WO2022200900A1

WO2022200900A1 - A technique and a system for testing a material sample using radiometry or infrared thermography

Info

Publication number: WO2022200900A1
Application number: PCT/IB2022/052151
Authority: WO
Inventors: Roberto LI VOTI
Original assignee: Li Voti Roberto
Priority date: 2021-03-24
Filing date: 2022-03-10
Publication date: 2022-09-29
Also published as: IT202100007148A1

Abstract

A technique and a system for testing a material sample using radiometry or infrared thermography" Thermographic technique and system for analyzing moving samples or moving particles using the thermographic Doppler effect. The system comprises a temporally modulated light source (3, 4), a transmission optics (6), a moving sample (1') or moving particles (2; 2') in the sample (1), detection means (8; 8a; 8b) and analysis means (10, 13) for the infrared light reemitted by the sample (1; 1'). The system and the technique allow to measure the thermal diffusivity of the sample and/or its velocity, and in another case the determination of the statistics of said moving particles in the sample (1).

Description

A technique and a system for testing a material sample using radiometry or infrared thermography Description Technical Field The present invention generally relates to material analysis and sample analysis by means of electromagnetic radiation, in particular through the examination of the temperature increase produced on the material surface by this radiation. Background Art The traditional Doppler effect is known for a long time to researchers and technicians. The change in frequency of an electromagnetic wave when a source and a receiver are in relative motion one with respect to the other has been described for the first time by Christian Doppler in 1842 [1]. He erroneously applied this effect for explaining the various colors of the stars. Later, Buys Ballot [2] did experiments with sound waves and in 1848 Fizeau [3] suggested that the lines of optical spectra could present frequency variations depending on the relative velocities of the source and the observer, and this prediction was confirmed later on by Sir William Huggins [4], who showed the frequency redshift of the hydrogen lines recorded from Sirius was an indication of a receding movement. The Doppler effect in its traditional conception has then resulted in innumerable applications for electromagnetic waves and ultrasonic waves. Actually, since its first discovery the Doppler effect has become essential for understanding/describing our world and for developing a plurality of applications, in the first place the determination of the velocity of moving objects. It has been applied to radar astronomy and to other forms of radars in order to measure the velocity of detected objects: speed trap, velocity of a clouds front in meteorology, etc. In biomedical applications there have been developed Eco-Doppler flowmeters, Acoustic Doppler Velocimeters (ADC), in which a source of sound waves (usually ultrasound) is adequately oriented. These sound waves are then reflected with a new frequency (according to the vector-valued velocity of blood particles), which thereafter is detected and processed so as to obtain the measured velocity. A further application is the laser Doppler imager, which is used in particular for studies concerning angiogenesis, endothelial disfunction, skin ulcers, the evaluation of pharmaceutical or cosmetological products for local application, and for the examination of burns. Doppler ultrasonography, or simply Doppler ultrasound, is a non-invasive technique which has been used for over three decades in medicine for studying in real time the anatomical and functional state of both arterial and venous blood vessels, as well as of the heart, in a simultaneous manner (Duplex-Scanner). The Doppler effect has also been relevant in photoacoustics. Actually, the Doppler effect of acoustic waves emitted from moving, amplitude modulated optical sources, has been explored several decades ago by soviet researchers like Bozhkov [5-8], Bunkin [5-7, 9] and Kolomenskii [7, 8], and by researchers in the United States [10]. Unfortunately, due to the proposed application to submarine communication, most of the published work of the soviet researchers focused on the problem of a moving laser beam directed to the interface between a transparent gas and an absorbing liquid in which the beam intensity has been modulated, thereby rendering more difficult to understand the form of the sound models in space and resulting in complicated mathematical formulas. Moreover, the non-modulated case has not been analyzed [5-9, 11-14]. More recently, a complete theory on the displacement of photoacoustic sources in one, two and three dimensions has been widely discussed by W. Bai and G.J. Diebold [15, 16], by applying the detection of gas traces with the dynamical photoacoustic spectroscopy (DPAS) [17-19]. The study of materials can also be carried out with a thermographic technique. It is well known that any kind of body emits a certain amount of electromagnetic radiation proportional to the fourth power of the absolute temperature (Kelvin scale) according to the Stefan-Boltzmann law [20]. Thermographic sensors can detect a portion of this radiation emitted from the body in the infrared range of the electromagnetic spectrum, thereby allowing to visualize the absolute values and the variations of the body temperature. Therefore, thermography is a non-destructive analytical technique based on image data acquisition in the infrared region, providing a temperature map of the emissivity of the objects framed/captured by an infrared camera. The thermographic analysis can be performed in active or passive conditions. In the first case, the element to be analyzed is heated in order to increase its thermographic response and at the same time to activate the heat flows allowing to obtain different responses from elements having different heat capacities. Instead, in passive conditions, the surface is analyzed as it is at the moment of investigation. The thermographic method can be applied to various fields, like the steel industry, building industry, medicine and veterinary science, chemical industry, cultural heritage, aeronautics, automotive sector, environment protection, etc. For instance, in the building industry the thermographic analyses permit to check insulation, impermeabilization and degradation due to humidity, as well as to do an investigation of the origin of water infiltrations and search hidden building components. In the more general case of the materials science, thermographic analyses allow to measure defects, subsurface fissures, residual stresses, fatigue limits, and they are widely applied in mechanical engineering for the non-destructive check of welds, suspension arms, and bolted connections. Infrared thermography also allows a quantitative evaluation of thermal properties of materials (for instance a measurement of thermal diffusivity). Recently a thermographic method has been introduced which is applicable to moving samples heated by a focused continuous-wave (c.w.) laser beam, with no time modulation whatever [21, 22]. It should be understood that this application technologically differs from the application shown in the present patent application, since it does not make use of a time modulated laser beam, with a consequent reduction of the signal-to-noise ratio leading to a limited diagnostic effectiveness and a limited estimate of thermal diffusivity, which instead can be largely improved at temporally modulated heating regimes. The inventor of the present patent application adopts a thermographic technique in which the Doppler effect plays a major role. Description of Invention The present invention is based in part on the Doppler effect in the field of thermal waves. Thermal waves in media are known for a long time. The Doppler effect on thermal oscillating fields is disclosed by the inventor of the present invention who shows its experimental and theoretical validity and indicates its various applications, for instance in the biomedical sector. The inventor throws light on the connection between the observable frequency shift, the relative velocity between source and detector, and the velocity of the thermal wave which is connected in turn with the thermal diffusivity of the medium. The discovery of precise functional relationships, between the thermophysical and kinematical parameters involved, provides a key to understand the subject and to develop new applications capable of making the most of this new effect, in order to measure the velocity of moving particles and/or the thermal diffusivity of materials along a production line, in different frequency intervals, velocity intervals and observability intervals of the phenomenon which are different and complementary to the standard applications of the Doppler effect in acoustics and electromagnetism. The object of the present invention generally consists in providing a technique for testing a sample of material using radiometry or infrared thermography, according to claim 1, and in providing a system for testing a sample of material using radiometry or infrared thermography, according to claim 18. The dependent claims are related to more specific aspects of the invention which offer particular advantages. In substance, the concept on which the present invention is based consists in irradiating with a high energy density light source (in particular a laser) a surface of the material (i.e. of the medium) to be analyzed, so as to heat it a few degrees. According to the present invention laser light is modulated using suitable modulation means (a chopper, an electrooptical system, a diode laser excited with a square wave, etc.) at a fixed, predetermined angular frequency ω of modulation. The laser wavelength is so chosen as to be able to adequately examine the sample of material irradiated by it. The laser could also have a tunable wavelength, selectable for the particular application. The modulator could also be realized with a tunable angular frequency of modulation ω, which is chosen selectively for each specific application. The thermal diffusion distance/length depends from the thermal diffusivity in the sample and from the modulation frequency, so that by choosing the latter appropriately it is possible to make one's way in the material up to the correct/required depth. Furthermore, according to the present invention it is essential that the medium – that is the sample – under examination be in relative motion with respect to exciting light source, e.g. a laser, or that internal particles of the sample be in relative motion with respect to the exciting light source (e.g. a laser). In the latter case, these particles may move orthogonally to the sample surface or parallel to it, by approaching the same or moving away from it, or moving permanently parallel to it. In general, these particles could also have a velocity pointing in any direction whatsoever, but this is not the preferred solution/application envisaged. In the following detailed description various practical applications of the invention are disclosed in which the particles move orthogonally to the sample surface (so-called “out of plane motion”) or parallelly to the sample surface (so-called “in plane motion”). In case of exciting a particle moving with a velocity V orthogonal to the sample surface (also called in the following “vertical motion” for brevity, that is V S), the laser light will be concentrated on a minimal

area/surface of the sample (for instance of 1 mm²) and will reach the region where the particle is located in order to excite it (that is, to heat it). Obviously, the wavelength of the laser will be chosen adequately so that the laser beam can penetrate in the material and incur a weak damping, while being finally strongly and selectively absorbed by the moving particles which thereby become heated. By absorbing the temporally modulated beam at angular frequency ω, the particles themselves become moving sources of thermal waves at said angular frequency ω = 2πf. Due to the mechanism of thermal conduction, heat is transmitted to the whole volume of the material which in this way is subjected to a slight temperature increase. The temperature induced on the sample surface also oscillates, but at an angular frequency ω' = 2πf' different than that of the modulated beam. Specifically, one observes a Doppler effect for thermal waves, wherein ω' > ω if the particle is approaching the sample surface and therefore a detector of infrared rays “integral with” (that is fixed with respect to the reference system of) the exciting laser, and conversely ω' < ω if the particle is moving away from said infrared detector. From the frequency shift it is possible to derive the particle velocity V, whereas the (initial) instantaneous particle position Z₀ is obtained both from the phase Φ and the shift Δω of the signal. Obviously, in case of a particle moving in the sample interior with a uniform motion, parallelly to the sample surface, it is necessary to irradiate a wider area/surface of the sample. Once again, one encounters a formula in which the (maximum) frequency shift is given by a formula analogous to the case of the particle's vertical motion. The particles' positions and velocities for the particles moving in the medium (sample) under examination, parallelly to its surface, are given by specific formulas included in the detailed description. An example of parallel motion is that pertaining to the cytometric study in capillaries, or capillaroscopic study. The system according to the invention may allow the determination of the position and velocity of red blood cells, platelets, platelets aggregates, microemboli, aggregates of cancer cells, inside blood vessels and thin capillaries (see the following detailed description). Obviously, the laser wavelength should be calibrated in such a way as to distinguish the contributions due to different species of moving particles, based on the different absorption properties of these various families of particles. Therefore, it is for instance imperative to choose a laser that operates at N possible wavelengths, N being the dissimilar particles. In case of particles moving with a horizontal motion

from the following formula (7) of the detailed description it can be seen that ΔTs, that is the temperature increase on the sample surface, depends on t, x, y, for z = constant. Therefore, the temperature increase generally represents a complicated spacetime response to laser excitation, in other words a function ΔTs of x and y, and of t, which provides information about particle statistics for particles present and moving inside the medium and which are being excited by the laser. The IR detector measures exactly a signal which directly results from ΔTs. Even in case of a parallel motion that is, the horizontal motion, one

encounters a frequency shift (Doppler effect), but the latter varies with the instantaneous particle position according to a sine law, sin(θ), θ being the angle of tilt to the vertical of the line segment joining the particle to the center of the local coordinate frame (0, 0), with the position of the detector on the plane (x, y) ≡ S. See in this connection the corresponding formula in the detailed description. The invention also comprises the case in which the medium is (as a whole) in relative motion with respect to the infrared detector and the light source. Also in this situation there is a relative motion between the material to be analyzed and the light source (pump laser). In the latter case, however, instead of detecting the velocimetric parameters of the particles, which by assumption all move in this case at the same uniform velocity V (that may either be known or unknown), one detects the thermal diffusivity of the medium, that is, of the material under investigation (if V is unknown then V will be measured at the same time). Contrary to the background art, according to which the sample is stationary/fixed with respect to the measuring apparatus, in order to measure the thermal diffusivity (or another thermophysical parameter) one uses in the present invention a sample which is moving. There are various applications for this situation and they will be discussed in the detailed description (quality check of industrial processes, railway security (railroad tracks, etc.)). Even in the situation in which the moving sample is formed by a material whose particles all move at the same uniform velocity V the light source is modulated by means of a modulator, but in this case no spectrum analyzer is required since the detected signal has a frequency equal to ω, that is, the frequency of the modulator (chopper, laser diode, electrooptical system, etc.) and therefore a lock-in demodulator will be used. The so-called “contour plots” of the phase (phase shift with respect to the harmonic signal of the modulator) and of the logarithm of the amplitude, of the signal (that is of the temperature induced on the surface), show level lines, that is lines of constant value, which for V = 0 are circles around the center of the detection zone/area if the laser gives rise to a gaussian spot on the surface S. But whilst the level lines of the phase continue to form circles even for V ≠ 0, the level lines of the logarithm of the signal amplitude form ellipses. From the absolute value of the gradient φ (r) (where φ is the phase and r the distance from the center of the pump beam) one experimentally obtains/measures the value of the thermal diffusion length μ, and finally the thermal diffusivity D of the sample (moving medium/material to be tested). (See the corresponding equations of the detailed description of the invention). Assuming that the velocity V of the sample is not available, then the inventor suggests to use an optical system (for instance a cylindrical lens) for focusing the beam on a strip extending along the y axis (axis perpendicular to V and parallel to S). In this case, it can be shown that the spacetime behavior of ΔTs is the one indicated in formula (17) of the detailed description. Even in this case, being the time dependency equal to exp(jωt) it is not written down in equation (17). In substance, the logarithm of the signal amplitude has two measurable slopes, sA+ and sA-, which combined with the slopes of the phase shift ± sph (equal to each other but of opposite sign) measured upstream and downstream of the plane x = 0, that is ahead and behind the central line of the strip of incidence of the pumping light beam on the sample surface S, allow the determination of both V and D (thermal diffusivity). (Compare this with the equations in the detailed description). In general, it is noted that in the present invention the spacetime behavior of the temperature increase induced on the sample in response to laser excitation, allows to measure velocimetric parameters (in case of particles moving in the interior of the sample, taken as a whole) and thermophysical parameters (D) in case the particles of the tested sample all move at the same constant velocity. In the present invention it is essential that the sample or parts thereof (internal moving particles) are in relative motion with respect to the light source which is always “integral with” (same reference system) the IR detector. The modulator is connected to the spectrum analyzer or to a control and data processing unit (first embodiment or second embodiment). The IR detector is connected to the analyzer or to the control and processing unit, depending on the situation (first embodiment or second embodiment of the invention). In the Figures, the optical systems are shown as lenses for illustrative and non-limitative purposes only; in reality, these lenses will/can be embodied by very complex optical systems of any kind, since only their function is important. For instance, the Ge lens (germanium lens) in Fig. 5 must form an image of the IR light (emitted by the portion of the surface S) free of optical distorsions on the sensitive surface of the IR detector, in all or part of this sensitive surface. It should be noted that if the sample velocity is not known/available (Fig. 10a), then the control unit can exchange a feedback signal with sensors or actuators (drive means) of the moving sample, in order to measure and adjust in real-time the velocity of the sample (Fig. 10(a)). This could be relevant in industrial production lines using product or workpiece conveyors. Brief Description of Drawings The present invention will now be described in detail, only for illustrative and non-limitative purposes with reference to two disclosed embodiments and with reference to the annexed drawings, which show these new methods based on the Doppler effect (Doppler thermography) of thermal waves, applied to the nondestructive measurement of the thermal diffusivity of materials and of the velocity of moving particles. These figures show in detail: FIGURA 1 the configuration of the test setup/arrangement according to the first embodiment of the present invention (first variant), used for measuring the velocimetric statistics (position and velocity) concerning particles in vertical motion in the interior of the test sample; FIGURE 2 a purely schematic representation of the embodiment of Fig. 1 of the present invention applied to the study of skin hydration; FIGURE 3a a diagram showing the IR signal as a function of time, for the arrangement of Figs. 1 and 2 and for certain realistic values of the parameters f, u, Z₀, V, D related to the application of Fig. 2, as well as for a particle approaching - and respectively moving away from – the sample surface; FIGURE 3b shows the behavior of the exponential gain of the signal modulus in a certain time period (5s); FIGURE 3c the curves of the velocity values V calculated again on the basis of the Δω obtained from Fig.3a, for that particular given (constant) velocity during the same time period (5s), by employing a blind test; FIGURE 3d the behavior of the depth Z₀ during the same time period, recalculated on the basis of Fig. 3a, in the same time period (5s), by employing a blind test; FIGURE 4 a schematical representation of a further possible practical application of the invention, once again concerning the first variant of the first embodiment, for the case of nondestructive measurement of glucose migration in skin interstitial fluid, employing a source with a wavelength selectively absorbable by the glucose particles (laser EC-QCL); FIGURE 5 the configuration of the test setup/arrangement for the situation of the first embodiment of the present invention, second variant, suited to measure the velocimetric statistics (position and velocity) concerning particles in horizontal motion in the interior of the test sample; FIGURE 6 the time dynamics of the IR signal (time being normalized to the modulator period), for two different values of the ratio of the particle velocity V and the velocity of the thermal wave (normalized velocity), for three different depths normalized to the thermal diffusion length, and compared with the reference signal of the pumping beam having angular frequency ω; Fig. 6 below also shows the frequency shift (normalized to ω) as a function of normalized time, for the three values of normalized depth, always in the same time period as that of the other diagrams of Fig. 6; FIGURE 7 upper part, the contour plots of the normalized frequency shift, drawn in the (x, z) plane for normalized values of x and z, for certain predetermined values of γ and Z₀, wherein the curves correspond to various constant values of the normalized shift; the lower part shows the diagrams of the behavior of the frequency shift as a function of the normalized distance x, always considering the “in plane motion” configuration of Fig. 5; FIGURE 8 a diagram of the normalized depth reconstructed/recovered (that is obtained from equation (13)) as a function of normalized depth (assigned to the particle as a predefined parameter); FIGURE 9 a possible application for the first variant of the first embodiment of the invention to the cytometric study in capillaries, or capillaroscopic study, wherein the various particle species move inside the capillary substantially parallel to the skin surface; FIGURE 10a a configuration of the setup (assembly of components) used for testing, in the situation corresponding to the first variant of the second embodiment of the present invention, for measuring the thermal diffusivity in a moving test sample whose velocity V relative to the light source and the IR sensor is assumed to be known; FIGURE 10b a configuration of the setup (assembly of components) used for testing, in the situation corresponding to the second variant of the second embodiment of the present invention, for measuring the thermal diffusivity D of a test sample and the latter's velocity V relative to the light source and the IR sensor; FIGURE 11 the contour plots (x/μ, y/μ) of the logarithm of the amplitude and of the phase of the IR sensor signal with respect to the modulation signal, referred to normalized coordinates of the (x, y)-plane of the sample surface, taking for the origin of the (x, y) coordinates the central point of incidence of the gaussian beam spot, for three different values of

(normalized velocity), in accord with the setup of Fig. 10a; FIGURE 12 the diagrams for the logarithm of the amplitude of the modulus of the IR signal, and for the latter's phase shift (with respect to the source modulation signal) as a function of the normalized distance (x/μ) from the center of the strip of incident laser light (y axis); FIGURE 13 a locomotive for nondestructive tests on rails according to an application of the second embodiment of the present invention. Description of Preferred Embodiments of the Invention In the following all details will be described which are useful for a skilled person in order to understand some preferred embodiments of the invention and their variants. However, all details will be omitted which are not strictly necessary because they are already known to those having a solid technical knowledge in the field. A) First preferred embodiment of the invention A1) Configuration “out of plane motion” (Fig. 1), variant n.1 In the interior of the material 1 there are some particles 2 located at a certain depth Z₀ from the surface S. They are moving with a velocity V directed along the local normal z to the surface S. It is assumed, by convention, that V > 0 for particles 2 which are approaching the surface, and that V < 0 in the opposite case of their receding. A pump laser beam 3 is used as a light source for exciting the moving particles 2. The wavelength λ is selected in such a way that the material 1 will be (partially) transparent, so that the beam 3 will penetrate in it with a weak damping to be finally strongly and selectively absorbed by the moving particles 2, which thereby become heated a few Celsius degree. The laser beam 3 is temporally modulated at an angular frequency ω = 2πf by means of a mechanical shutter (chopper) 4, or by means of an electrooptical system (not shown), or lastly by means of a switch which is controlled by a square wave generator, in case of laser diodes (not shown). The modulated beam 5 is finally focused by means of a lens system 6 on a adequate area of interest 7 of the material (typically 1mm²), so as to be able to reach (light up) even moving particles 2 located deep. Said particles 2, while absorbing the modulated beam 5, become moving sources of thermal waves at angular frequency ω = 2πf. Due to the thermal conduction mechanism, heat is transmitted to the whole bulk/volume of material, which thereby slightly increases its temperature. As shown in the appendix, the temperature induced on the surface of the material sample 1 also oscillates, but at a different angular frequency ω' = 2πf' than that of the ω- modulated beam, as a consequence of the Doppler effect on thermal waves recently discovered by the inventor of the present invention. The temperature increase at the surface, ΔTs, has been shown to have the following time dynamics (see Note 1 of the Appendix):

wherein, the following notation has been used: t: time; I: intensity absorbed by the particle; ω: angular modulation frequency; D: thermal diffusivity in the sample; k: thermal conductivity in the sample;

thermal diffusion length;

thermal effusivity of the sample; Z₀ : depth at which the particle is initially located; V: particle velocity; Ratio between the particle velocity V and that of the thermal wave

The temperature increase induced on the surface is detected by means of a stationary/fixed radiometric apparatus operating in “remote sensing” at a distance of about 20 cm from the surface S of the material sample 1. The measuring apparatus may be one of the following: - an IR microbolometer camera denoted 8 in Fig.1, operating within the range LWIR 8- 14 micron and including a focusing optics; - a less expensive infrared system formed by a Germanium lens (not shown in Fig. 1), for collecting the infrared radiation emitted by the surface, connected to an IR sensor of the type HgCdZnTe Peltier cooled operating in the infrared range SWIR 3-5 micron. The choice of apparatus is also dictated by the infrared range suited for a specific application, in order to receive an infrared radiation 9 exclusively from the surface S of the sample 1. The output of the infrared sensor or camera is connected to the input of a spectrum analyzer 10 which receives on a line 11 also the modulation signal of the exciting beam 3, as in the usual “lock-in” techniques. The analyzer 10 determines the difference between the modulation frequency ω and the new frequency ω' as detected by the infrared sensor (reference number 8), providing a signal which is proportional to the surface temperature increase ΔTs of Eq. (1), and decomposing the signal into its modulus and phase. The analysis of this information is then managed by an ad hoc software program. The output of the spectrum analyzer 10 is connected through a line 12 to a computer 13 which processes these data by means of a dedicated software in order to compute the kinematical parameters of an ensemble of moving particles 2. The principle of operation is hereinafter schematically outlined for a single moving particle 2. The signal detected by the sensor 8, which is proportional to the temperature increase ΔTs, is decomposed into its modulus and phase by the spectrum analyzer 10, which also outputs the angular frequency shift according to the following formulas (see Note 1 of the Appendix):

where A is an amplitude factor which takes account of all constants of the measurement apparatuses. An estimate of the particle velocity V is obtained after simple algebraic steps (see Note 2 of the Appendix) by inverting Eq. (2), thereby arriving at the following simple expression which depends on the frequency shift:

A second expression for the velocity V is obtained in an alternative way from the exponential amplification to which the modulus is subjected over time when the particle is approaching, this being experimentally measurable by means of the time constant g (s^-1) of the exponential gain of the modulus from which V can be derived (see Note 3 in the Appendix) as follows:

The position of the particle 2 starting from a depth Z₀ is finally calculated from the measurement of the phase Φ (see Note 4 in the Appendix) in the following way:

Application examples for the “out of plane motion” configuration For illustrative purposes some applications of the present method are given below. 1) The first one, concerning the biomedical field, is the study of skin hydration. One of the still open problems is the determination of the amount and migration of water in skin tissues. Whilst in the dermis, which is vascularized, the content/amount of water is homogeneous and comparable to that of the body, that is, equal to about 70%, in the epidermis (where water penetrates by diffusion from the underlying dermis) the water amount varies from about 70% in the basal layer to about 20% in the stratum corneum (see Figure 2). The velocity of diffusion depends on the concentration gradient and can vary in a wide range from 10^-7 m/s to 10^-5 m/s also due to the application of moisturizing cremes. In this case the exciting laser will be the Er:YAG laser which emits radiation of infrared wavelength 2.94 μm located at the water absorption peak, shows a good penetration in the skin layer and has negligible absorption effects on hemoglobin (see Figure 2). This permits to excite only the water particles which diffuse towards the surface. The sensor 8 in the LWIR range (IR camera) allows instead to measure exclusively the skin temperature. The thermal diffusivity in the epidermis and in the stratum corneum is D = 1x10^-7 m²/s. The thickness of the stratum corneum is about 20 μm. The modulation frequency can be chosen in the interval [1Hz – 100Hz] so as to have a thermal diffusion length μ [10μm-100μm] which allows to study the migration phenomenon up to the correct/required depth. In this example the following parameters are used: f = 3Hz, μ = 100μm, Z₀ = 20μm, V = 4.10- ⁶ m/s. The graphs in Fig.3a refer to a numerical simulation of the signal detected for a particle approaching the surface (red curve) compared with that of the same particle travelling in the opposite direction (blue curve). The graphs of Fig. 3b represent simulations for the modules which, as expected, show an increasing exponential behavior (exp(g.t) with g > 0) for the approaching particle and a decreasing one in the opposite case (with g < 0). For the analysis of the signal a “blind” data processing procedure was adopted, wherein the simulated data in Figure 3a) have been processed by a spectrum analyzer together with the reference data of the modulator, without any information on the velocity and position of the particle set during the simulation. In practice, the spectrum analyzer computes the angular frequency ω' from the time interval ǻt0 that elapses between two consecutive zero (0) passages of the IR signal, by using the formula ω'=π/Δt₀. It compares the perceived angular frequency ω' with the original one used for the modulation, by computing the frequency shift Δω = ω' - ω. In the example in Figure 3a) the perceived angular frequency for the red curve is evaluated 14 times during an observation period of 5 seconds, giving an averaged value ω' = 18.888 rad/s as compared to the original angular frequency ω = 18.850 rad/s, with a frequency shift Δω=

From this frequency shift Δω, assuming the thermal diffusion length of the skin

= 103μm to be known, the particle velocity has been computed using Eq. 3 during the observation period of 5 seconds. Fig. 3c gives the estimates obtained through this procedure for the two velocities ± 4.10^-6 m/s (the positive sign corresponding to the red curve and the negative one for blue). The velocities that have been so “reconstructed”/recovered from “blinded” data processing are in very good agreement with the velocities which were set at the beginning of the simulation, showing a deviation of ± 1% of random, non-systematic nature, due to the resolution of the spectrum analyzer and therefore to the sampling time of the IR signal, therefore open to improvement provided the precision of the employed instrumentation is increased/improved. The spectrum analyzer also measures a phase shift value Φ = -0.98rad, starting from which and applying Eq. 5 the estimate of the initial position Z₀ = 20μm is computed (shown in Fig. 3d), in full accord with the initially preset value in the simulations. The velocity of the particle is also computed by applying a second method that takes advantage of the formula in Eq. 4. Actually, starting from the IR signal amplitude according to the simulation given in Figure 3b), the time constant of the exponential law, of value g=0.0039 s- 1, is computed first, and then – by applying Eq. (4) with D = 1x10^-7 m²/s - an estimate of the particle velocity is obtained which is very near to the real value + 4·10-6m/s (red curve). Also in this case the same observations already made above are valid for the measurement error linked to the precision of the instrumentation and in particular to the total signal-to-noise ratio in the measuring chain. Moreover, it is emphasized that for an ensemble of moving particles which move at different velocities, due to the linearity of the system the IR signal results from the superposition of the effects produced by the motion of each individual particle. Thus, the total signal processed by the spectrum analyzer shows a frequency band corresponding to the distribution of the various velocities. From the signal deconvolution a module M( ω') is computed for each individual frequency ω', and said module is proportional to the concentration of particles travelling at the corresponding speed V( ω'). Thus, a statistic of the velocities of the ensemble of particles can be recovered/reconstructed from the modulus spectrum M( ω'). 2) A further example, still in the biomedical field, is the nondestructive measurement of glucose migration in the interstitial fluid of the epidermis (Fig. 4). In this case an EC-QCL laser is used which can be selectively absorbed by glucose. In this case the frequency regime is [0.05Hz – 1Hz] so as to have a thermal diffusion length μ [100μm – 1 mm], in such a way as to be able to analyze the phenomenon of migration in the dermis and epidermis using the same method described above. 3) Further applications in the field of nondestructive checks/inspections concern the kinematics of microbubbles of air, oils, and other aggregates in the production of mixed liquid products, as well as the determination of the concentration and kinematical parameters of impurities, of aggregate and/or thickened products in production processes of oils, wines, juices and generally of fluid products. A2) Configuration “in plane motion” (Fig. 5), variant n.2 This configuration/arrangement is used for measuring particles 2' which move along the (x,y)- plane or surface of the sample 1. It is assumed that within a material 1 there are particles 2' at a certain depth Z₀ from the surface S, moving with velocity V pointing in any direction in the xy plane. Without loss of generality, in the schematical representation of Fig. 5 the x axis has been chosen as the axis of motion: the convention about the sign of the velocity is chosen so that V>0 for a particle approaching the area/zone where the temperature is measured, whereas V<0 holds for the opposite case of a particle moving away. The excitation system and the experimental measuring apparatus are the same as for the configuration “out of plane motion”, the only difference concerning the focusing of the instruments. In particular, in the configuration “in plane motion” (Fig. 5) the pump beam 3 is not focused, instead it is collimated so as to be incident on an area/zone 7' of about 1cm², in order to follow the dynamics of the particles 2' along the x axis. Moreover, the infrared detector 8a is calibrated in its aperture in such a way as to limit its sensitive area (0.5mm x 0.5mm). This allows to receive the signal only from a limited zone on the sample surface (0.5mm x 0.5mm), employing a Germanium lens 8b that reproduces in 1:1 scale the image of the sensitive area of the detector. The individual particle 2' absorbs the modulated beam 5 and becomes a moving source of thermal waves at the angular frequency ω=2πf. Heat is transferred by conduction to the whole volume of the material 1 which as a consequence experiences a slight increase in temperature. Numerical simulations of the induced temperature are performed in this case by calculating in the first place the response function of a point-like particle located at a point r_S ≡ (x_S, y_S, z_S) and which is impulsively heated with an energy of 1J. The study of such a function that can satisfy the boundary conditions at the interface between the air and the material, leads to the following expression, as follows:

This expression is then used also for the case of power absorbed according to the harmonic law P.exp(j ωt). Thus, the temperature increase ΔT is obtained from the convolution integral of the impulsive response in Eq. (6) with the expression of the absorbed power according to the harmonic law:

where the following notation is used t: actual time,

time at the moment the particle is heated; P: power absorbed by the particle; angular modulation frequency; D: thermal diffusivity of the sample; C: specific heat of the sample;

sample density; particle velocity V and thermal wave velocity ratio

thermal diffusion length;

and where additionally the source point travels at a velocity V as indicated in the Figure, in which: z_S =Z_o: constant depth at which the particle moves; x_S=x_o-V particle position at the moment it is heated y_S=0; since the motion occurs only on the x-axis. From various simulations performed by varying all parameters in Eq. (7) it is shown that, even in the configuration “motion in plane”, a particle 2' lit up by the light 3 modulated at the angular frequency ω and travelling at a depth Z₀ along x with velocity V gives rise to a thermal wave detected at the surface by an IR sensor 8a at an augmented angular frequency ω' > ω during the time the particle 2' approaches the detection zone and which thereafter decreases ( ω' < ω) as the particle recedes, in analogy – in a certain sense - to the Doppler effect in acoustics. Fig. 6 shows two examples of time dynamics of the IR signal for normalized velocities γ = 0.03 and γ=0.1 as a function of t/T, that is of time normalized to the period. These curves relate to different depths Z₀/μ varying from 0.25 to 1 normalized to the thermal diffusion length, and they are compared to the reference signal of the pump beam of angular frequency ω. All curves show a maximum of the signal when the particle transits along the vertical beneath the detector reception area/zone (for t/T ≈ 3), which moment separates the initial phase of the approaching particle, with ω'> ω, from the final phase of the receding particle, ω' < ω. As a further proof, Fig.6 shows the percentage variation of frequency Δω/ ω computed from the IR signal during the motion of particle 2' for γ=0.03 at different depths. This figure elucidates how Δω/ ω changes from positive (approaching particle) to negative (recession). The maximum frequency shift coincides with that described by Eq. (2)

in which the signs +/- are to be used for the approaching phase and for the receding phase respectively. By inverting Eq. (8) it can be shown that the estimate of the particle velocity V starting from the Δω data is obtainable by an expression analogous to Eq. (3) used for the first configuration

An estimate of the depth Z₀ at which the particle is travelling can be derived by examining the dynamics of the frequency shift Δω(t)/ ω. The proof is given in Figure 7, in which theoretical results are plotted for Δω/ ω observable at each point of the xz plane, for a particle moving with a normalized velocity γ=0.03 at a normalized depth Z₀/μ=1.5. The contour plot reveals that the frequency shift observed at a point of the surface is also linked to the angle θ of tilt/inclination between the particle, located at the position (0, Z₀), and the observation point on the surface, which lies at position (x, 0), according to the law

The validity of Eq. (10) is proven in Figure 7 (lower part) where the simulation results for (using Eq.7) are plotted as a function of x/μ and for different values of Z₀/μ,

together with the expected values obtained from formula (10) (dark curves). The curves Δω/ ω show their maximum variation at x = 0 (when the particle passes beneath the detector and θ = 0). From Eq. (10) one calculates the value of the time derivative of the frequency shift

which reaches its maximum at x = 0

Eq. (12) is used to find the depth Z₀ at which the particle is moving

Applying Eq. (13) it is therefore possible to provide an estimate for Z₀. Even for this case a virtual experiment has been conducted with a “blind” procedure, using numerical simulations in order to compute the IR signal of a particle travelling with speed V at depth Z₀. Then, this signal was processed by a spectrum analyzer which measured the relative frequency shift Δω/ ω over time (Fig. 6) without any information about the particle velocity and position set during the simulation. By processing this datum/information as provided by Eq. (13) the depth Z_rec of the particle was recovered/reconstructed. After this virtual, “blind” experiment, the value Z_rec was compared to the real values for the depths Z₀ set in the simulation. In Fig.8 this estimate is plotted for the depth Z_rec as a function of the real depth Z₀. This is a universal graph normalized to the thermal diffusion length μ. The bisectrix shown in dark color corresponds to the ideal case of a perfect reconstruction of the depth. The deviations from this ideal situation are < 5%. More important deviations will occur when Z₀ > 1.5μ, that is, when the particle 2' is located in a region too deep compared to the thermal diffusion length. Application examples for the “in plane motion” configuration 1)For illustrative purposes an application of this method will be given for the biomedical field, specifically to the cytometric study of capillaries, or capillaroscopic study. Such a system can allow the determination of the position and velocity of red blood cells, platelets, platelet aggregates, aggregates with cancer cells, and microemboli inside blood vessels and thin capillaries. The wavelength of the exciting beam 3 is chosen in such a way to penetrate in the epidermis barrier and be selectively absorbed by the red blood cells or the microemboli. To this regard, the use of a laser operating at 4 possible different wavelengths (532, 671, 820 and 1064 nm) allows to discriminate/distinguish the contributions from the various species, which are in a moving state, based on the different absorption properties of these different families of moving particles 2'. On the other hand, the sensor operating in the LWIR range permits to measure the skin temperature only. The thermal diffusivity in the dermis is D = 1x10^-7 m²/s. The zone of interest is located in the dermis and in the subcutaneous tissue from 0.5 to 2 mm beneath the surface. The modulation frequency ω can be chosen in the interval [0.05 Hz – 0.5 Hz] so as to have a thermal diffusion length μ [0.2 mm – 1 mm] so that the phenomenon can be studied up to the correct depth. The velocity V of the blood cells in the thinner capillaries may be very low, in the range [0.1 mm/s – 1 mm/s], consequently the normalized velocity γ will be in the range [0.1 – 3]. In this range of values, it is possible to employ the formulas given by Eq. (9) to Eq. (13) for evaluating the position and velocimetric parameters of the moving particles in the capillaries. B) Second preferred embodiment of the invention In this second embodiment of the invention a technique is described for measuring in “remote sensing” the thermal diffusivity of materials, by employing radiometric or thermographic infrared methods. One among the most relevant applications in the field of thermal engineering concerns the accurate measurement of thermal diffusivity in solids. In the last few years, various different experimental setups have been suggested for measuring thermal parameters of materials of various kinds and shape: bulk, thin films, etc. In all these experimental apparatuses the sample under examination was fixed on a sample holder/support and then it was heated with laser sources that were either frequency modulated or pulsed. According to the present invention, an innovative method is suggested for measuring the thermal diffusivity of materials which are moving at a constant speed. This new approach assumes/requires the use of a fixed measuring apparatus (or which is in relative motion with respect to the sample), which analyzes a material/sample in motion (relative to the measuring apparatus) and which, for instance, is moved/shifted along a production line. This measuring technique therefore meets the requirements of industrial processes, for production, on-line inspection and on-line quality control, where local thermal parameters need to be assessed in real time, without interrupting the production chain. In Fig. 10 there is shown an exemplificative scheme of such a measuring apparatus. The sample 1' is subjected to a translation at constant speed V along the horizontal x-axis in the same manner as in a production line. The material 1' is heated with a pump laser beam 3 which is “fixed/stationary”, modulated at an angular frequency ω, and focused on the sample 1' by means of a cylindrical lens 6 (Fig. 10b), thereby generating a planar thermal wave along the plane yz. Alternatively, in a second configuration (Fig.10a) a lens 6 is chosen which can focus the beam on a small-sized gaussian spot [10 – 50 μm]. For the nondestructive, remote sensing inspection and check, an infrared “stationary” camera 8 (that is, “integral with” the exciting system) is used, said camera employing the lock-in technique in order to detect both the amplitude and phase of the infrared signal emitted from the sample surface S. In this case, the detected angular frequency ω coincides with that which is imposed by the beam modulation ω, since the light/heat source 3 and the detector 8 are not in relative motion, one with respect to the other. It is emphasized that the method described herein is innovative and differs from other recent methods, where the moving sample 1' is heated by means of a focused continuous (c.w.) laser beam, with no time modulation whatever [21]. With regard to this anterior method, it is necessary to point out that the application of the thermographic technique under continuous heating offers on the one hand the advantage of simplifying the experimental arrangement (no modulator 4 and no lock-in demodulation system 15), but on the other, it has a number of drawbacks compared to the modulation techniques: a) a too large sensitivity to noise, caused for instance by thermal sources external to the system; b) the difficulty of filtering undesired signals due to beams that are reflected or scattered by the sample and which accidentally enter the sensitive area of the IR thermal camera; c) the need to use high power values in order to improve the signal-to-noise ratio, but these heat up the material by various tens of degrees, with the risk of deteriorating biological materials and of causing nonlinear thermal effects due to the excessive variability of thermal parameters with temperature. Instead, these drawbacks are eliminated by the temporally modulated technique disclosed in the present patent application. From various simulations performed on the basis of Eq. (6) and (7), when varying all parameters, it is shown that the infrared images of the surface (xy plane) present a distorsion and asymmetries due to the fact that the sample 1' is moving, as demonstrated by the numerical simulations plotted in Figure 11 which relate to the configuration of Figure 10a. The contour plots of Figure 11 show the logarithm of the signal amplitude (Figures 11, a, c, e), and the phase shift with respect to the harmonic signal of the modulator (Figures 11 b, d, f). The level curves are shown as a function of position on the sample surface, with both the abscissae x/μ and the ordinates y/μ normalized to the thermal diffusion length for a greater universality of these plots. These Figures refer to three values of the normalized velocity (note that these figures are perfectly symmetrical for γ = 0, when the

sample stands still). However, from Figure 11 (b, d, f) it can be seen that the signal phase maintains its radial symmetry in the xy plane, independently of the velocity value γ. The signal phase can be expressed as

where

is the distance from the center of the pump beam, and as before

Eq. (14) shows a phase behaviour linearly decreasing with distance r. From this linear behaviour it is possible to compute the absolute value of the slope sph

which is related to the thermal diffusion length μ and consequently to the thermal diffusivity. After some algebraic manipulation summed up in Note 5 of the Appendix, it is possible to obtain the expression for the estimate/evaluation of the thermal diffusivity, according to the following formula:

It is easy to verify that in the particular case where the sample is not moving (V=0), Eq.(16) becomes the well-known expression

which is used for the determination of the diffusivity of materials in conventional static measurements on a non-moving sample. In this sense Eq. (16) reflects a new approach and represents a new original formula, allowing to extend the measurement of the diffusivity to the case of moving samples, which for instance move with a controlled speed V along a production line. However, Eq. (16) can be used only if the translation velocity of the sample 1' is known, that is, available. Instead, in case both the thermal diffusivity D and the velocity V are not available, it is recommended to make use of the second configuration shown in Fig. 10b, which makes use of an optical cylindrical lens 6 to focus the beam on a strip along the y-axis. This configuration is particularly robust due to the simplicity in collecting the infrared signal, which is measured and analyzed along the x-axis only, this circumstance obviously leading to time savings during the measurement performed by the infrared sensor 8. In this case, a simple analytical expression has been found for the complex signal (modulus and phase) on the left (x<0) and right (x>0) of the strip where the sample is hit by the light rays, at x= 0. The IR signal is proportional to the temperature increment ΔTs, which in this case is given by

where A=ΔTs(0) is the temperature value at x=0, which plays no role in the data analysis. The results of the numerical simulations are plotted in Fig. 12 which shows the logarithm of the amplitude (Fig.12a) and the phase (Fig.12b) as a function of the normalized horizontal offset (x/μ) for various entrainment speeds of the sample. Both the phase and the logarithmic amplitude behave linearly as the offset varies. Looking at Eq. (17), there are 3 relevant slopes: the two slopes s_A+ e s_A-, computed from the linear behavior of the logarithm of the amplitude for x> 0 and x<0 (the amplitude is not symmetrical with x), and the slope sPh calculated from the phase (the phase is symmetrical with x). From Eq. (17) one obtains this expression for the three slopes:

where, for the sake of convenience, the definition of the symbols appearing in (18) are repeated h^ere:

After simple algebraic manipulations one arrives at

Combining the equations and using the property a·b = 1 it is possible to explicitly write the dependence of the thermal diffusion length μ and of the normalized speed γ from the three experimentally measurable slopes:

From Eq. (19) one finally obtains the unknown quantities, that is, the thermal diffusivity D and sample translation velocity V

It is emphasized that Eq. (20) is fundamental for an accurate measurement of the local thermal diffusivity, during an on-line quality check of industrially manufactured products moving on a conveyor belt, which are inspected by means of the lock-in thermography of the arrangement shown in Fig. 10b; however, it can also provide/detect the translation speed V, which could vary as a consequence of unexpected events or simply because the translation modality has changed. A control unit 14 connected to the modulator 4 through line 15 (in the present case a spectrum analyzer obviously is not needed), would allow to adjust the speed V in case of deviations from a nominal value (see Figure 10a and 10b). In case of very high, normalized translation speeds, with γ >>1, the slope sA- becomes very high and cannot be easily measured. Then, since sA- is unknown, Eq. (20) cannot be applied, but in Note 6 of the Appendix it is shown that an alternative method exists for measuring the thermal diffusivity, using only measurements on the right for sph e s_A+ in accord with the approximate expression

which is applicable if the translation velocity V is known. Application examples for the second embodiment of the invention For illustrative purposes an application scheme in the automotive field is reported. Among the rapidly developing fields there are the nondestructive checks on railway networks by means of specially equipped locomotives. Usually, ultrasound techniques are employed in order to check the railroad but they do not succeed in accurately investigating the thermomechanical properties in certain head zones of the rail. Instead, the thermographic Doppler system is suited to measure in a nondestructive manner the superficial diffusivity along the rail during the displacement of an appropriately outfitted locomotive. From the measured value of the thermal diffusivity, it is possible to calculate the surface hardness along the rail and verify the presence of possible dangerous points in the railroad (this will be possible after gauging of the material forming the railroad and using a known correlation table between hardness and thermal diffusivity values). This thermographic analysis further allows to check the railroad superficial homogeneity and to verify the presence of superficial or subsurface fissures. Fig. 13 shows the system already described in Fig. 10b, mounted on a locomotive 17. This system comprises a laser 20 for heating the rail 18 and various infrared sensors 19 in order to follow the induced temperature, when the locomotive 17 is moving at high speeds [5-20 km/h]. In this application the thermal diffusivity D of the rail 18 usually is in the range [5·10^-6 - 2·10- ⁵ m²/s]. The range of useful frequencies is [1-100 Hz] so that the normalized velocity γ will be in the range [5-50], which can noticeably increase (up to 50 times) the thermal diffusion length μph perceived by the sensors, thereby allowing a good measurement of the phase. For illustrative purposes and referring to Fig.13 results are reported which were obtained from a numerical simulation performed with a 10-Watt laser diode operating at 808 nm, voltage- modulated at a frequency of 5 Hz and mounted on a locomotive travelling at 5 km/h, which inspects a railroad of unknown thermal diffusivity (in the simulations we set D=1·10^-5 m²/s). In order to study a practical and viable case it is necessary to place the two IR sensors of Fig. 131.5 m apart, so that x2-x1 = 1.5 m (this can be done in the locomotive carriage). After setting these parameters, the two IR sensors measure the following: a) a mutual phase difference

33.93 rad; and b) a ratio between modules M2/M1=0.9945. From these experimental data it is possible to calculate the phase slope sph=22.62 rad/m and the slope of the amplitude logarithm on the right side s_A+=0.00368 m^-1 , both on the right side of the pump laser. The data on the left in Fig. 13, that is leftwards from the laser 20, are not measurable in this case. In these conditions, assuming V = 5 km/h is known, and applying Eq. (16), one obtains a very good estimate of the thermal diffusivity D=1·10^-5 m²/s with a computational error of 0.07% due to rounding, whereas by applying Eq. (21) one gets the same estimate but with a systematic error of about 0.13%, due to the approximation in the formula. Lastly, an application of the present invention could possibly concern the installation on a drone of a system used for analysing material samples in accord with the present invention. References [1] C Doppler, Gesellschaft d. Wiss. 2, 465, (1842) [2] C.H.D. Buys Ballot, Pogg Ann B 66, 321-351, (1855) [3] M.H. Fizeau, Ann. Chimie Physique, 19, 211-221, (1870) [4] W Huggins, Phil Trans Soc Roy London, 158, 529-564, (1868) [5] A. I. Bozhkov and F. V. Bunkin, Sov. J. Quantum Electron. 5, 956 (1976). [6] A. I. Bozhkov, F. V. Bunkin, I. B. Esipov, A. I. Malyarovskii, and V. G. Mikhalevich, Sov. Phys. Acoust. 26, 100 (1980). [7] A. I. Bozhkov, F. Bunkin, and A. A. Kolomenskii, Sov. J. Quantum Electron. 7, 536 (1977). [8] A. I. Bozhkov and A. A. Kolomenskii, Sov. J. Quantum Electron. 8, 1449 (1978). [9] F. V. Bunkin, A. I. Malyarovskii, V. G. Mikhalevich, and G. P. Shipulo, Sov. J. Quantum Electron. 8, 270 (1978). [10] A. D. Pierce and Y. H. Berthelot, J. Acoust. Soc. Am. 83, 914 (1988). [11] A. A. Zaitsev, Sov. Phys. Acoust. 19, 234 (1973). [12] V. N. Lugovoi and V. N. Strel'tsov, Sov. Phys. JETP 38, 701 (1974). [13] F. V. Bunkin, V. G. Mikhalevich, and G. P. Shipulo, Sov. J. Quantum Electron. 6, 238 (1976). [14] A. I. Bozhkov, F. V. Bunkin and A. A. Kolomenskii, Sov. Tech. Phys. Lett.4, 516 (1978). [15] W. Bai and G. J. Diebold, Phys. Rev. E, 98, 032125 (2018) [16] W. Bai and G. J. Diebold, J. Appl. Phys. 125, 060902 (2019); [17] C. M. Wynn, S. T. Palmacci, M. L. Clark, and R. R. Kunz, Opt. Eng. 53, 021103 (2013). [18] C. M. Wynn, S. Palmacci, M. Clark, and R. Kunz, Appl. Phys. Lett.101, 184103 (2012). [19] R. Sullenberger, M. Clark, R. Kunz, A. Samuels, D. Emge, M. Ellzy, and C. Wynn, Opt. Express 22, A1810 (2014). [20]. “La Fisica di Amaldi”, vol. 3, elettromagnetismo, fisica atomica e subatomica, ed. Zanichelli, 2012, pag. 408 e 416 [21] L. Gaverina, M. Bensalem, A. Bedoya, J. González, A. Sommier, J.L. Battaglia, A. Salazar, A. Mendioroz, A. Oleaga, J.C. Batsale, C. Pradere, International Journal of Thermal Sciences 145106000 (2019) [22] A. Bedoya, J. González, J. Rodríguez-Aseguinolaza, A. Mendioroz, A. Sommier, J.C. Batsale, C. Pradere, A. Salazar, Measurement 134, 519–526 (2019) Appendix Note 1: Diffusion equation for a moving source The heat diffusion equation when a stationary source irradiates an absorbing material which is moving with velocity V, is given by the diffusion equation

where T is the induced temperature increase, D the thermal diffusivity of the material, k the thermal conductivity of the material, w the induced heat in the material per unit time and unit volume, the nabla operator as known from ordinary physics courses. In case of a planar thermal source along the xy-plane, as shown in the experimental configurations in Fig. 1 and Fig. 5, the temperature becomes a function only of the spatial variable z and the diffusion equation becomes

Finally, if the source is modulated at angular frequency ω, all quantities oscillate at the same angular frequency, and the equation at the harmonic regime/condition becomes

assuming an absorption of light intensity I from a particle layer at depth Z_o. The diffusion equation in harmonic conditions is a homogeneous differential equation of second order having a general solution given by the superposition of two possible functions

where F e G are arbitrary constants to be determined by the boundary conditions, and the two factors

in the exponentials must satisfy the equation

Introducing the thermal diffusion length

these two factors become

Finally, introducing the normalized velocity

, it is possible to rewrite the two factors in the final form

where for simplicity we put

in the standard complex number form

Assuming that the heat source is planar at the depth Z_S=Z_o-Vt, the solution for the temperature in the half plane z>0 can be specified in the different zones: T1 in the zone 0<z<Z_S and T₂ for

The coefficients F, G, H are determined imposing the following boundary conditions: 1) continuity of the temperature at the interface z=ZS, from which it follows that T₁=T₂ or F+G=H 2) thermal flow injected by the light source I subdivided in two thermal flows (for z=Z_S it must be I= k·dT1/dz - k·dT₂/dz) 3) null thermal flow at the surface z=0 with the insulating air (condition k·dT1/dz=0) Imposing the three conditions described above, it is possible to obtain the coefficients F, G, H in algebraic form and finally calculate the expression for the temperature increase observable at z=0 on the surface, given by the expression

where

is defined as the thermal effusivity of the sample. Furthermore, since the particle, initially at depth Zo, moves towards the surface with uniform rectilinear motion according to the law

this implies, in the expression for the surface temperature, a plurality of simplifying algebraic manipulations on the term

which lead to the final expression of the surface temperature increase

Note Starting from the equation of the frequency variation

squaring both sides

isolating the square root

squaring and simplifying

isolating the velocity term and raising to the power 1/4

and finally

Note 3 Starting from the exponential time law of the signal modulus in Eq. (2) exp (g·t) = exp[(a+γ)ωγt] one obtains the time constant g in the exponential term

from which the particle velocity is derived as:

Note 4 Starting from the expression of the signal phase in Eq. (2)

one obtains the initial particle depth Then, substituting V with the final expression

taken from Note 2 one derive

and after some algebraic manipulations

Nota 5 Squaring Eq. (15)

. Isolating the radical one obtains

Simplifying the term

and substituting

one finally arrives at

and from this,

Nota 6 Starting from Eq. (18), if it is only possible to measure the slopes on the right side of the pump laser, only the two data

are available. Multiplying these data of the two slopes one obtains

. On the other hand, if γ>>1 then the factor b·γ (stopping the Taylor series at the second order) tends to

Introducing this approximate result in the above relation one arrives at

List of reference symbols 1 sample, with moving (internal) particles 1' sample 2 particle in vertical motion 2' particle in horizontal motion 3 light source (laser) 4 modulator of 3 5 modulated light beam 6 transmission optics 7 zone/area of light incidence 8 camera 8a sensor, detector 8b receiving optics, germanium lens 9 reemitted light 10 spectrum analyzer 11 “lock in” connection line 12 connection line 13 computer, laptop 14 control unit 15 “lock in” connection line 16 connection line (regulation of sample velocity) 17 locomotive 18 rail 19 camera (mounted on the locomotive) 20 laser (mounted on the locomotive) S sample surface

Claims

Claims 1. Technique for testing a sample of material using radiometry or infrared thermography, characterized in that it comprises the following steps: a) providing a sample to be examined, which (a1) substantially forms a material whose particles are all at rest with respect to each other, at the level of macroscopic physics, or (a2) forms a material in which some particles are in motion compared to the remaining and main part of the sample, at the level of macroscopic physics; b) providing a light source (3), preferably infrared, such as a pump laser beam (3), and a modulator (4) for temporally modulating the light transmitted by said light source (3) at an angular frequency ω; c) providing a transmission optics (6) for collimating and/or focusing and/or modeling the beam of transmitted light, and for projecting it onto an area of incidence (7) of the light on the surface (S) of the sample; d) providing at least a detection system (8; 8a, 8b), formed by at least a receiving optics (8b) with detector (8a) or by at least an IR camera (8), such a detection system (8; 8a, 8b) receiving the infrared light re-emitted by said incidence area (7) of the light and by a surrounding heat diffusion area, and carrying the corresponding IR detection signal to a data control and analysis unit (10, 13, 14), which is connected to said detection system (8; 8a, 8b); e) connecting (11; 15), said modulator (4) to said data control and analysis unit (10, 13, 14); f) wherein, in case a1) the sample is moving at a speed V with respect to the detection system (8; 8a, 8b) and to the light source (3), and in case a2) said moving particles, inside the sample, move with respect to the detection system (8; 8a, 8b) and the light source (3); and in that it also comprises the following steps g) analyzing the IR signal data collected by the control and analysis unit, on the basis of the space-time distribution of the temperature increase ΔTs in said light incidence area (7) and in a surrounding heat diffusion area, both located on the surface (S) of the sample, and in particular analyzing the IR signal phase and modulus; h) determining in case a1) the thermal diffusivity D of the sample and/or the velocity V of the sample itself, or, in case a2) obtaining a statistic of the position and velocity parameters using the frequency shift Δω due to the Doppler effect on the thermal waves produced by the single moving particles (2; 2') heated by the light source. 2. Technique for testing a sample of material using radiometry or infrared thermography according to claim 1, characterized in that in case a2), said data control and analysis unit comprises a spectrum analyzer (10) connected to the modulator (4), and a computer (13). 3. Technique for testing a sample of material using radiometry or infrared thermography according to claim 1, characterized in that in case a1) said control and analysis unit comprises a control unit (14) and a computer (13), wherein the modulator (4) is connected to the control unit (14) which uses a lock-in demodulator. 4. Technique for testing a sample of material using radiometry or infrared thermography according to claim 3, characterized in that the control unit (14) is connected electrically or wirelessly to actuators or drive means of the sample (1'), to provide a feedback signal to said actuators or actuation means of the sample, so as to adapt in real time the velocity V of the sample if this deviates from a substantially constant nominal value thereof. 5. Technique for testing a sample of material using radiometry or infrared thermography according to claim 1, wherein the modulation carried out by the modulator (4) can be obtained for example with a chopper of the light source, with a diode laser controlled by a square wave, or with an electro-optical system. 6. Testing technique according to claim 1, characterized in that the modulation frequency ω of the modulator (4) is selected so as to have a thermal diffusion length μ which overlaps at least in part with the values of the depth range of the positions of the moving particles with respect to the surface S of the sample. 7. Testing technique according to claim 1, 2, 5 or 6, characterized in that the moving particles (2) move substantially in a vertical direction, i.e. orthogonal to the surface S of the sample, or the moving particles (2') move in a substantially horizontal direction, i.e. parallel to the surface S of the sample. 8. Testing technique according to claim 7, characterized in that if the moving particles (2) move in a substantially vertical direction, then the transmitted light beam is collimated o^{n a narrow area, for example 1 mm2, while if the particles (2’) move in a substantially} horizontal direction, then the transmitted light beam of the light source is not focused but collimated so as to illuminate a larger area, for example 1 cm², to follow the motion of the particles moving along the direction defined by their velocity. 9. Testing technique according to claim 8, characterized in that the control and analysis unit (10, 13) processes the IR signal data provided by the IR sensor for substantially vertical moving particles (2) and uses the following formulas for the calculation of the vertical velocity and the position thereof:

where Δω is the frequency shift, g the exponential gain of the IR signal, ĭ the phase of the latter, obtained by the spectrum analyzer (10). 10. Testing technique according to claim 7 or 8, characterized in that the control and analysis unit (10, 13) processes the IR signal data provided by the IR sensor for substantially horizontal moving particles (2') and uses the following formulas for the calculation of the horizontal velocity and the position thereof:

11. Testing technique according to claim 1, characterized in that in the case of a Gaussian spot formed by the transmitted light source, and assuming the variable V is known, the control and analysis unit (13, 14) calculates the thermal diffusivity D based on the following formula:

sph being obtained from the control and analysis unit as an absolute value of the gradient of the phase of the signal IR with respect to the radius r equal to the distance from the center of the spot of the light source beam on the surface S of the sample. 12. Testing technique according to claim 1, characterized by focusing through said transmission optics (6) the beam of light transmitted on the surface S of the sample along a strip perpendicular to the direction of the motion V of the sample, and by using the control and analysis unit (13, 14) to calculate the thermal diffusivity D of the sample and the velocity V of the sample, which in this case is considered unknown, using the following formulas:

the slopes sA+, sA- and sph being quantities obtainable by the control and analysis unit from the IR signal measured respectively downstream and upstream of said strip, from the logarithmic amplitude and from the phase of said IR signal. 13. Testing technique according to claim 1, characterized by focusing through said transmission optics (6) the beam of light transmitted on the surface S of the sample along a strip perpendicular to the direction of the motion V of the sample, and by using the control and analysis (13, 14) to calculate the thermal diffusivity D of the sample using the following approximate formula, valid for high values of γ:

the slopes s_A+ and s_ph being quantities obtainable by the control and analysis unit from the IR signal measured downstream of said strip, from the logarithmic amplitude and from the phase of said IR signal. 14. Testing technique according to any one of the preceding claims, characterized in that the transmission light source, for example a laser, can be tuned to, or has, N different wavelengths, λ1, λ2 …. λn, corresponding to the absorption wavelengths for N different species, i.e. families of moving particles. 15. Testing technique according to any one of the preceding claims, wherein the wavelength or wavelengths of the laser are selected so that the sample material is at least partially transparent to the light beam of the transmission light source so that the latter can penetrate therein with weak attenuation, to finally be strongly and selectively absorbed by the moving particles. 16. Testing technique according to any one of the preceding claims, characterized in that said detection system is adapted to a specific application, i.e. to receive infrared radiation only from the surface S of the sample, blocking other disturbing light. 17. Testing technique according to any one of the preceding claims, wherein in case a2) the sample to be examined can be an outermost portion S of the human body, and the moving particles can be for example glucose, water particles, corpuscles present in a blood vessel or capillary, or the like, and in case a1) the sample can be an iron path to be examined for possible defects or a series of products moving on a production line, for example on a conveyor belt, to carry out a quality control, or similar samples of an industrial production process. 18. System for testing a sample of material using radiometry or infrared thermography, characterized in that it comprises: a) a sample to be examined, which (a1) substantially forms a material whose particles are all at rest with respect to each other, at the level of macroscopic physics, or (a2) forms a material in which some particles are in motion compared to the remaining and main part of the sample, at the level of macroscopic physics; b) a light source (3), preferably infrared, such as a pump laser beam (3), and a modulator (4) for temporally modulating the light transmitted by said light source (3) at an angular frequency; c) a transmission optics (6) for collimating and/or focusing and/or modeling the beam of transmitted light, and for projecting it onto an area of incidence of the light on the surface (S) of the sample; d) at least a detection system (8; 8a, 8b), formed by at least a receiving optics (8b) with detector (8a) or by at least an IR camera (8), such a detection system (8; 8a, 8b) receiving the infrared light re-emitted by said incidence area of the light and by a surrounding heat diffusion area, and carrying the corresponding IR detection signal to a data control and analysis unit (10, 14), which is connected to said detection system (8; 8a, 8b); e) wherein said modulator (4) is connected to said data control and analysis unit (10, 13, 14); f) wherein, in case a1) the sample is moving at a speed V with respect to the detection system (8; 8a, 8b) and to the light source (3), and in case a2) said moving particles, inside the sample, move with respect to the detection system (8; 8a, 8b) and the light source (3); and in that g) the control and analysis unit analyzes the IR signal data collected, on the basis of the space-time distribution of the temperature increase ΔTs in said light incidence area (7) and in a surrounding heat diffusion area, both located on the surface (S) of the sample, and analyzes them with respect to the IR signal phase and module; h) the control and analysis unit determines in case a1) the thermal diffusivity D of the sample and/or the velocity V of the sample itself, or, in case a2) obtains a statistic of the position and velocity parameters using the frequency shift Δω due to the Doppler effect on the thermal waves produced by the single moving particles (2; 2') heated by the light source. 19. System for testing a sample of material using radiometry or infrared thermography according to claim 17, characterized in that in case a2), said data control and analysis unit (10, 13, 14) comprises a spectrum analyzer (10) connected to the modulator (4), and a computer (13). 20. System for testing a sample of material using radiometry or infrared thermography according to claim 18, characterized in that in case a1) said control and analysis unit (13, 14) comprises a control unit (14) and a computer (13), wherein the modulator (4) is connected to the control unit (14) which uses a lock-in demodulator. 21. System for testing a sample of material using radiometry or infrared thermography according to claim 20, characterized in that the control unit (14) is connected electrically or wirelessly to actuators or drive means of the sample, to provide a feedback signal to said actuators or actuation means of the sample, so as to adapt in real time the velocity V of the sample if this deviates from a substantially constant nominal value thereof. 22. System for testing a sample of material using radiometry or infrared thermography according to claim 18, characterized in that the modulation carried out by the modulator (4) is obtained for example with a chopper of the light source, with a diode laser controlled by a square wave, or with an electro-optical system. 23. Testing system according to claim 18, characterized in that the modulation frequency ω of the modulator (4) is selected so as to have a thermal diffusion length μ which overlaps at least in part with the values of the depth range of the positions of the moving particles with respect to the surface S of the sample. 24. Testing system according to claim 18, 19, 22 or 23, characterized in that the moving particles (2) move substantially in a vertical direction, i.e. orthogonal to the surface S of the sample, or the moving particles (2') move in a substantially horizontal direction, i.e. parallel to the surface S of the sample. 25. Testing system according to claim 24, characterized in that if the moving particles move in a substantially vertical direction, then the transmitted light beam is collimated on a narrow area, for example 1 mm2, while if the particles move in a substantially horizontal direction, then the transmitted light beam of the light source is not focused but collimated so as to illuminate a larger area, for example 1 cm², to follow the motion of the particles moving along the direction defined by their velocity. 26. Use of a testing system according to the preceding claims on or for a drone, for analyzing samples during the movement of the drone.