NON-INVASIVE METHOD FOR MEASURING A PHYSICAL QUANTITY REPRESENTATIVE OF THE ELASTICITY OF A MATERIAL

Abstract

A non-invasive method for measuring a physical quantity representative of the elasticity of a material, including: determining the phase velocities of the fundamental mode of the various components of a shear wave generated at the surface of the material, along a measurement axis, the set of pairs, each formed by a frequency f, and the phase velocity Vi of the fundamental mode determined for the frequency fi, forming a dispersion curve of the fundamental mode in a measurement direction parallel to the measurement axis, wherein the index i is an order number of the frequency fi and of the phase velocity Vi, and transforming the dispersion curve into a profile of phase velocities as a function of depth, the phase velocity at a given depth being a physical quantity representative of the elasticity of a material at the depth.

Claims

1-12. (canceled)

13. A non-invasive method for measuring a physical quantity representative of the elasticity of a material, the method comprising the following steps of: a) deforming the material at an impact point using a stimulator to generate a shear wave comprising components at different frequencies, these various components propagating at the surface of the material and causing a displacement of the surface of the material, b) measuring, using a measurement device, the displacement of the surface of the material over time at at least three measurement points aligned one behind the other along a measurement axis, wherein the method also comprises the following steps of: c) determining the phase velocities of the fundamental mode of the various components of the shear wave generated, along the measurement axis, from the measurements of the measurement device, the set of pairs, each formed by a frequency f.sub.i and the phase velocity V.sub.i of the fundamental mode determined for said frequency f.sub.i, forming a dispersion curve of the fundamental mode in a measurement direction parallel to the measurement axis, wherein the index i is an order number of the frequency f.sub.i and of the phase velocity V.sub.i, and d) transforming said dispersion curve into a profile of phase velocities as a function of depth, the phase velocity at a given depth being a physical quantity representative of the elasticity of the material at said depth.

14. The method according to claim 13, wherein transforming the dispersion curve into a profile of phase velocities in the measurement direction comprises the following operations of: 1) converting each frequency f.sub.i of the dispersion curve, into a corresponding wavelength .sub.i using the following relationship: .sub.i=V.sub.i/f.sub.i, and then 2) calculating the value of a coefficient for said measurement direction using the following relationship: =Z.sub.max/.sub.max, where: Z.sub.max is equal to half the distance separating the two furthest measurement points along the measurement axis, and .sub.max is the largest of the wavelengths .sub.i obtained after executing the operation 1) for said measurement direction, 3) converting each wavelength .sub.i obtained after executing operation 1) into a corresponding depth p.sub.i using the following relationship: p.sub.i=.sub.i, where is the coefficient calculated in the operation 2).

15. The method according to claim 14, wherein the method comprises performing steps a), b), c) and d) for at least a first and a second measurement axes angularly offset from each other, said first and second measurement axes passing through the same impact point.

16. The method according to claim 13, wherein step c) of determining the phase velocities of the fundamental mode comprises reiterating the following operations for several different frequencies f.sub.i: for each measurement point: filtering, using a bandpass filter centred on the frequency f.sub.i and whose 3 dB bandwidth is between the frequencies f.sub.i1 and f.sub.+1, the signal u(x,t), measured at the measurement point of coordinate x along the measurement axis by the measurement device, to obtain a filtered signal u.sub.i(x,t), identifying a time instant t.sub.i,m(x) at which the filtered signal u.sub.i(x,t) passes through its absolute minimum, and then calculating the velocity V.sub.i of propagation of this minimum along the measurement axis from the time instants t.sub.i,m(x) and the positions x at which this minimum occurs, the velocity V.sub.i thus calculated being the phase velocity of the fundamental mode at said frequency f.sub.i.

17. The method according to claim 16, wherein step c) comprises: an operation of automatically identifying, among the set of frequencies f.sub.i, a minimum frequency f.sub.min below which the frequencies f.sub.i no longer verify the following condition (1): $\underset{p=1}{\overset{P_{\max }}{.Math.}}{\left(t_{i,m}\left(x_p\right)-{}_{i,1}{x}_p-{}_{i,0}\right)}^2{\mathrm{err}}_{\max }$ where: .sub.i,1 and .sub.i,0 are the coefficients of the straight line, determined by the least squares method, best approximating the points of coordinates (x; t.sub.i,m(x)), x.sub.p is equal to the position x of the p-th measurement point counted from the first measurement point closest to the impact point, P.sub.max is equal to the number of measurement points distributed along the measurement axis, err.sub.max is a predetermined constant, and then only the frequencies f.sub.i greater than or equal to said frequency f.sub.min are retained to form the dispersion curve.

18. The method according to claim 17, wherein step c) comprises: an operation of automatically identifying, from the set of frequencies f.sub.i, a maximum frequency f.sub.max above which the frequencies f.sub.i no longer verify the condition (1), this operation of automatically identifying the frequency f.sub.max being carried out by testing this condition (1) for several frequencies f.sub.i, and then only the frequencies f.sub.i lower than or equal to said frequency f.sub.max are retained to form the dispersion curve.

19. The method according to claim 13, wherein all frequencies f.sub.i are between 1 Hz and 3,000 Hz.

20. A non-invasive apparatus for measuring a physical quantity representative of the elasticity of a material, for implementing a method in accordance with claim 13, the apparatus comprising: a stimulator capable of deforming the material at an impact point to generate a shear wave comprising components at different frequencies, these various components propagating at the surface of the material and causing a displacement of the surface of the material, a measurement device capable of measuring the displacement of the surface of the material over time at at least three measurement points aligned one behind the other along a measurement axis, wherein the apparatus comprises a processing unit capable of: determining the phase velocities of the fundamental mode of the various components of the shear wave generated along the measurement axis from the measurements of the measurement device, the set of pairs, each formed by a frequency f.sub.i and the phase velocity V.sub.i of the fundamental mode determined for said frequency f.sub.i, forming a dispersion curve of the fundamental mode in a measurement direction parallel to the measurement axis, wherein the index i is an order number of the frequency f.sub.i and the phase velocity V.sub.i, and transforming said dispersion curve into a profile of phase velocities as a function of depth, the phase velocity at a given depth being a physical quantity representative of the elasticity of the material at said depth.

21. The apparatus according to claim 20, wherein the processing unit is configured to execute the following operations to transform the dispersion curve into a profile of phase velocities in the measurement direction: 1) converting each frequency f.sub.i of the dispersion curve, into a corresponding wavelength .sub.i using the following relationship: .sub.i=V.sub.i/f.sub.i, and then 2) calculating the value of a coefficient for said measurement direction using the following relationship: =Z.sub.max/.sub.max, where: Z.sub.max is equal to half the distance separating the two furthest measurement points along the parallel measurement axis, and .sub.max is the largest of the wavelengths .sub.i obtained after executing the operation 1) for said measurement direction, 3) converting each wavelength .sub.i obtained after the operation 1) into a corresponding depth p.sub.i using the following relationship: p.sub.i=*.sub.i, where is the coefficient calculated in the operation 2).

22. The apparatus according to claim 20, wherein: the measurement device comprises an array of sensors each capable of measuring the amplitude of the deformation of the surface of the material at a respective measurement point, this array comprising at least three sensors each of which measures displacement of the surface of the material at three respective measurement points aligned one behind the other along a measurement axis, and the apparatus comprises a hinged arm to which the sensor array is mounted, said hinged arm being capable of rotating the sensor array through a predetermined angle about an axis of rotation, to align the measurement axis of the sensor array with a first measurement axis and, alternately, with a second measurement axis angularly offset from the first measurement axis.

23. The apparatus according to claim 22, wherein: the sensor array comprises: a row of optical sensors that sense light reflected from each measurement point, and a microprocessor configured to determine displacement of the surface of the material at each measurement point lit from the reflected light sensed by the row of optical sensors, the measurement device comprises an emitter of a light beam which lights each measurement point aligned along the measurement axis.

24. The apparatus according to claim 20, wherein the stimulator is capable of projecting a jet of fluid onto the surface of the material which causes the material to deform at the impact point.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0056] The invention will be better understood upon reading the following description, which is given solely by way of non-limiting example and is made with reference to the drawings in which:

[0057] FIG. 1 is a schematic illustration of the architecture of an apparatus for measuring a physical quantity representative of the elasticity of a material;

[0058] FIG. 2 is a schematic illustration of a stimulator and a measurement device of the apparatus of FIG. 1;

[0059] FIG. 3 is a flow chart of a method for measuring a physical quantity representative of the elasticity of a material using the apparatus of FIG. 1;

[0060] FIG. 4 is a three-dimensional graph illustrating displacement measurements acquired by the apparatus of FIG. 2:

[0061] FIG. 5 is a graph illustrating the calculation of the displacement velocity of a shear wave;

[0062] FIG. 6 is a three-dimensional graph illustrating, for a frequency component, displacement measurements acquired by the apparatus of FIG. 2;

[0063] FIG. 7 is a graph illustrating determination of a phase velocity of the frequency component of FIG. 6;

[0064] FIG. 8 is a graph illustrating damping of the frequency component of FIG. 6;

[0065] FIG. 9 is a graph representing a dispersion curve determined using the apparatus of FIG. 1;

[0066] FIG. 10 is a graph showing a profile of phase velocities determined using the apparatus of FIG. 1;

[0067] FIG. 11 is a graph illustrating tomography constructed by the apparatus of FIG. 2;

[0068] FIG. 12 is a graph showing damping of the frequency component of FIG. 6 as a function of depth;

[0069] FIG. 13 is a graph representing, on a same graphical representation, the phase velocities measured using the method of FIG. 3 and those determined using another known method for determining phase velocities.

[0070] In these figures, the same references are used to refer to the same elements. In the remainder of this description, characteristics and functions well known to the person skilled in the art are not described in detail.

DETAILED DESCRIPTION

[0071] In this description, a detailed example of an embodiment is first described in a chapter I with reference to the figures. Then, in a chapter II, alternatives to this embodiment are set forth. Finally, the advantages of the different embodiments are set forth in a chapter III.

Chapter I: Exemplary Embodiment

[0072] In the exemplary embodiment described hereinafter, the material measured is human skin. Of course, the apparatus and method as described can be implemented to measure other materials.

[0073] FIG. 1 represents a non-invasive apparatus 2 for measuring a physical quantity representative of elasticity of the skin. The apparatus 2 comprises: [0074] a hinged arm 4, [0075] a stimulator 8 and a measurement device 10, attached to a distal end of the arm 4, and [0076] a computing processing unit 12 connected to the stimulator 8 and the measurement device 10.

[0077] A proximal end of the arm 4 is attached without any degree of freedom to a fixed support 14. The arm 4 comprises several hinges 20 which allow both the stimulator 8 and the measurement device 10 to be rotatably moved simultaneously about a projection axis 22. In FIG. 1, the axis 22 is vertical. Here, the hinges 20 allow the stimulator 8 and the measurement device 10 to be moved relative to the support 14 with six degrees of freedom.

[0078] Once the arm 4 has been deformed to place the stimulator 8 and measurement device 10 into the desired position, the arm 4 holds the stimulator 8 and measurement device 10 stationary in that position. The hinges 20 are, for example, manually actuated by a user or actuated by electric motors. The arm 4 also serves as a support for electrical conductors that connect the stimulator 8 and the measurement device 10 to the processing unit 12.

[0079] The stimulator 8 deforms the skin of a human being at an impact point when actuated. The impact point is located at the intersection of the projection axis 22 and the skin surface. The deformation of the skin produced by the stimulator 8 is such that it generates a shear wave which then propagates along the skin surface. This shear wave comprises frequency components at several different frequencies. Typically, in the case of human skin, the frequencies of these components are between 1 Hz and 3,000 Hz and, typically, between 1 Hz and 1,000 Hz.

[0080] The device 10 measures deformation of the skin surface, caused by the shear wave, at several measurement points aligned one behind the other along a measurement axis. This measurement axis extends parallel to a direction called the measurement direction in this text. Typically, the device 10 comprises more than three, ten or one hundred measurement points. Here, the device 10 comprises 400 measurement points. Hereinafter, the position of a measurement point along the measurement axis is marked by its abscissa x, for example expressed in mm or m, measured from an origin O. Here, the measurement axis and the projection axis 22 intersect substantially at right angles. The origin O is taken to be the intersection point of these two axes.

[0081] The distance between the measurement point closest to the impact point and the measurement point furthest from the impact point is denoted as L.sub.max. Here, by way of illustration, the distance L.sub.max is equal to 7 mm. In this embodiment, the measurement points are evenly distributed along the measurement axis. The distance between two consecutive measurement points is therefore 17.5 m.

[0082] The processing unit 12 is connected to the device 10 to acquire measurements of this device. More precisely, the unit 12 acquires over time, with a sampling frequency f.sub.e, the displacement measured at each of the measurement points. Hereinafter, the displacement measured at a measurement point of abscissa x at time instant is denoted as u(x, t). For example, here the frequency f.sub.e is equal to 8 kHz.

[0083] The unit 12 is able to process the signals u(x, t) thus acquired in order to extract therefrom a physical quantity representative of the elasticity of the skin at different depths. To this end, the unit 12 comprises a central processing unit 30 and a machine interface 32. The central processing unit 30 comprises: [0084] a memory 34 comprising instructions for executing the method of FIG. 3, and [0085] a programmable microprocessor 36 capable of executing the instructions stored in the memory 34.

[0086] The interface 32 allows the physical quantity measured representative of the elasticity of the skin to be displayed. Typically, to this end, the interface 32 comprises a screen 38. Here, the interface 32 also comprises a keyboard 40 for, for example, acquiring a control for triggering the execution of the measurement method of FIG. 3.

[0087] FIG. 2 represents the stimulator 8 and the measurement device 10 in more detail. In FIG. 2, the skin is schematically represented with the reference 46 and the surface of the skin 46 bears the reference 48. In this figure, the surface 48 is represented in a deformed form after being subjected to an impact applied by the stimulator 8. The impact point on the skin surface bears the reference 49.

[0088] To create the shear wave that propagates at the skin surface, the stimulator 8 uses, in this embodiment, a jet of air to impact the skin at the impact point 49. To this end, the stimulator 8 comprises: [0089] a pressurised air tank 50, [0090] a pressure reducing valve 52 fluidly connected to the tank 50, [0091] a controllable solenoid valve 54, and [0092] a nozzle 56 fluidly connected to an outlet of the solenoid valve 54.

[0093] For example, the air pressure contained in the tank 50 is greater than 0.6 or 0.8 MPa. Here, the pressure reducing valve 52 lowers the air pressure. For example, the air pressure at the outlet of the pressure reducing valve 52 is between 0.1 MPa and MPa or between 0.1 and 0.4 MPa.

[0094] The solenoid valve 54 can be moved from an open position to a closed position and vice versa under the control of the unit 12. In the closed position, the solenoid valve 54 prevents air from escaping from the tank 50. In the open position, on the contrary, the solenoid valve 54 allows air to escape from the tank 50. The air escaping from the tank 50 is then guided by the nozzle 56 to form a jet of air along the axis 22 which impacts the surface 48 of the skin 46 at the impact point 49.

[0095] The solenoid valve (54) allows the duration of the jet of air projected onto the surface 48 to be adjusted. Typically, the duration of the jet of air is less than 20 ms or 10 ms. Here, the duration of the jet of air is between 5 ms and 10 ms.

[0096] At least one part of the nozzle 56 extends along the axis 22 to direct the jet of air along the axis 22. The end of the nozzle 56, facing the surface 48, is mechanically separated from said surface, such that there is no direct mechanical contact between the apparatus 2 and the surface 48 in use thereof.

[0097] The measurement device 10 is an optical measurement device. In this embodiment, it comprises to this end: [0098] an emitter 60 of a light beam that lights each measurement point, [0099] a row 62 of optical sensors which sense the light reflected from each of the measurement points, and [0100] a microprocessor 64 programmed to determine the displacement of the surface 48 at each of the measurement points from the reflected light sensed by each of the optical sensors.

[0101] Here, the device 10 is positioned relative to the stimulator 8 such that the measurement point closest to the impact point 49 is separated from that impact point by a distance greater than 0.5 mm or 0.8 mm and typically less than 5 mm. Preferably, the distance between the measurement point closest to the impact point and this impact point is between 0.7 mm and 1.3 mm or between 0.9 mm and 1.1 mm. Here, this distance is equal to 1 mm.

[0102] Such measurement devices are known and marketed. For example, in this embodiment, the device 10 is that marketed by the company KEYENCE under the reference LJ-V 7020. In this case, the emitter 60 is a laser source which emits a monochromatic and collimated light beam. Thus, the device 10 is not described in more detail hereinafter.

[0103] The operation of the apparatus 2 will now be described using FIG. 3 and with reference to the graphs of FIGS. 4 to 13.

[0104] In an initial step 68, the arm 4 is deformed to place the stimulator 8 and the measurement device 10 in proximity to a part of the human body covered with the skin to be studied. The apparatus 2 allows any part of the human body to be studied. For example, experimental results set forth in FIGS. 4 to 13 have been obtained on the forearm of a human being. Typically, the stimulator 8 and the device 10 are placed relative to the surface 48 of the skin such that the axis 22 of projection is at an angle of between 75 and 110, and preferably between 80 and 100, to the direction normal to the skin at the impact point 49.

[0105] The lower end of the nozzle 56, facing the surface 48, is separated from the impact point 49 by a distance greater than 1 mm or 2 mm or 5 mm, and generally less than 20 mm.

[0106] Once the apparatus 2 is correctly positioned with respect to the skin 46, a phase of acquiring the signals u(x, t) is carried out.

[0107] More precisely, once the stimulator 8 and the device 10 are correctly positioned relative to the surface 48, in a step 72, the unit 12 controls the stimulator 8 to cause the emission of a jet of air and deform the skin. Here, the unit 12 controls the solenoid valve 54 to generate this jet of air. This jet of air then impacts the skin at the impact point 49. This causes a brief deformation of the surface 48 at this impact point 49. This deformation of the surface 48 in turn generates a shear wave which propagates along the surface 48 in all directions, and thus especially along the measurement axis of the device 10.

[0108] In a step 74, the device 10 measures, at each of the measurement points, displacement of the surface 48 caused by the shear wave propagating at the surface of the skin.

[0109] In parallel, in a step 76, at each sampling time instant and for each measurement point, the unit 12 acquires the measurement from the device 10. Thus, the unit 12 acquires each of the signals u(x, t).

[0110] FIG. 4 represents, on a three-dimensional graph, an example of the signals u(x, t) acquired. In this graph: [0111] the horizontal axis represents time in milliseconds, [0112] the vertical axis represents amplitude, in millimetres, of the displacement of the surface 48, and [0113] the depth axis represents, in m, the position x of the measurement point along the measurement axis.

[0114] Once the various signals u(x, t) are acquired, the acquisition phase 70 ends and a phase 80 of processing the signals u(x, t) begins. Phase 80 is carried out by unit 12.

[0115] In a step 82, for each signal u(x, t), the unit 12 searches for and identifies the time instant t.sub.min(x) at which the signal u(x, t) passes through its absolute minimum.

[0116] Then, in a step 84, the unit 12 determines the equation of the straight line D that best approximates the point cloud formed by the points of coordinates (x; t.sub.min(x)). The equation of the straight line is as follows: t=.sub.1x+.sub.0. The coefficients .sub.1 and .sub.0 are those obtained by implementing the least squares method.

[0117] FIG. 5 represents the point cloud formed by the points of coordinates (x; t.sub.min(x)) and the straight line D obtained by the least squares method.

[0118] The shear wave propagating in the skin 46 is a dispersive wave, that is, its phase velocity depends on the frequency. The phase velocity is therefore not the same for each frequency component of this shear wave. By phase velocity, it is meant here, unless otherwise stated, the phase velocity of the fundamental mode of the shear wave. The fundamental mode corresponds to the mode for which the amplitude of the displacement of the surface 48 is maximum. This phase velocity is denoted as V.sub.i for the frequency f.sub.i, wherein the index i is an order number identifying the frequency f.sub.i. Here, the frequencies are ranked from the lowest frequency, denoted as f.sub.1, to the highest frequency denoted as f.sub.Pmax.

[0119] In the case of the skin, it has been observed that the different frequency components that propagate in the skin 46 are typically of between 1 Hz and 3,000 Hz and, most often, between 1 Hz and 1,000 Hz or between 1 Hz and 500 Hz or between 1 Hz and 400 Hz. By way of illustration, here, the frequencies f.sub.i are chosen in this interval ranging from 1 Hz to 1,000 Hz.

[0120] Of particular importance is the lowest frequency, denoted as f.sub.min, for which there is a phase velocity. It has been observed that this smallest frequency f.sub.min is generally between 1 Hz and 10 Hz. Thus, in this method, the sampling pitch of the frequencies f.sub.i in the interval [1 Hz; 10 Hz] is chosen to be small, that is, here less than 2 Hz or 1 Hz. Conversely, in the interval [10 Hz, 1000 Hz], the sampling pitch of the frequencies f.sub.i is chosen to be larger. For example, in this interval [10 Hz; 1,000 Hz], the sampling pitch is greater than 5 Hz or 10 Hz or 20 Hz. Thus, the frequencies f.sub.i are separated from each other by a pitch of 1 Hz in the interval [1 Hz; 10 Hz] while they are separated from each other by a pitch greater than 5 Hz or 10 Hz in the interval [10 Hz; 1,000 Hz].

[0121] In a step 86, the unit 12 determines, for each selected frequency f.sub.i, if any, the corresponding phase velocity V.sub.i.

[0122] For this, in an operation 88, the unit 12 filters each signal u(x, t) by means of a bandpass filter centred on the frequency f.sub.i. The signal u(x, t) filtered at the frequency f.sub.i is hereinafter denoted as u.sub.i(x, t). The 3 dB bandwidth of this bandpass filter is between the frequencies f.sub.i1 and f.sub.i+1. Typically, this bandwidth is less than 20 Hz or 10 Hz for the frequencies f.sub.i in the interval [10 Hz; 1,000 Hz] and less than 2 Hz for the frequencies f.sub.i in the interval [1 Hz; 10 Hz].

[0123] FIG. 6 represents different signals u.sub.i(x, t) obtained by filtering, at a frequency of Hz, the signals u(x, t) of FIG. 4. This graph is identical to the graph of FIG. 4 except that it represents the signals u.sub.i(x, t) and not the signals u(x, t).

[0124] In an operation 90, the unit 12 searches for and identifies, for each signal u.sub.i(x, t), the time instant t.sub.i,m(x) at which that signal passes through its absolute minimum. For this, if the time instant t.sub.i1,m(x) or t.sub.i+1,m(x) has already been identified for the frequency f.sub.i1 or the frequency f.sub.i+1, respectively, the unit 12 searches for the time instant t.sub.i,m(x), as a priority, in a time interval centred on this time instant t.sub.i1,m(x) or t.sub.i+1,m(x).

[0125] If no time instant t.sub.i1,m(x) or t.sub.i+1,m(x) has previously been identified, then the time instant t.sub.i,m(x) is searched for in a time interval centred on the time instant t.sub.min(x) identified in step 82.

[0126] In an operation 92, the unit 12 calculates the phase velocity V.sub.i for the frequency f.sub.i from the signals u.sub.i(x, t). For this, the unit 12 determines the equation of the straight line Di that best approximates the point cloud formed by the points of coordinates (x; t.sub.i,m(x)). The equation of the straight line Di is as follows: t.sub.i,e(x)=.sub.i,1x+i,0. The coefficients .sub.i,1 and .sub.i,0 are obtained by implementing the least squares method as described for step 84.

[0127] FIG. 7 represents the point cloud of coordinates (x, t.sub.i,m(x)) as well as the line Di.

[0128] Once the equation of the straight line Di is determined, the unit 12 also estimates the approximation error, that is, the deviation between points of coordinates (x; t.sub.i,m(x)) and points of coordinates (x; t.sub.i,e(x)) which have the same abscissa and lie on the straight line Di.

[0129] If this error exceeds a predetermined threshold err.sub.max, and then it is considered that there is no phase velocity for the frequency f.sub.i because energy of the frequency component of frequency f.sub.i of the shear wave is negligible. Here, for example, the approximation error is estimated using the following relation (1):

[00002]$\begin{array}{cc}\underset{p=1}{\overset{P_{\max }}{.Math.}}{\left(t_{i,m}\left(x_p\right)-{}_{i,1}{x}_p-{}_{i,0}\right)}^2{\mathrm{err}}_{\max }& \left[\mathrm{MATH}2\right]\end{array}$

[0130] where: [0131] .sub.1,i and .sub.i,0 are the coefficients of the straight line Di, [0132] x.sub.p is equal to the position x of the p-th measurement point counted from the first measurement point closest to the impact point, [0133] P.sub.max is equal to the number of measurement points distributed along the measurement axis, [0134] err.sub.max is a predetermined constant.

[0135] If this approximation error is less than or equal to the threshold err.sub.max, then the phase velocity V.sub.i is taken to be equal to 1/.sub.i,1. The phase velocity V.sub.i thus obtained is the phase velocity of the fundamental mode at the frequency f.sub.i. Indeed, it is only obtained from the minimums of the signals u.sub.i(x, t), that is, from the points where the amplitude of the displacement is maximum.

[0136] In an operation 94, the unit 12 also determines the attenuation A.sub.i(x) of the frequency component at the frequency f.sub.i. Here, the attenuation A.sub.i(x) is taken to be equal to the amplitude of the minimum of the signal u.sub.i(x, t) identified in operation 90. Thus, in this embodiment, the attenuation A.sub.i(x) is equal to u.sub.i(x; t.sub.i,m(x)).

[0137] FIG. 8 represents the change in the attenuation A.sub.i(x) as a function of the position x for the signals u.sub.i(x,t) of FIG. 4.

[0138] Steps 88 to 94 are reiterated for each of the frequencies f.sub.i. Hereinafter, the smallest and largest of the frequencies f.sub.i for which a phase velocity V.sub.i has been determined are denoted as f.sub.min and f.sub.max, respectively. The curve formed by the set of points of coordinates (V.sub.i; f.sub.i) is called the dispersion curve. FIG. 9 represents the dispersion curve obtained from the u(x,t) signals of FIG. 4.

[0139] The longer the wavelength .sub.i of a frequency component of the shear wave, the deeper said frequency component propagates under the surface 48 of the skin 46. Thus, the velocity V.sub.i of a frequency component of wavelength .sub.i represents the mechanical properties of the skin at a depth p.sub.i. At this point, it is reminded that the phase velocity V.sub.i is related to the mechanical properties of the skin 46 by the following relationship: V.sub.i=(E.sub.i/(2.sub.i(1+v.sub.i)).sup.0.5, where: [0140] E.sub.i is the Young's modulus of the skin at depth p.sub.i, [0141] .sub.i is the density of the skin at depth p.sub.i, and [0142] v.sub.i is the Poisson coefficient of the skin at depth p.sub.i.

[0143] Thus, considering that the density i and the coefficient v.sub.i are known constants, the velocity V.sub.i is directly representative of the Young's modulus E.sub.i at depth p.sub.i. Thus, the velocity V.sub.i is representative of the elasticity of the skin at depth p.sub.i.

[0144] Therefore, the profile of velocities V.sub.i as a function of depth p.sub.i corresponds to a cross-sectional view, along the measurement axis, of the mechanical properties of the skin.

[0145] In a step 100, the unit 12 transforms the dispersion curve into a profile of velocities as a function of depth p.sub.i.

[0146] For this, in an operation 102, the unit 12 converts each frequency f.sub.i into a corresponding wavelength .sub.i. Indeed, the unit 12 uses the following relationship (2): .sub.i=V.sub.i/f.sub.i.

[0147] Then, in an operation 104, the unit 12 calculates the value of a coefficient that converts each wavelength .sub.i into a corresponding depth p.sub.i. Here, the depth p.sub.i is the distance separating a point, buried under the skin, and the surface 48 of the skin. This coefficient relates each wavelength .sub.i to the corresponding depth p.sub.i according to the following relationship (3): p.sub.i=.sub.i.

[0148] This coefficient is a constant for a given measurement axis. By contrast, in the case of anisotropic viscoelastic materials such as the skin, the coefficient varies as a function of the measurement direction. In other words, the coefficient depends on the direction in which the measurements are made.

[0149] Here, the coefficient is calculated by the unit 12 using the following relationship (4): =Z.sub.max/.sub.max, where: [0150] Z.sub.max is equal to half the distance L.sub.max, and [0151] .sub.max is the largest of the wavelengths .sub.i obtained after the operation 102.

[0152] Once the value of the coefficient is calculated, in an operation 106, the unit 12 converts each wavelength .sub.i into a depth p.sub.i using the relationship (3) above. Thus, a frequency f.sub.i corresponds to a wavelength .sub.i which in turn corresponds to a depth p.sub.i. By replacing in each coordinate point (V.sub.i; f.sub.i), the frequency f.sub.i by the corresponding depth p.sub.i, the profile of velocities measured by the apparatus 2 is obtained. An example of such a profile of velocities is represented in FIG. 10.

[0153] Here, step 68 and phases 70 and 80 are reiterated several times, each time rotating the measurement axis by a predetermined angle about the axis 22. For this, during each new iteration of step 68, the arm 4 is deformed so as to rotate the stimulator 8 and the measurement device 10 on themselves. This rotation does not modify the position of the projection axis 22, and thus the position of the impact point 49. For example, during each new iteration of step 68, the measurement axis is angularly offset from its previous position by at least 1 or 5, and for example by 10 or 20.

[0154] During each new iteration of the phase 80 of processing the data acquired, step 100 is again executed. Indeed, as previously explained, the value of the coefficient highly depends on the direction of the measurement axis in the case of human skin.

[0155] Finally, in a step 110, the mechanical properties of the skin as a function of the depth p.sub.i are displayed on the screen 38. Different graphical representations are possible. For example, the profile of velocities, such as that represented in FIG. 10, is displayed on the screen 38. However, preferably, the different profiles of velocities obtained for different measurement directions are simultaneously displayed on a same graph to form a tomography of the skin 46 at the impact point 49. Such a tomography is represented in FIG. 11. In this tomography, the axis of ordinates represents the depth p.sub.i. The axis 22 corresponds to the projection axis of the apparatus 2. Different measurement planes Pl.sub.1 to Pl.sub.6 are represented. These planes Pl.sub.1 to Pl.sub.6 are angularly offset from each other. Here, each of these measurement planes contains the axis 22 and extends parallel to a respective measurement direction. Each measurement plane contains the profile of velocities measured along the measurement axis parallel to that respective measurement direction. The axes of abscissas thus represent the coordinates V.sub.ix and V.sub.iy of the velocity V.sub.i measured.

[0156] FIG. 12 represents the attenuation A.sub.i(x) as a function of depth. In addition, the axis of abscissas represents the position x of the measurement point. The axis of ordinates represents the depth p.sub.i in millimetres. The colour of each point of coordinates (x; p) codes attenuation of the velocity V.sub.i for that depth p and that abscissa x. For this, the depth is transformed into a corresponding wavelength .sub.i using the relationship (3), and then the wavelength .sub.i thus obtained is transformed into a corresponding frequency f.sub.i using the relationship (2). In step 94, the attenuation A.sub.i(x) as a function of the position x has been plotted for all frequencies f.sub.i, and thus for the particular frequency f.sub.i corresponding to that depth p. This has been illustrated in the graph in FIG. 8. In the graph in FIG. 8, the attenuation A.sub.i(x) corresponding to the abscissa is plotted. It is the value of this measured attenuation A.sub.i(x) that is coded with a particular colour at the point of coordinates (x; p) in the graph in FIG. 12.

[0157] The different phase velocities V.sub.i can be determined from the signals u(x,t) by other methods, such as for example the method known as MASW (Multichannel Analysis of Surface Waves). The MASW method makes it possible to determine, for each frequency f.sub.i, the velocity V.sub.i of the fundamental mode as well as the phase velocities of the modes of higher order than the order of the fundamental mode.

[0158] FIG. 13 represents on a same graph the phase velocity V.sub.i determined by the method of FIG. 3 and the different phase velocities determined by the MASW method. The axis of abscissas represents the frequency f.sub.i, the axis of ordinates represents the amplitude of the determined phase velocity. The velocities V.sub.i determined by the method in FIG. 3 are represented by a dotted curve 120.

[0159] The phase velocities for a given frequency f.sub.i as determined by the MASW method are coded with a colour which is darker the greater the amplitude of this phase velocity. For a same frequency f.sub.i, the MASW method determines several phase velocities corresponding, respectively, to the fundamental mode and to the other higher order modes. From these determined phase velocities, that with the largest amplitude corresponds to the phase velocity of the fundamental mode. As shown in this graph, in most cases the velocity V.sub.i determined by the method in FIG. 3 passes through the darkest location in the graph in FIG. 13. This indicates that the phase velocities of the fundamental mode determined by the two different methods coincide.

[0160] By contrast, there are zones, surrounded by ellipses on the graph in FIG. 13, where this is not the case. This is particularly true for high frequencies, that is, frequencies above 240 Hz, but also for some lower frequencies. In these zones, the phase velocity of the fundamental mode, as determined by the MASW method, sharply drops and then rises again just as sharply. Hereinafter, these sudden drops in the phase velocity of the fundamental mode are called phase jumps. Such a phase jump is circled near 90 Hz in FIG. 13. Conversely, the method in FIG. 13 does not produce such phase jumps. In addition, the method in FIG. 13 allows the phase velocity of the fundamental mode to be determined at much higher frequencies than is possible by implementing the MASW method. Because of this, the method in FIG. 13 is considered to be more accurate than known methods.

Chapter II: Alternatives

Alternatives to the Measurement Device

[0161] In one particular alternative, the device is capable of measuring, simultaneously and along several measurement axes angularly offset from each other, the displacement of the surface of the skin or other material. Thus, with such a measurement device, it is not necessary to rotate it about the projection axis 22 or the number of rotations to be performed is smaller. For example, such a measurement device comprises an array of optical sensors for each measurement axis.

[0162] In another embodiment, the measurement axis does not pass through the impact point 49 but next to that impact point.

[0163] The device 10 may also be implemented using a camera that acquires images of the surface 48 at a high frequency.

[0164] Other embodiments of the stimulator 8 are possible. For example, in one alternative, the jet of air is replaced by a jet of another gas, such as for example carbon dioxide, or by a jet of liquid such as water.

[0165] The stimulator does not necessarily emit a jet of fluid to generate the shear wave at the surface of the material, or substrate, to be measured. Such a shear wave may also be generated by a stimulator directly contacting the material using utensil. For example, the stimulator may be a hammer which strikes the material at the impact point 49. It may also be a projectile such as a rubber ball or the like that is projected along the axis 22 to impact the material at the impact point 49.

[0166] The measurement device is not necessarily an optical measurement device. This is particularly true when the apparatus 2 is applied to a large surface area substrate where overall size restrictions are relaxed. For example, the signals u(x, t) can also be measured by arranging a displacement sensor directly on each of the measurement points. There are a large number of known displacement sensors likely to be suitable for such an application. For example, the displacement sensor may be an accelerometer.

[0167] In another embodiment, an element radiating electromagnetic waves or reflecting electromagnetic waves at a particular wavelength is arranged at each of the measurement points. The sensors of the measurement device measure the displacement of the surface at each of these measurement points from the electromagnetic radiation emitted or reflected at the measurement point.

Alternatives to the Method

[0168] Other methods are possible for constructing the phase velocity of the fundamental mode as a function of depth. For example, as shown with FIG. 13, the method known by the acronym MASW can be applied although this is now considered to be less accurate. In another embodiment, one alternative to the MASW method is applied, this alternative having been modified to reduce the problem of phase jumps observed in FIG. 13. Finally, other methods than the MASW method have been developed in other technical fields such as, for example, geophysics and can be transposed here as long as these methods determine the phase velocity of the fundamental mode.

[0169] Alternatively, the sampling pitch of the frequencies f.sub.i is the same over the whole analysis interval. For example, in the previous exemplary embodiment, the sampling pitch is the same over the entire interval ranging from 1 Hz to 1000 Hz.

[0170] Other methods for searching and identifying the time instant t.sub.i,m(x) are possible. For example, the time instants t.sub.i,m(x) are searched for without limiting the search to a predetermined time interval. In this case, the search is performed without taking account of the time instants t.sub.i1,m(x) or t.sub.i+1,m(x) or t.sub.min(x). Thus, steps 82 and 84 can be omitted.

[0171] The approximation error can be estimated differently. In particular, many other relationships are possible to calculate this approximation error. For example, the following relationship (5) can be used instead of relationship (1):

[00003]$\begin{array}{cc}\underset{p=1}{\overset{P_{\max }}{.Math.}}{\left(t_{i,m}\left(x_p\right)-{}_{i,1}{x}_p-{}_{i,0}\right)}^2{\mathrm{err}}_{\max }& \left[\mathrm{MATH}3\right]\end{array}$

[0172] In another embodiment, the coefficient is not determined as a function of the signals u(x, t) measured by the device 10. For example, in a simplified embodiment, the coefficient , used for a given measurement direction, is provided by the user of the device 12.

[0173] Instead of rotating the stimulator 8 on itself to make measurements in different measurement directions, it is also possible to keep the measurement direction constant and move the impact point along a straight line to progressively scan a portion of the material or substrate.

[0174] Measurements along a same measurement axis may be repeated at different time instants to see the change over time in these measurements. For example, this may be applied to measure the change over time in the mechanical properties of a material or substrate, for example the change over time in the mechanical properties of skin following the application of a moisturising product.

Other Alternatives

[0175] Of course, and as previously mentioned, the apparatus 2 described herein may be applied to other viscoelastic and anisotropic materials than skin. For example, it can be applied to any similar viscoelastic material such as artificial skin. It can also be applied to animal skin, including marine animal skin such as fish skin.

[0176] The apparatus 2 can also be applied to other viscoelastic materials such as for example vegetable or fruit skin.

[0177] When the apparatus 2 is applied to other viscoelastic materials than skin, the interval of frequencies f.sub.i for which the unit 12 calculates the velocity V.sub.i may be different from the interval [1 Hz; 1,000 Hz]. Similarly, if the viscoelastic material to which the apparatus 2 is applied is not anisotropic, the coefficient can be calculated for a first measurement direction and the same value of this coefficient is then used for other measurement directions angularly offset from the first measurement direction. In this case, for these other measurement directions, the operation 104 is not reiterated.

[0178] Other mechanical properties than the Young's modulus of the material or substrate at different depths can be deduced from the phase velocity V.sub.i. For example, the viscosity can also be estimated from the velocity V.sub.i.

[0179] The method in FIG. 3 for constructing the dispersion curve can be implemented in any non-invasive application for measuring a physical quantity representative of mechanical properties of a substrate. Indeed, as previously explained, this method allows a more accurate phase velocity of the fundamental mode to be obtained. For example, the method in FIG. 3 can also be implemented in a non-invasive apparatus for measuring mechanical properties in depth of a substrate such as a road surface or any multilayer structure. In the case of such substrates, it is not necessary to measure the profile of velocities in several different directions angularly offset from each other. Nor is it necessary to determine the value of the coefficient for each of the measurement directions. Finally, in the case of substrates other than the skin, the stimulator 8 and the measurement device 10 are adapted to that substrate. For example, in the case of a road surface, the stimulator 8 is formed by a mass which impacts the road surface. In the case of a road surface, the device measures the shear wave over a distance typically greater than 7 mm.

[0180] Determining the value of the coefficient as a function of the measurements of the measurement device can also be implemented in any other apparatus for measuring the mechanical properties of a material or substrate from a profile of phase velocities of the fundamental mode. Indeed, calculating the value of the coefficient as previously described increases accuracy of the conversion of the dispersion curve into a profile of velocities.

Chapter III: Advantages of the Embodiments Described

[0181] As the embodiments of the measurement apparatus and method have been described for measurements on human skin, technical advantages and effects listed below apply equivalently to the apparatus and method according to the invention when implemented with other viscoelastic and/or deformable materials or substrates.

[0182] The measurement method described herein allows the phase velocity of the fundamental mode of the shear wave to be measured at different depths and not just at the surface. It therefore allows mechanical properties of a material or substrate to be revealed at different depths under the surface of the material or substrate and not just at the surface. In addition, the apparatus 2 allows mechanical properties to be revealed at different depths while remaining non-invasive, that is, without the need for incision of the material or substrate.

[0183] For measurements on human skin, calculating the value of the coefficient from the measured signals u(x, t) and more precisely from the dispersion curve, allows the value of the coefficient to be automatically adapted to the skin on which the measurement is made and to the measurement direction chosen. Indeed, in contrast to other substrates, it has been observed that the value of the coefficient significantly varies from one human being to another and also significantly varies depending on the measurement direction chosen. Thus, the automatic calculation of the value of the coefficient improves the accuracy of the profile of phase velocities. Thus, a better accuracy on the depth of observation is obtained.

[0184] Constructing a profile of phase velocities for several directions angularly offset from each other makes it possible to generate a tomography of a mechanical property of the measured skin or material. Such a tomography especially allows anisotropy of this mechanical property to be observed as a function of the measurement direction. It is thus possible to quantify tensile forces in all directions measured in depth, and this tension can be represented in three dimensions. For example, healing of wounds can be analysed and monitored by measuring tensile forces, which indicate cell activity.

[0185] Calculating the phase velocity of the fundamental mode from the time instants t.sub.i,m(x) and the positions x where the minimum of the signal u.sub.i(x, t) occurs, makes it possible to accurately determine phase velocity of the fundamental mode at the frequency f.sub.i. This therefore increases accuracy of the constructed profile of phase velocities, and hence accuracy of the measurement of the mechanical properties of the material or substrate.

[0186] Automatically identifying the frequency f.sub.min makes it possible to increase reproducibility of the measurement method as this minimum frequency is not manually determined by the user. Additionally, when the condition (1) is used, this allows the wavelength .sub.max to be determined more accurately, which also improves the accuracy of the determination of the value of the coefficient , and thus ultimately the accuracy of the profile of phase velocities.

[0187] Automatically identifying the frequency f.sub.max avoids determining phase velocities for frequency components of the shear wave that do not exist or are negligible. This therefore improves the accuracy of the profile of phase velocities constructed by the apparatus 2.