Dans les aciers cementes, la durete varie en raison inverse de la conductivite thermique. Cette c... more Dans les aciers cementes, la durete varie en raison inverse de la conductivite thermique. Cette correlation peut etre mise a profit pour elaborer une technique de determination indirecte du profil de durete. La methode d'evaluation que nous proposons a l'avantage d'etre rapide, non destructive et sans contact. Elle repose sur une technique photothermique : la surface est chauffee par un laser impulsionnel et l'on mesure l'evolution de la temperature a l'aide d'un detecteur infrarouge. Nous avons developpe une technique d'inversion pour extraire le profil d'effusivite thermique (ou de conductivite) a partir de l'evolution transitoire de la temperature de surface. La robustesse et la precision de la methode ont ete verifiees sur quelques profils theoriques simples. Des resultats experimentaux obtenus sur des aciers cementes durcis sur des epaisseurs variables sont finalement presentes ainsi que la correspondance avec le profil de durete obtenu p...
Remote Sensing for Agriculture, Ecosystems, and Hydrology XI, 2009
The triangle/trapezoid method is a well known method for retrieving spatialized soil moisture fro... more The triangle/trapezoid method is a well known method for retrieving spatialized soil moisture from remotely sensed temperature and vegetation index (NDVI). We selected three approaches with different requirements for ancillary data (triangle empirical method by Sandholt et al. [7], trapezoid method by Moran et al. [2], SVAT triangle method by Carlson et al. [3]-[6]). The empirical inversion is well suited
... 2). Infrared radiation from 175 Particle Fiber optic cable to coincidence sensor particle gas... more ... 2). Infrared radiation from 175 Particle Fiber optic cable to coincidence sensor particle gas inlet plasma torch # sh fiber optic cable to doublewavelength pyrometer Fig. ... optic cable from optic cable from coincidence head pyrometer head 1 2 Detection ii,! ...
The through-thickness thermal diffusivity can be evaluated by the classical flash method. If an h... more The through-thickness thermal diffusivity can be evaluated by the classical flash method. If an homogeneous and extended source is used to irradiate the surface and a thermographic camera is used to monitor the temperature evolution of the opposite side, a map of the through-thickness thermal diffusivity can be obtained in a single experiment and without any contact with the sample under inspection. In order to measure the in-plane thermal diffusivity of a plate-like sample or in one of the principal directions of its plane, a thermal gradient across the plane of the material has to be settled. The ratio of the Fourier transform of temperature at two different spatial frequencies is an exponential function of time multiplied by the diffusivity in the considered principal direction. This can be used to evaluate the diffusivity in an homogenous material. In order to maximise the signal-to-noise ratio, it is better if heat is absorbed over a series of periodic parallel strips (grid fla...
Reflective cavity pyrometers are increasingly used for on-line temperature sensing of metal sheet... more Reflective cavity pyrometers are increasingly used for on-line temperature sensing of metal sheets. The presence of the reflector increases the effective emissivity of the sheet, thus reducing the measurement error. Hemispherical geometries have been mostly used in the past for the reflector. This paper presents a Monte-Carlo analysis for a number of different cavity configurations. The value of the effective emissivity is evaluated for different cavity parameters and standoff range over the sheet as well as for different degrees of the metal sheet real emissivity. It will be shown, in particular, that a trucated hemisphere with centre of curvature belowthe sheet is preferable to the more conventional full hemisphere to reduce losses due to sheet fluttering. Applications to infurnace temperature monitoring of steel sheets will be indicated.
SUMMARY A thermographic technique to inspect structures using an internal perturbation source suc... more SUMMARY A thermographic technique to inspect structures using an internal perturbation source such as a sudden change of the liquid temperature flow is presented. After a brief survey of the apparatus the technique is applied to detect wall thickness loss due to cavitation corrosion in liquid or gas carrying pipes. The same technique was used to reveal the internal structure of turbine blades after proper image processing.
Vegetation and soil temperatures have long been recognized as an indicator of water availability.... more Vegetation and soil temperatures have long been recognized as an indicator of water availability. When plotting the twodimensional distribution of temperature and vegetation index (T-VI) corresponding to an area with well distributed vegetation cover and moisture content, one gets a triangular or trapezoidal shape. Iso-moisture lines range between two edges of the distribution: the dry edge and the wet edge. This description is based on a simplified representation of the thermal and radiative properties of the soil/ ...
The triangle/trapezoid method is a well known method for retrieving spatialized soil moisture fro... more The triangle/trapezoid method is a well known method for retrieving spatialized soil moisture from remotely sensed temperature and vegetation index (NDVI). We selected three approaches with different requirements for ancillary data (triangle empirical method by Sandholt et al.[7], trapezoid method by Moran et al.[2], SVAT triangle method by Carlson et al.[3]-[6]). The empirical inversion is well suited when no information on meteorological data is available.
This work deals with the exact analytical modeling of transfer phenomena in heterogeneous materia... more This work deals with the exact analytical modeling of transfer phenomena in heterogeneous materials exhibiting one-dimensional continuous variations of their properties. Regarding heat transfer, it has recently been shown that by applying a Liouville transformation and multiple Darboux transformations, infinite sequences of solvable profiles of thermal effusivity can be constructed together with the associated temperature (exact) solutions, all in closed-form expressions (vs. the diffusion-time variable and with a growing number of parameters). In addition, a particular class of profiles, so-called ŝech-type profiles, exhibit high agility and at the same time parsimony. In this paper we delve further into the description of these solvable profiles and their properties. Most importantly, their quadrupole formulation is provided, enabling smooth synthetic profiles of effusivity of arbitrary complexity to be built, and allowing the corresponding temperature dynamic response to be obtained very easily thereafter. Examples are given with increasing variability of the effusivity and an increasing number of elementary profiles. These highly flexible profiles are equally relevant for providing an exact analytical solution to wave propagation problems in 1D graded media (i.e., Maxwell's equations, the acoustic equation, the telegraph equation, etc.). From now on, whether it be for diffusion-like or wave-like problems, when the leading properties present (possibly piecewise-) continuously heterogeneous profiles, the classical staircase model can be advantageously replaced by a "high-level" quadrupole model consisting of one or more ŝech-type profiles, which makes the latter a true Swiss-Army knife for analytical modeling.
This paper presents a series of new high-level analytical tools for the modeling of one-dimension... more This paper presents a series of new high-level analytical tools for the modeling of one-dimensional, transient or periodic, heat transfer in media presenting graded thermal properties (conductivity and/or specific heat), possibly in a layered configuration. They capitalize on a recent work on sequences of analytically solvable profiles and the related exact temperature solutions. These profiles describe the square root of thermal effusivity or its inverse; the independent variable is the square root of the integrated diffusion time along the considered path, as obtained after a Liouville transformation. The profiles addressed here are linear, hyperbolic or trigonometric functions of this variable. A systematic presentation is given on how to build these profiles in both partner forms, on the so-called Liouville inverse transformation to step back into the physical-depth space, and on the three quadrupole formulations. As compared to other graded profiles from the literature, the three transfer matrices are very easy to compute (only elementary functions are involved). The quadrupole approach is particularly suitable for modeling multilayers. We apply it to calculate the thermal response of a two-layer system with a graded coating of one or other of the three classes. The modulated and the transient regime have been considered. The ease of obtaining these results indicates that, upon proper arrangement, these three classes of solvable profiles may be used to compute the thermal response of continuously (or piece-wise continuously) heterogeneous media of arbitrary complexity (e.g., functionally graded materials). This also paves the way to new methods for photothermal inversion. Other research fields could benefit from these tools insofar as the evolution equation governing the observed phenomena involves variable coefficients (e.g., advection-diffusion equation, wave equation, etc.).
Proceedings of the 2000 International Conference on Quantitative InfraRed Thermography
Robin comparison II of the capabilities of various thermographic techniques in the detection of d... more Robin comparison II of the capabilities of various thermographic techniques in the detection of defects in carbon fibre composites', Paper presented at Quantitative Infrared Thermography (QIRT2000) Eurotherm Seminar 64,
Proceedings of the 1996 International Conference on Quantitative InfraRed Thermography
The amplitude and phase space distributions of EM (electromagnetic) fields (X-and Ku bands) are i... more The amplitude and phase space distributions of EM (electromagnetic) fields (X-and Ku bands) are imaged and measured using microwaves interferometry revealed by photothermal films and lock-in infrared thermography. Such EM fields imaging is a powerful tool for NDE (non Destructive Evaluation) of dielectric and radar absorbing materials.
Proceedings of the 1998 International Conference on Quantitative InfraRed Thermography
We present recent advances about the application of the photothermal camera for the detection of ... more We present recent advances about the application of the photothermal camera for the detection of cracks on metallic surfaces of industrial quality. We describe a normalization procedure designed to clean the photothermal images of the optical noise and thereby to increase the propability of detection of the cracks. A theoretical analysis about the spatial resolution of the photothermal camera is finally exposed.
Proceedings of the 1998 International Conference on Quantitative InfraRed Thermography
Results of inspecting an impact damaged carbon fibre composite specimen are reported. Several phy... more Results of inspecting an impact damaged carbon fibre composite specimen are reported. Several physical test procedures and processing .algorithms have been analysed within the framework of the international Round Robin Test. A statistical means for rating non-destructive testing techniques is proposed to convert otiginal infrared images to defect maps that are of special interest for end-users. The :potentials of the techniques for oharacterising shape and depth distribution of impact damage in carbon fibre composites are discussed, 'including comparison with ultrasonic C-scan results.
The Darboux transformation is a differential transformation which, like other related methods (su... more The Darboux transformation is a differential transformation which, like other related methods (supersymmetry quantum mechanics-SUSYQM, factorization method) allows generating sequences of solvable potentials for the stationary 1D Schrödinger equation. It was recently shown that the heat equation in graded heterogeneous media, after a Liouville transformation, reduces to a pair of Schrödinger equations sharing the same potential function, one for the transformed temperature and one for the square root of effusivity. Repeated joint PROperty and FIeld Darboux Transformations (PROFIDT method) then yield two sequences of solutions: one of new solvable effusivity profiles and one of the corresponding temperature fields. In this paper we present and discuss the outcome in the case of a graded half-space domain. The interest in this methodology is that it provides closed-form solutions based on elementary functions. They are thus easily amenable to an implementation in an inversion process aimed, for example, at retrieving a subsurface effusivity profile from a modulated or transient surface temperature measurement (photothermal characterization). arbitrary distributions, even in the one-dimensional (1D) case with respectively z c and z profiles. Until recently, exact analytical solutions were known only for a limited number of z c and z profiles or for diffusivity c z a and effusivity c z b profiles [1]-[9]. These solutions are available in closed-form in the Laplace or Fourier space (the corresponding property profiles will be called solvable profiles). In addition, series solutions were also proposed; they are either based on the use of the successive derivatives of conductivity [10], on the Generalized Integral Transform Technique (GITT) [11], or on the Spectral Parameter Power Series (SPPS) method [12]. Approximate methods were also developed which are restricted to the situations where the thermal properties variations are slow and/or of low amplitude ([2], [5], [13]-[15], just to name a few). Another type of approximate method consists in discretizing the domain and assuming that, in each interval, the property profile follows one of the solvable profiles mentioned before. The easiest way is of course to assume that the properties are constant in each interval. For reducing the model error one can either increase the number of intervals or select solvable profiles of higher order, e.g. linear profiles for conductivity or for effusivity. There is actually a need for solvable profiles that present a higher
Proceedings of the 2012 International Conference on Quantitative InfraRed Thermography, 2012
We first present a review of the so-called triangle/trapezoid method for soil moisture evaluation... more We first present a review of the so-called triangle/trapezoid method for soil moisture evaluation from optical remote sensing data obtained in the red, near infrared and thermal infrared bands. Recent improvements based on additional vegetation indexes obtained for example from multiwavelength signals in SWIR band will also be presented. In a second part we describe the results we obtained for this purpose by using a microbolometer camera onboard of a motorglider. Signal processing for atmosphere correction and orthorectification was specifically developed for this application. First results on the path for identification of soil water content with this approach will be presented.
Proceedings of the 1998 International Conference on Quantitative InfraRed Thermography, 1998
A theoretical analysis is presented about the performances of a series of four different algorith... more A theoretical analysis is presented about the performances of a series of four different algorithms for modulation thermography: standard lock-in method, 4-bucket method, variance method and leastsquares method. The precision on the amplitude and on the phase lag is evaluated versus the number of integrated images; depending on the input noise level, on the actual signal amplitude and on the quantisation level.
Dans les aciers cementes, la durete varie en raison inverse de la conductivite thermique. Cette c... more Dans les aciers cementes, la durete varie en raison inverse de la conductivite thermique. Cette correlation peut etre mise a profit pour elaborer une technique de determination indirecte du profil de durete. La methode d'evaluation que nous proposons a l'avantage d'etre rapide, non destructive et sans contact. Elle repose sur une technique photothermique : la surface est chauffee par un laser impulsionnel et l'on mesure l'evolution de la temperature a l'aide d'un detecteur infrarouge. Nous avons developpe une technique d'inversion pour extraire le profil d'effusivite thermique (ou de conductivite) a partir de l'evolution transitoire de la temperature de surface. La robustesse et la precision de la methode ont ete verifiees sur quelques profils theoriques simples. Des resultats experimentaux obtenus sur des aciers cementes durcis sur des epaisseurs variables sont finalement presentes ainsi que la correspondance avec le profil de durete obtenu p...
Remote Sensing for Agriculture, Ecosystems, and Hydrology XI, 2009
The triangle/trapezoid method is a well known method for retrieving spatialized soil moisture fro... more The triangle/trapezoid method is a well known method for retrieving spatialized soil moisture from remotely sensed temperature and vegetation index (NDVI). We selected three approaches with different requirements for ancillary data (triangle empirical method by Sandholt et al. [7], trapezoid method by Moran et al. [2], SVAT triangle method by Carlson et al. [3]-[6]). The empirical inversion is well suited
... 2). Infrared radiation from 175 Particle Fiber optic cable to coincidence sensor particle gas... more ... 2). Infrared radiation from 175 Particle Fiber optic cable to coincidence sensor particle gas inlet plasma torch # sh fiber optic cable to doublewavelength pyrometer Fig. ... optic cable from optic cable from coincidence head pyrometer head 1 2 Detection ii,! ...
The through-thickness thermal diffusivity can be evaluated by the classical flash method. If an h... more The through-thickness thermal diffusivity can be evaluated by the classical flash method. If an homogeneous and extended source is used to irradiate the surface and a thermographic camera is used to monitor the temperature evolution of the opposite side, a map of the through-thickness thermal diffusivity can be obtained in a single experiment and without any contact with the sample under inspection. In order to measure the in-plane thermal diffusivity of a plate-like sample or in one of the principal directions of its plane, a thermal gradient across the plane of the material has to be settled. The ratio of the Fourier transform of temperature at two different spatial frequencies is an exponential function of time multiplied by the diffusivity in the considered principal direction. This can be used to evaluate the diffusivity in an homogenous material. In order to maximise the signal-to-noise ratio, it is better if heat is absorbed over a series of periodic parallel strips (grid fla...
Reflective cavity pyrometers are increasingly used for on-line temperature sensing of metal sheet... more Reflective cavity pyrometers are increasingly used for on-line temperature sensing of metal sheets. The presence of the reflector increases the effective emissivity of the sheet, thus reducing the measurement error. Hemispherical geometries have been mostly used in the past for the reflector. This paper presents a Monte-Carlo analysis for a number of different cavity configurations. The value of the effective emissivity is evaluated for different cavity parameters and standoff range over the sheet as well as for different degrees of the metal sheet real emissivity. It will be shown, in particular, that a trucated hemisphere with centre of curvature belowthe sheet is preferable to the more conventional full hemisphere to reduce losses due to sheet fluttering. Applications to infurnace temperature monitoring of steel sheets will be indicated.
SUMMARY A thermographic technique to inspect structures using an internal perturbation source suc... more SUMMARY A thermographic technique to inspect structures using an internal perturbation source such as a sudden change of the liquid temperature flow is presented. After a brief survey of the apparatus the technique is applied to detect wall thickness loss due to cavitation corrosion in liquid or gas carrying pipes. The same technique was used to reveal the internal structure of turbine blades after proper image processing.
Vegetation and soil temperatures have long been recognized as an indicator of water availability.... more Vegetation and soil temperatures have long been recognized as an indicator of water availability. When plotting the twodimensional distribution of temperature and vegetation index (T-VI) corresponding to an area with well distributed vegetation cover and moisture content, one gets a triangular or trapezoidal shape. Iso-moisture lines range between two edges of the distribution: the dry edge and the wet edge. This description is based on a simplified representation of the thermal and radiative properties of the soil/ ...
The triangle/trapezoid method is a well known method for retrieving spatialized soil moisture fro... more The triangle/trapezoid method is a well known method for retrieving spatialized soil moisture from remotely sensed temperature and vegetation index (NDVI). We selected three approaches with different requirements for ancillary data (triangle empirical method by Sandholt et al.[7], trapezoid method by Moran et al.[2], SVAT triangle method by Carlson et al.[3]-[6]). The empirical inversion is well suited when no information on meteorological data is available.
This work deals with the exact analytical modeling of transfer phenomena in heterogeneous materia... more This work deals with the exact analytical modeling of transfer phenomena in heterogeneous materials exhibiting one-dimensional continuous variations of their properties. Regarding heat transfer, it has recently been shown that by applying a Liouville transformation and multiple Darboux transformations, infinite sequences of solvable profiles of thermal effusivity can be constructed together with the associated temperature (exact) solutions, all in closed-form expressions (vs. the diffusion-time variable and with a growing number of parameters). In addition, a particular class of profiles, so-called ŝech-type profiles, exhibit high agility and at the same time parsimony. In this paper we delve further into the description of these solvable profiles and their properties. Most importantly, their quadrupole formulation is provided, enabling smooth synthetic profiles of effusivity of arbitrary complexity to be built, and allowing the corresponding temperature dynamic response to be obtained very easily thereafter. Examples are given with increasing variability of the effusivity and an increasing number of elementary profiles. These highly flexible profiles are equally relevant for providing an exact analytical solution to wave propagation problems in 1D graded media (i.e., Maxwell's equations, the acoustic equation, the telegraph equation, etc.). From now on, whether it be for diffusion-like or wave-like problems, when the leading properties present (possibly piecewise-) continuously heterogeneous profiles, the classical staircase model can be advantageously replaced by a "high-level" quadrupole model consisting of one or more ŝech-type profiles, which makes the latter a true Swiss-Army knife for analytical modeling.
This paper presents a series of new high-level analytical tools for the modeling of one-dimension... more This paper presents a series of new high-level analytical tools for the modeling of one-dimensional, transient or periodic, heat transfer in media presenting graded thermal properties (conductivity and/or specific heat), possibly in a layered configuration. They capitalize on a recent work on sequences of analytically solvable profiles and the related exact temperature solutions. These profiles describe the square root of thermal effusivity or its inverse; the independent variable is the square root of the integrated diffusion time along the considered path, as obtained after a Liouville transformation. The profiles addressed here are linear, hyperbolic or trigonometric functions of this variable. A systematic presentation is given on how to build these profiles in both partner forms, on the so-called Liouville inverse transformation to step back into the physical-depth space, and on the three quadrupole formulations. As compared to other graded profiles from the literature, the three transfer matrices are very easy to compute (only elementary functions are involved). The quadrupole approach is particularly suitable for modeling multilayers. We apply it to calculate the thermal response of a two-layer system with a graded coating of one or other of the three classes. The modulated and the transient regime have been considered. The ease of obtaining these results indicates that, upon proper arrangement, these three classes of solvable profiles may be used to compute the thermal response of continuously (or piece-wise continuously) heterogeneous media of arbitrary complexity (e.g., functionally graded materials). This also paves the way to new methods for photothermal inversion. Other research fields could benefit from these tools insofar as the evolution equation governing the observed phenomena involves variable coefficients (e.g., advection-diffusion equation, wave equation, etc.).
Proceedings of the 2000 International Conference on Quantitative InfraRed Thermography
Robin comparison II of the capabilities of various thermographic techniques in the detection of d... more Robin comparison II of the capabilities of various thermographic techniques in the detection of defects in carbon fibre composites', Paper presented at Quantitative Infrared Thermography (QIRT2000) Eurotherm Seminar 64,
Proceedings of the 1996 International Conference on Quantitative InfraRed Thermography
The amplitude and phase space distributions of EM (electromagnetic) fields (X-and Ku bands) are i... more The amplitude and phase space distributions of EM (electromagnetic) fields (X-and Ku bands) are imaged and measured using microwaves interferometry revealed by photothermal films and lock-in infrared thermography. Such EM fields imaging is a powerful tool for NDE (non Destructive Evaluation) of dielectric and radar absorbing materials.
Proceedings of the 1998 International Conference on Quantitative InfraRed Thermography
We present recent advances about the application of the photothermal camera for the detection of ... more We present recent advances about the application of the photothermal camera for the detection of cracks on metallic surfaces of industrial quality. We describe a normalization procedure designed to clean the photothermal images of the optical noise and thereby to increase the propability of detection of the cracks. A theoretical analysis about the spatial resolution of the photothermal camera is finally exposed.
Proceedings of the 1998 International Conference on Quantitative InfraRed Thermography
Results of inspecting an impact damaged carbon fibre composite specimen are reported. Several phy... more Results of inspecting an impact damaged carbon fibre composite specimen are reported. Several physical test procedures and processing .algorithms have been analysed within the framework of the international Round Robin Test. A statistical means for rating non-destructive testing techniques is proposed to convert otiginal infrared images to defect maps that are of special interest for end-users. The :potentials of the techniques for oharacterising shape and depth distribution of impact damage in carbon fibre composites are discussed, 'including comparison with ultrasonic C-scan results.
The Darboux transformation is a differential transformation which, like other related methods (su... more The Darboux transformation is a differential transformation which, like other related methods (supersymmetry quantum mechanics-SUSYQM, factorization method) allows generating sequences of solvable potentials for the stationary 1D Schrödinger equation. It was recently shown that the heat equation in graded heterogeneous media, after a Liouville transformation, reduces to a pair of Schrödinger equations sharing the same potential function, one for the transformed temperature and one for the square root of effusivity. Repeated joint PROperty and FIeld Darboux Transformations (PROFIDT method) then yield two sequences of solutions: one of new solvable effusivity profiles and one of the corresponding temperature fields. In this paper we present and discuss the outcome in the case of a graded half-space domain. The interest in this methodology is that it provides closed-form solutions based on elementary functions. They are thus easily amenable to an implementation in an inversion process aimed, for example, at retrieving a subsurface effusivity profile from a modulated or transient surface temperature measurement (photothermal characterization). arbitrary distributions, even in the one-dimensional (1D) case with respectively z c and z profiles. Until recently, exact analytical solutions were known only for a limited number of z c and z profiles or for diffusivity c z a and effusivity c z b profiles [1]-[9]. These solutions are available in closed-form in the Laplace or Fourier space (the corresponding property profiles will be called solvable profiles). In addition, series solutions were also proposed; they are either based on the use of the successive derivatives of conductivity [10], on the Generalized Integral Transform Technique (GITT) [11], or on the Spectral Parameter Power Series (SPPS) method [12]. Approximate methods were also developed which are restricted to the situations where the thermal properties variations are slow and/or of low amplitude ([2], [5], [13]-[15], just to name a few). Another type of approximate method consists in discretizing the domain and assuming that, in each interval, the property profile follows one of the solvable profiles mentioned before. The easiest way is of course to assume that the properties are constant in each interval. For reducing the model error one can either increase the number of intervals or select solvable profiles of higher order, e.g. linear profiles for conductivity or for effusivity. There is actually a need for solvable profiles that present a higher
Proceedings of the 2012 International Conference on Quantitative InfraRed Thermography, 2012
We first present a review of the so-called triangle/trapezoid method for soil moisture evaluation... more We first present a review of the so-called triangle/trapezoid method for soil moisture evaluation from optical remote sensing data obtained in the red, near infrared and thermal infrared bands. Recent improvements based on additional vegetation indexes obtained for example from multiwavelength signals in SWIR band will also be presented. In a second part we describe the results we obtained for this purpose by using a microbolometer camera onboard of a motorglider. Signal processing for atmosphere correction and orthorectification was specifically developed for this application. First results on the path for identification of soil water content with this approach will be presented.
Proceedings of the 1998 International Conference on Quantitative InfraRed Thermography, 1998
A theoretical analysis is presented about the performances of a series of four different algorith... more A theoretical analysis is presented about the performances of a series of four different algorithms for modulation thermography: standard lock-in method, 4-bucket method, variance method and leastsquares method. The precision on the amplitude and on the phase lag is evaluated versus the number of integrated images; depending on the input noise level, on the actual signal amplitude and on the quantisation level.
Uploads
Papers by J. Krapez