viscoelastic bodies, and one mechanosorptive element. Viscoelastic and mechanosorptive parameters will be identified from the experimental data, over a 1 year period. Elastic and dilatation parameters in each orthotropic direction, as well as Poisson rations, were estimated from the literature [START_REF] Guitard | Mécanique du matériau bois et composites[END_REF]).

Material orientation

In order to avoid the use of the 2D version of TransPore that is much more time-consuming that the 1D version, the response of a board with complex material orientation along the cross-section was interpolated between a radial and tangential board behavior calculated by Transpore. The orientation of the board was determined in accordance with the previous observations. According to Figure 7, we can predict the orientation of the rings with regards to the painted layer, i.e. our case corresponds to configuration 1 or 2. The observation of results in Figure 9 shows us that: transient moistening results in a transient diminution of the cupping (normal effect of the painted layer); wet period (3 months for example) results in global reduction of the cupping compared to a dry period. We conclude that the board of St Didier's panel is of configuration 2 (see Figure 9). Combining this with the anatomical observations and optical measurements, we get a global idea of the original plank position in the trunk for the simulations.

Results

Here we present preliminary results of our simulations. Parameter identification is not complete but the next figures illustrate some points discussed before. Figure 12 shows results of radial and tangential simulations, with interpolation between the two curves according to the material orientation deduced in previous chapters. On Figure 13 we show preliminary results: parameters were estimated on first period from 07 May 1 st to 07 February 1 st ; then we attempted a prediction, i.e. a simulation with identical parameter set during another period from 2008 December to 2009 September. This first trial shows small discrepancy with experimental data: in near future we plan to improve the identification technique. In addition we aim at quantifying the prediction error, so we can obtain a reliable model able to determine conservation risks in any other climatic condition.

Conclusion

In this paper we presented an on-going study on panel painting conservation. We have presented the use of several techniques (anatomy, in-situ long-term monitoring, optical measurements, and computational modeling) in order to study the case of a poplar panel on display in St Didier's church in Avignon (France). In the near future, we will provide further results on parameters identification and simulation results.

  Figure 1 : "Couronnement d'épines", anonymous, 1563, exhibited in the Saint Didier church (Avignon, France). Length: 143cm, Width: 178cm. Front (a) and back (b) faces of the panel with indication of boards position (white dotted lines).

Figure 2 :

 2 Figure 2 : general deformation of the panel measured by stereo-correlation (scales in mm).

Figure 3 :

 3 Figure 3: Possible orientation of the upper plank estimated from anatomical samples.

Figure 4 :

 4 Figure 4 : shape of board n°1 (2006 dec 12th) by stereocorrelation

Figure 5 :

 5 Figure 5: Fiber orientation deduced from deflection peaks across the board width, calculated from 3D image.

Figure 6 :

 6 Figure 6 : description of permanent deformation on panel paintings.

Figure 7 :

 7 Figure 7 : deformation of two different board types under a climatic variation.

Figure 8 :

 8 Figure 8 : Cupping deformation of a board cross section, and measurement apparatus with deflection at two different times.

Figure 9 :

 9 Figure 9 : Relative humidity and temperature behind the panel, and deflection of the upper board, over a 2 year period.

Figure 11 :

 11 Figure 11 : rheological model with parameters

Figure 12 :

 12 Figure 12 : interpolation between radial and tangential simulation


The wireless measurement of various physical quantities from the analysis of the RADAR Cross Sections variability of passive electromagnetic sensors is presented. A millimetre-wave Frequency-Modulated Continuous-Wave RADAR is used for both remote sensing and wireless identification of sensors. Long reading ranges (up to some decameters) may be reached at the expense of poor measurement resolution (typically 10%).

I. INTRODUCTION

he wireless measurement of a physical quantity from the analysis of the RADAR Cross Section (RCS) variability of passive sensors was proposed for the first time by the authors in 2008 [START_REF] Jatlaoui | Pressure Sensing Approach Based on Electromagnetic Transduction Principle[END_REF] while the proof-of-concept was demonstrated in 2010 [START_REF] Chebila | Pressure Measurement from the RADAR Interrogation of Passive Sensors[END_REF]. A Frequency-Modulated Continuous-Wave (FMCW) RADAR was used for the measurement of pressure-dependent RCS variation and for the remote derivation of the applied pressure changes. The wireless sensing technique based on RCS-variability measurement has been successfully applied to the remote estimation of other physical quantities, such as temperature [START_REF] Thai | A Novel Passive Ultrasensitive RF Temperature Transducer for Remote Sensing and Identification utilizing RADAR Cross Sections Variability[END_REF]- [START_REF] Traille | A Wireless Passive RCSbased Temperature Sensor using Liquid Metal and Microfluidics Technologies[END_REF]. We have not found reports published before our first papers [START_REF] Jatlaoui | Pressure Sensing Approach Based on Electromagnetic Transduction Principle[END_REF] [START_REF] Chebila | Pressure Measurement from the RADAR Interrogation of Passive Sensors[END_REF] where the physical quantity is directly used for the RCS amplitude modulation of passive electromagnetic (EM) sensors and then remotely measured from FMCW RADAR interrogation. Recently Mandel et al. [START_REF] Mandel | A Wireless Passive Strain Sensor[END_REF] has reported a very similar technique applied to strain sensors.

The wireless identification of passive and chipless EM sensors may be based on multi-band microwave resonators for encoding data into a specific spectral signature or microwave barcode [START_REF] Jalaly | Capacitively-tuned split microstrip resonators for RFID barcodes[END_REF]- [START_REF] Preradovic | Multiresonator-Based Chipless RFID System for Low-Cost Item Tracking[END_REF]. By using an Ultra-WideBand (UWB) interrogator, such barcode may be remotely read. An alternative approach consists of creating a low-frequency barcode in the beat frequency (or Intermediate Frequency) H. AUBERT, F. CHEBILA, A. TRAILLE, S. BOUAZIZ, A. RIFAÏ , P. PONS and P. MENINI are with LAAS-CNRS, 7 avenue du Colonel Roche, F-31077 Toulouse, France and University of Toulouse; UPS, INSA, INP, ISAE; F-31077 Toulouse, France; M. JATLAOUI is currently with IPDIA, 2 rue de la Girafe, 14000 Caen, France, and was with LAAS-CNRS when working on passive pressure EM sensors ; H. HALLIL is currently with University of Bordeaux, Laboratory IMS, CNRS UMR 5218, IPB, Univ. Bordeaux 1, Talence, France and was with LAAS-CNRS when working on passive gas and temperature sensors, T. THAI is with School of ECE, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A and was also with LAAS-CNRS when working on passive temperature and strain EM sensors; M. TENTZERIS is with School of ECE, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A. spectrum synthesized by the FMCW RADAR [START_REF] Jatlaoui | Original Identification technique of passive EM Sensors using Loaded Transmission Delay Lines[END_REF]. The wireless identification of sensors may then be based on FMCW RADAR measurement of the time-arrivals of multiple echoes controlled by delay lines. This approach features the advantage of eliminating the challenging fabrication of UWB readers requiring, e.g., an Analog-to-Digital Converter with very high sampling rate. Our wireless system uses the same FMCW RADAR reader for both remote sensing and sensors identification. As shown in this communication it is convenient for long reading ranges (up to some decameters) but does not yield, at least in its present version, to high measurement resolution of physical quantities.

II. PASSIVE CHIPLESS DEVICES FOR WIRELESS SENSING

Passive (battery-less) and wireless sensors are very good candidates for measuring physical quantities in harsh environment (e.g., high radiation or extreme temperature) and/or for applications requiring sensing devices with lowcost of fabrication, small size and long-term measurement stability. In 2007 the authors report the first passive pressure sensing device based on an electromagnetic (EM) transduction [START_REF] Jatlaoui | Radio-Frequency pressure transducer[END_REF]. The EM sensing device converts the variation of an applied pressure into a variation of millimetre-wave resonant frequency of a resonator. In general passive EM sensing devices convert the variation of a physical quantity (such as, e.g., pressure or temperature) into a known/specific variation of a given electromagnetic wave descriptor. These devices are battery-free and chipless. Based on the EM transduction the first gas sensor was presented in 2004 by Grath et al. [START_REF] Mcgrath | Development of nanobased resonator gas sensors for wireless sensing systems[END_REF] and the first strain sensor was reported in 2005 by Chuang et al. [START_REF] Chuang | Embeddable wireless strain sensor based on resonant RF cavities[END_REF]. Unlike devices based on Surface Acoustic Waves (see, e.g., [START_REF] Buff | Passive remote sensing for temperature and pressure using SAW resonator devices[END_REF]- [START_REF] Pereira | Wireless Acoustic Wave Sensors and Systems for Harsh Environment Applications[END_REF]) EM sensing devices do not require electromagnetic-toacoustic wave conversion and consequently avoid high losses involved in this conversion (the survey of original passive EM sensing devices developed by the authors since 2007 is reported in [START_REF] Pons | Electromagnetic transduction for wireless passive sensors[END_REF]).

The remote sensing technique based on the RCS variability measurement described in the next Section is applied, for illustration purposes, to a passive EM pressuresensing device. This device is composed of a high resistivity silicon membrane and a planar half-wavelength resonator deposited inside a circular Pyrex cavity (see Figure 1). The membrane and the resonator are separated by a thin air slab.

Wireless Sensing and Identification of Passive Electromagnetic Sensors based on

Millimetre-wave FMCW RADAR H. AUBERT, Senior Member, IEEE, F. CHEBILA, M. JATLAOUI, T. THAI, H. HALLIL, A. TRAILLE, S. BOUAZIZ, A. RIFAÏ , P. PONS, P. MENINI, M. TENTZERIS, Fellow, IEEE T Electromagnetic coupling between the resonant mode in the planar resonator and the transverse stationary waves in the dielectric membrane takes place through the evanescent transverse EM field in the air slab. A pressure force applied to the membrane generates a deflection, modifies the air slab thickness, which consequently alters the electromagnetic coupling. As a result the resonant frequency of the sensing device is shifted (~1GHz/µm between 0.25µm and 6µm [START_REF] Jatlaoui | Pressure Micro-sensor based on Radio-Frequency Transducer[END_REF]). High sensitivity of the resonant frequency to the applied pressure may be obtained due to the abrupt spatial variation of the transverse evanescent EM field in the air slab. The sensor exhibits a measured sensitivity of 370MHz/bar between 0 to 3 bars [START_REF] Jatlaoui | New Electromagnetic Transduction Micro-sensor Concept For Passive Wireless Pressure Monitoring Application[END_REF].

III. REMOTE READING AND IDENTIFICATION OF PASSIVE EM SENSORS BASED ON THE RCSS VARIABILITY MEASUREMENT

A solution for the remote sensing and wireless identification of passive and chipless sensors in a wireless network consists of allocating a unique and controlled spectral distribution of RCSs to each sensor. Such specific RCSs distribution may be used as a signature of the sensor, as proposed in [START_REF] Jalaly | Capacitively-tuned split microstrip resonators for RFID barcodes[END_REF][10] while analyzing the RCS variation at a particular frequency -or else, tracking the frequency for which the RCS is maximum-allows in principle the remote derivation of the physical quantity fluctuation [START_REF] Jatlaoui | New Micro-sensors Identification Techniques Based on Reconfigurable Multi-band Scatterers[END_REF] [START_REF] Aubert | Measurement Device Comprising an Electromagnetic Diffuser[END_REF]. An illustrative example of passive sensors having specific and reconfigurable RCSs can be found in [START_REF] Chebila | Reconfigurable Multi-band Scatterers for Micro-sensors Identification[END_REF]. Spectral barcodes are created in [START_REF] Jalaly | Capacitively-tuned split microstrip resonators for RFID barcodes[END_REF]- [START_REF] Preradovic | Multiresonator-Based Chipless RFID System for Low-Cost Item Tracking[END_REF] by using multiple resonant frequencies in the microwave frequency range. An alternative approach consists of creating the spectral barcode at low-frequency range, i.e., in the beat frequency (or Intermediate Frequency) spectrum synthesized by the FMCW RADAR [START_REF] Jatlaoui | Original Identification technique of passive EM Sensors using Loaded Transmission Delay Lines[END_REF]. This remote wireless technique is described in the next sections.

A. Remote Sensing based on FMCW RADAR Reader

In FMCW RADAR, the transmitted signal (transmitted power P T ) or chirp has a linear sawtooth variation of frequency with time. For such modulation the frequency is tuned linearly as a function of time by using a Voltage-Controlled Oscillator (VCO). The chirp of carrier frequency f, bandwidth (or excursion frequency) ∆F and sawtooth modulation period T R is radiated by using a transmitting antenna (gain G T ) and is back-scattered by the target or scatterer. In free-space the back-scattered signal or echo consists of an attenuated replica of the chirp delayed by the two-way propagation delay ∆t=2R/c where R designates the range and c denotes the vacuum celerity of light. The instantaneous frequency difference between the chirp and its delayed replica is constant and given by 2∆F∆t/T R . In order to measure this difference and deriving the range R the echo received by the RADAR receiving antenna (Gain G R ) is mixed with the transmitted chirp (homodyne principle). An Analog-to-Digital conversion and Fast Fourier Transform by Hamming windowing at the mixer output signal are finally performed for obtaining the beat frequency -or Intermediate Frequency-spectrum. A millimetre-wave carrier frequency for the FMCW RADAR is preferred here to a lower frequency. As a matter of fact, higher frequencies allow for reducing the sensor and antenna sizes and/or designing directional (high gain) antennas for beamforming, multibeam (for increasing interrogation beam width) or beamsteering RADAR reader. Moreover, higher frequency improves the sensor immunity to objects located at its vicinity by increasing the electrical length separation distance to them. Additionally using millimetre-wave carrier frequency offers high bandwidth ∆F: as range resolution scales as 1/∆F, higher bandwidth enables spread-spectrum for identification of greater number of sensors in a wireless network. In the proof-on-concept experiment dated on 2010 [START_REF] Chebila | Pressure Measurement from the RADAR Interrogation of Passive Sensors[END_REF], a millimetre-wave FMCW RADAR operating at f=29,45GHz (∆F=650 MHz, T R =1ms, P T =13dBm=20mW, G T =14dB and G R =14dB) is used for the remote derivation of applied pressure from the measurement of the RCS of passive sensor. Such sensor was composed of an antenna (Gain G A =20dB at the carrier frequency) connected to a 50Ω coaxial cable of physical length L=1m and relative permittivity ε r =1,7 (or refractive index n=1,3), which is in turn connected to one port of the pressure EM sensing device described in Section II. This cable could be replaced by a millimetre-wave delay line providing a propagation delay of 4,3ns at the carrier frequency over a 2% bandwidth. The other port of the sensing device is loaded by 50Ω. The transmitted chirp interrogates the sensor, placed at a distance R=1,4m from the RADAR antennas, at a frequency near the resonant frequency of the sensing device. The pressure is applied on sensing device via a nozzle placed at 40µm high from the thin sensing device membrane.

Figure 2 displays the beat frequency spectrum synthesized by the millimetre-wave FMCW RADAR reader when no pressure is applied. As expected this spectrum exhibits two spikes or echoes at specific frequencies: at the beat frequency f str =12KHz≈2(∆F/T R )(2R/c), the echo level A str corresponds to the backscattering from the sensor antenna while the second echo level A ant occurring at a beat frequency f ant =24KHz≈2(∆F/T R )[2(R+nL)/c] is associated with the reflection of the millimetre wave on the sensing device after reception by the sensor antenna and propagation inside the coaxial cable. Fig. 2: Measured beat frequency spectrum synthesized by the RADAR reader when the pressure is not applied on the sensing device As displayed in Figure 3 the echo level A str does not depend on the applied pressure (the echo level accuracy is estimated at ±0,5dB) and is called the structural scattering mode: it is not useful for the remote measurement of the applied pressure but the corresponding beat frequency f str allows the remote derivation of the sensor range with a resolution c/2∆F≈23cm. Moreover, as shown in Figure 4, the echo level A ant depends on the applied pressure. It is called the antenna scattering mode. Between 0 and 2.5bars the measured sensitivity is 0.8dBm/bar. The full-scale echo measurement range is 5dBm when the applied pressure ranges from 0 to 3,5bars. When a pressure is applied on the membrane of the sensing device, the RCS of antenna-scattering-mode is varied, received backscattered power P R changes and as a result echo level A ant is modified. The measurement of this modification allows, at least in principle, the remote estimation of the applied pressure variation. This summarizes the wireless reading principle based on the FMCW RADAR measurement of sensor-RCS variation. The unambiguous identification of echoes associated with the structural and antenna scattering modes among the multiple spikes in the beat frequency spectrum (as shown in Figure 2) is possible only for sensor having a structural-scattering-mode RCS sufficiently high, that is, providing an echo A str significantly higher than the other peaks. It is the limitation of the proposed technique in its present form. The beat frequency f str can then be derived and since the delay between the structural-and antennascattering-modes is known (fixed by the delay line), the location in the spectrum of the antenna-scattering-mode beat frequency f ant can be deduced. Following the proposed remote sensing technique based on RCS-variability measurement, the passive EM sensor yields to a full-scale echo measurement range ∆A=10log 10 (A 2 /A 1 ) (in dB) [or equivalently a full scale RCS range ∆σ = σ 2 -σ 1  (in dB)] for a physical quantity range ∆ϕ=ϕ 2 -ϕ 1 . Consider a passive scatterer composed of a horn antenna (G horn =20dB and size 30mm x 40mm) loaded by a passive EM having an input impedance of 50Ω when ϕ=ϕ 1 and 0Ω when ϕ=ϕ 2 . The RADAR transmitting antenna operating at 29,75GHz is a parabolic antenna (G T =35dB) and the RADAR receiving antenna is horn antenna (G R =14dB). The transmitted power is P T =13dBm (20mW). In this out-door experiment the distance between the RADAR and the loaded scatterer is R=30m (Figure 5). The Figure 6 displays the resulting measured lowfrequency spectrum provided by the millimetre-wave FMCW RADAR reader when ϕ=ϕ 1 and ϕ=ϕ 2 . The sensitivity of the reader or minimum detectable received power is -70dBm. At the expected beat frequency 260kHz≈2(∆F/T R )(2R/c), (∆F=650MHz and T R =1 ms) a high echo level is observed when ϕ=ϕ 2 . Fig. 5 : Outdoor environment for the measurement of the beat frequency spectrum synthesized by a FMCW RADAR operating at 29,75 GHz. The scatterer is placed on the ground surface at 30m from the RADAR.

A low but still measurable echo level of -48dBm (just above the noise level A noise ≈ -50dBm) is measured when ϕ=ϕ 1 (as expected, if the scatterer is removed or is moved away from the RADAR, this echo level disappears at 260kHz). The fullscale measurement range at 30m is then found to be ∆A=10dB. Since the accuracy on the echo level measurement is here δA~1dB, the resulting resolution δA/∆A is low (approximately 10%). SAW devices sensors offer high measurement resolution but with reading range significantly lower.

Fig. 6 : Measured beat frequency spectrum in the out-door environment shown in Fig. 4 for two values of the physical quantity ϕ : ---for ϕ=ϕ1 (or equivalently, the scatterer is loaded by 50Ω); -for ϕ=ϕ2 (or equivalently, the scatterer is short-circuited);

B. Remote Identification of Passive EM Sensors using FMCW RADAR Reader

The FMCW-RADAR reader used for the remote reading of passive sensors can also be utilized for identification purposes. When the passive sensor is composed of an antenna connected to a transmission line (or delay line) which loads in turn the sensing device, the measurement of the difference between the beat frequencies of the antennascattering-mode f ant and structural-scattering-mode f st allows the remote estimation of the transmission line electrical length (or propagation delay). By allocating a specific electrical length (or delay) to each sensor in a wireless network, this simple measurement may be used, at least in principle, for identification purpose. In the proof-of-concept experiment reported recently by the authors in [START_REF] Jatlaoui | Original Identification technique of passive EM Sensors using Loaded Transmission Delay Lines[END_REF] the identification is based on an antenna connected to multiple transmission lines, each being loaded by various fixed impedances. All transmission lines used in this experiment are 50Ω-coaxial lines filled with dielectric material of relative permittivity ε r =1,7 and having 2dB/m of losses. The set up is composed of two horn antennas at distances R 1 =1m and R 2 =2,5m from the RADAR antennas (see Figure 7). One horn antenna is connected to a coaxial cable denoted by cable 1 of physical length L 1 =30cm which is loaded by an open-circuit (the load impedance Z 1 is infinite). The second horn antenna is connected to a coaxial cable denoted by cable 2 of physical length L 2 =75cm. This cable is in turn connected to the input port of a splitter. One splitter output is directly connected to an open-circuit (the load impedance Z 2 is infinite) while the second output is connected to a coaxial cable (cable 3) of physical length L 3 =75cm which is loaded by an open-circuit (the load impedance Z 3 is infinite). Figure 8 displays the resulting beat frequency spectrum synthesized by the millimetre-wave FMCW RADAR Reader (f=29,75GHz, ∆F = 700MHz and T R = 1 ms). As expected five echoes are detected in this spectrum: two echoes (at 9KHz and 23KHz) correspond to the time-arrivals of structural scattering mode of the two horn antennas while the three others (at 14KHz, 33KHz and 43KHz) are associated with the reflection of the millimetre-wave on the loads Z 1 , Z 2 and Z 3 . The unique and controlled distribution of these peaks can then be advantageously used for the remote identification of the scatterer. IV. CONCLUSION

The use of a millimetre-wave FMCW Radar reader for both the wireless reading identification of passive EM sensors been presented in communication. It is shown that the wireless measurement of various physical quantities is possible from the analysis of the RADAR Cross Sections variability of passive electromagnetic sensors. Additionally the same FMCW RADAR can be used for identifying the passive sensors in a wireless network. However, the measurement resolution is poor (typically 10% of the full-scale measurement range). An alternative solution would consist of tracking in the beat frequency spectrum the frequency at which the RCS reaches its maximum value as the physical quantity varies [24][26]. This solution, under investigation by the authors, may achieve higher measurement resolution while not significantly alters the reading range.

Fig. 1 :

 1 Fig. 1 : The first passive pressure-sensing device based on electromagnetic transduction and operating in the millimetre-wave frequency range (dimensions: 3,8mm x 5,8mm x 1,4mm): (a) top view of the planar halfwavelength resonator deposited inside a circular Pyrex cavity and (b) top view of the high resistivity silicon membrane placed at the top of the planar resonator.

Fig. 3 :

 3 Fig.3: Measured echo level of passive EM pressure sensor versus applied pressure at the beat frequency fstr of the structural scattering mode.

Fig. 4 :

 4 Fig.4: Measured echo level of passive EM pressure sensor versus applied pressure at the beat frequency fant of the antenna scattering mode.

Fig. 7 :

 7 Fig. 7 : (a) Proof-of-concept set-up for demonstrating the feasibility of the wireless identification of passive sensors based on the millimetre-wave FMCW-RADAR used for remote sensing and (b) Schematic of the experimental set-up (the load impedance Z1, Z2 and Z3 are infinite).

Fig. 8 :

 8 Fig.8: Beat frequency spectrum synthesized by the millimetre-wave FMCW RADAR Reader when interrogating the scatterer shown in Fig.5

ACKNOWLEDGMENTS

The authors wish to thank the two following institutions for financial support: the French Radioactive Waste Management Agency (ANDRA) through the contract N° 045985 and the Pole de Competitivité Aéronautique, Espace et Systèmes Embarqués (AESE) through the projet Système Autonome Communicant En Réseau (SACER).