In Search of Early Time : An Original Approach in the Thermographic Identi�cation of Thermophysical Properties and Defects

Active thermography gives the possibility to characterize thermophysical properties and defects in complex structures presenting heterogeneities. e produced thermal �elds can be rapidly 3D. On the other hand, due to the size of modern thermographic images, pixel-wise data processing based on 1Dmodels is the only reasonable approach for a rapid image processing.eonlyway to conciliate these two constraints when dealing with time-resolved experiments lies in the earlier possible detection/characterization. is approach is illustrated by several different applications and compared tomore classical methods, demonstrating that simplicity of models and calculations is compatible with e�cient and accurate identi�cations.


Introduction
e evolution of thermophysical properties metrology and nondestructive evaluation (NDE) is characterized by the increased use of re�ned inverse techniques �1] requiring the establishment of models taking into account many parameters, although among these parameters oen only one parameter is of interest for the experimenter.is complexity is particularly important when the analyzed thermal �elds are 3D, a situation characteristic of the experiments realized with thermographic systems producing sequences of large thermal images of complex structures presenting important heterogeneities in their thermal properties, internal geometries, and boundary conditions.is approach leads to time-consuming calculations that may be prohibitive for thermographic data processing.Furthermore, it happens that in many situations the reality remains more complex than the sophisticated model used.
How to conciliate the existence 3D thermal situations involving numerous parameters and the necessity to have rapid calculations compatible with the very high number of information to process in a thermographic image sequence?
A solution lies in the use of 1D thermal models for pixelwise data processing and the choice of a limited early time domain (for time-resolved techniques) or high frequency domain (for modulated techniques) for which the measured temperatures are essentially depending on the sole parameter to be identi�ed and weakly affected by the 3D heat transfer.To achieve that, the proposed approach consists in performing the identi�cation at the earlier possible time (or at the higher possible frequency) aer the thermal stimulation.Here, we will mainly consider time-resolved techniques and early time detection (emerging signal).
e present work wants to show the following.
(i) A detailed procedure can be de�ned for early detection and characterization (see Section 2).(ii) at this approach is not new.In a �rst step, it has been applied in the �eld of thermophysical properties measurements (period 1970-1990).is review is the subject of Section 3. (iii) e application to NDE, started at the beginning of the 90's, continues to give rise to new developments (Section 4).

Application in the Field of Thermophysical Properties Measurements
e early detection approach de�ned in Section 2 is illustrated in Section 3.1 in the case of a simple con�guration (rear face �ash diffusivity experiment), universally known under the name of Parker's method [2], applied to the diffusivity measurement of an homogeneous slab.In Section 3.2, a more complex procedure is presented dealing with the same type of experiment (rear face �ash diffusivity), identifying the in situ diffusivities of the components (matrix and reinforcement) of a 3D C/C composite and the thermal contact resistance characterizing the interface between them.

Rear Face Flash Diffusivity Measurement.
In �ash thermal diffusivity measurements on the face opposite to the pulsed heat deposition the sample heat losses distort the rear face temperature time history.ese thermal losses occurring necessarily a�er the �ash, the temperature is all the less disturbed as time is nearer the origin.Consequently, the diffusivity identi�cation by extrapolating towards the initial time the apparent diffusivity-versus-time history resulting from the use of an adiabatic solution was proposed in 1982 ) F 1: Test no. 2 on plaster identi�ed apparent diffusivity law and regression parabola with a uniform weight and with a nonuniform weight linked to the accuracy of the measurement, taken from [4].[3,4].It was demonstrated that the early phase of the thermogram (for instance for a defect Fourier number Fo  =  2  < 0.1, where  is the diffusivity of the material and   the defect depth) may be used for this early detection if an estimate of the �nal adiabatic temperature increase, Δ lim , is deduced without any assumption concerning the heat losses from the maximum temperature reached with losses, Δ max .A relation between these two parameters was proposed where  max and  12 are, respectively, the measured occurrence times of the maximum and half maximum temperature increase at the center of the sample.is relation allows to normalize the thermogram: ΔΔ lim = ΔΔ max × Δ max Δ lim , and using a look-up table to build an apparent diffusivity curve, , from the analytical solution for the 1D rear face adiabatic sample submitted to a pulsed stimulation.Whatever is the accuracy of the estimated Δ lim , it was veri�ed that the law  starts at  = 0 from the actual diffusivity value, and that if the estimation is sufficiently accurate, the apparent diffusivity evolution in the early times Fo  < 0.1 can be approximated by a parabolic law whose peak is obtained for  = 0. To improve the accuracy of the parabolic �tting using least mean squares, the experimental points were weighted by the accuracy of the diffusivity measurement deduced from the a sensitivity analysis.It was imposed to the parabola to have a zero slope at  = 0. Figure 1 presents, taken from [4], the extrapolation in the case of a measurement on a 10 mm thick disk-shaped plaster sample, with a radius over thickness ratio  = 1.206.An extrapolated value of diffusivity is found 3.65⋅10 −7 m 2 s −1 .
Table 1 summarizes the diffusivity results obtained by this method and compares them to results obtained with exactly the same samples by three methods (round robin tests) as follows.(ii) e more precise method at the time of the publication of the present method: the partial times method of Degiovanni [5].e method of partial times considers for the identi�cation several pairs of points of the thermogram corresponding to the following normalized temperature increases ΔΔ max : 1/3 and 5/6, 1/2 and 5/6, 2/3 and 5/6.It is interesting to compare the Degiovanni's method with the present early detection approach because, as shown in Figure 2, the extrapolation method results are coherent with the evolution with time of the identi�ed diffusivities of the points considered in the data processing of the Degiovanni's partial times method.We see that the present method corrects the bias of this method, which increases with identi�cation times.
(iii) e method of partial moments, proposed by Degiovanni [6] that is still considered as a reference.ere is a perfect agreement with this method.e results of the partial moments are not plotted in Figure 2 because they would not be distinguishable from those of the present method.

Rear Face Flash Measurement of the In Situ Diffusivities of the Components of Periodic
Directional-Reinforced Composites

Periodic Directional Reinforced Composites (PDRCs).
e types of materials here considered are PDRCs (periodic directional reinforced composites) in which the reinforcement is arranged following preferential directions.For instance, unidirectional carbon/epoxy composites and 3D carbon/carbon composites belong to this family of materials and the identi�cation method here presented can be applied to them.ese materials are difficult to homogenize when there is a large difference between the thermal conductivities of the composite components (matrix and reinforcement) and when the main heat transfer is parallel to a reinforcement direction [7].
Considering the same type of measurements as in the previous section (rear face �ash diffusivity), a more complex procedure is presented, which identi�es the in situ diffusivities of the matrix and reinforcement and the thermal contact F 2: Compared results of Degiovanni's partial times method and present method, taken from [4].
resistance characterizing the interface between them in the case of a 3D C/C composite [8][9][10].e method supposes that the composite sample is quasi adiabatic (no heat losses).e simplest PDRCs that can be imagined are presented in Figure 3. ey are unidirectional PDRCs.e two components are arranged in alternated slabs parallel to the imposed heat �ux (Figure 3(a)) or following a chessboard pattern (Figure 3(b)).e dimensional geometric parameters are the space period of the pattern, , the thickness of the medium, , and the volume ratio of the components (  ).For these �rst two composites  1   2  5.e more thermally conductive component is supposed to be the reinforcement, since it is usually the case (i.e., in C/epoxy or C/C composites).
A slightly more general arrangement for 1D PRDC is given in Figure 4(a).Figure 4(b) corresponds to a more realistic arrangement representative of carbon/epoxy composite and Figure 4(c) to a 3D C/C material with orthogonal    reinforcements.
Based on numerous numerical simulations [9], it has been demonstrated that the transient thermal behavior of 1D  PDRCs, when considering the mean temperature evolution,  depends only on �ve nondimensional parameters: (i) volume content of the reinforcement,   ; (ii) the reinforcement-to-matrix ratio of thermal conductivities,   =     ; (iii) the reinforcement-to-matrix ratio of volume speci�c heats,   =     ; (iv) the speci�c contact surface between reinforcement and matrix per unit surface of composite:  = , where  is the sample thickness, and  the speci�c contact surface between reinforcement and matrix per unit volume, parameter which depends on the shape of the section of the reinforcement; (v) the speci�c contact thermal resistance between reinforcement and matrix:  =   ,  being the contact thermal resistance of the interface.
is mean temperature  is easily measured by using IR radiometer or thermography if the emissivity of the surfaces are homogenized by a black coating insuring uniform emissivity.

�.�.�. �rinciple of the �denti�cation of the Reinforcement Diffu� sivity and Homogenized Diffusivity from the Time Evolution of the Rear Face Mean Temperature 𝑇𝑇𝑇𝑇𝑇𝑇 in the Case of 1D DRC.
Let us consider a 1D PDRC with a periodic pattern such as those of Figures 4(a) and 4(b).A typical mean temperature evolution of the rear face of the sample in �ash diffusivity measurement is given in Figure 5(a) and compared to the theoretical response of a homogeneous material.
At the beginning, the energy that arrives at the rear face of a sample of thickness  has travelled through the more conductive component of the PDRC, here the reinforcement.If the identi�cation is performed for each and every points of the curve, the identi�ed diffusivity varies with time and the earlier the considered point, the nearer of the reinforcement diffusivity it is.us, following the early detection approach, by �tting the early part of the apparent diffusivity law and extrapolating it to zero time, an estimate of the reinforcement diffusivity is reached.is diffusivity is depending on  ( )    ⟶   () . ( Using several samples of different thicknesses the law   () can be extrapolated to zero thickness and the soextrapolated diffusivity can be considered as the best possible estimate of the reinforcement diffusivity   ()    ⟶   . ( On the contrary, the energy arriving at the end of the experiment can be considered as representative of a partially homogenized material.In effect, for long times, 3D heat transfers have enough time to become important and homogenize the temperature of the two components (reinforcement and matrix).ese 3D effects, which are generally considered as a disturbing phenomenon, have in the present case a bene�cial role, becoming a source of information about the material.e identi�ed diffusivity law presents a �nal asymptote that can be considered as an approximate estimate of the fully homogenized material  ( )    ⟶  () .
(4) anks to the series of measurements performed with the different samples of various thicknesses, the law of partially homogenized diffusivity versus thickness can be extrapolated to an in�nite thickness and the so-extrapolated value can be considered as the best estimate of the diffusivity of the fully homogenized material equivalent to the composite  ()    ⟶ . ( In a third step, with a few assumptions which depends on the considered composite, from   and , it is possible to deduce the value of the diffusivity of the less conductive component (generally the matrix),   , and the thermal resistance, , characterizing the interface between the two components (see in particular [10,12,13]).

Application to 3D C/C
Composites. e method has been applied to two 3D C/C composites in which the reinforcement is constituted of bundles of carbon �bers highly anisotropic and highly axially conductive, oriented in the three Cartesian directions   .
e �rst step consists to consider the 1D PDRC model of Figure 4(a) as an approximation equivalent to the 3D PDRC of Figure 4(c) in the case of the 3D C/C composite, considering that, due to the anisotropy of the reinforcement and the same chemical nature of the matrix and the reinforcement, it is possible to replace the actual matrix and the transverse reinforcement (following  and  directions) by an equivalent matrix.e identi�cation procedure of �ection 3.2.2 is then applied to this 1D PDRC.e operation can be repeated with the two other orientations of the samples to obtain the diffusivity of the three reinforcements if the composite is not equilibrated.
Figure 6 presents the experimental thermograms obtained for the 3D C/C no. 3 the �ux being parallel to the -reinforcement.ey are compared to the thermograms of the equivalent homogenized material with the identi�ed homogenized diffusivity, , and the thermograms calculated using the equivalent 1D PDRC model with the identi�ed parameters.e identi�ed parameters are presented in Table 2 for two materials (3D C/C no. 1 and 3D C/C no. 3 for two orientations).ese results show that even for a coupon thickness of 8.2 mm, the material transient behavior is not exactly that of a homogeneous material.is thickness, knowing that the -space period is 0.8 mm, represents ten times the space period.ese results were obtained with an IR radiometer viewing an area of the rear face much larger than a mesh of material to obtain a mean temperature measurement.It could be easily performed with an IR camera.
e main merit of the method is the fact that the measured properties are relative to in situ materials, which is of prime importance since the material process has a strong in�uence on the resulting �nal thermal properties of the product, in particular the axial diffusivity of the reinforcement.

Complementarity of Front-Face and Rear Face Pulse
Measurements.e front-face and rear face pulse experiments are complementary [14].In effect, let us apply the zerotime extrapolation to the apparent diffusivity identi�ed from the rear face mean-temperature time evolution (see Figure 7(a)) and to the apparent effusivity identi�ed from the frontface mean-temperature time evolution (see Figure 7(b)).ese operations permit, respectively, the identi�cation of characteristic thermal properties of the reinforcement parallel to the �ux (longitudinal diffusivity) and of the equivalent matrix resulting from the homogenization of the matrix (isotropic effusivity) and of the two reinforcements perpendicular to the heat �ux (radial effusivity).In other words, at the beginning of the pulse experiments, on the front-face the heating is driven by the less conductive component of the composite and on the rear face by the more conductive component.

Application to Nondestructive Evaluation (NDE)
4.1.Notion and Interest of the Emerging Contrast.For NDE, the experimental data from which defect parameters can be identi�ed are not thermograms (temperature increase, a function of time: Δ            0) but the time evolution of the contrasts between the temperature rise of a defective zone and the one of a sound zone taken as a reference,     Δ     Δ    /Δ    ).Consequently, the early detection approach in NDE consists in exploiting the contrast when it is just emerging from the noise, reason why we proposed to call it "the emerging contrast." Figure 8 presents the principle of the detection of the emerging contrast.is attitude is contrary to common practice.In effect, traditionally, pulse thermography users favored the maximum contrast to identify the depth and thermal resistance of defects, starting from the a priori justi�ed reason that it corresponds to the best SNR.is choice, which could be understood when the performances of cameras were limited (NETD ≥ 100 mK), is unfortunate and inappropriate.Nevertheless, it is still used by most of the users of the pulse technique.e early detection approach by the use of the emerging contrast is an efficient alternative that deserves to be promoted, as it will be demonstrated here.

"Universality" of the Emerging Contrast (Pulse ermography)
. �et us consider the simple 1D con�guration of a thermally imperfect interface (thermal resistance) inside two layers of solid materials.e interface is characterized by an extrinsic parameter, its location depth,   , and by an intrinsic thermal property, its thermal resistance,   .If    0, the structure is considered as sound and if   > 0, it is considered as being defective, with a resistive defect which has to be detected and characterized.e problem is that the time-evolution of Cr depends on a large number of factors: the depth   , the thermal resistance,   , but also the total thickness of the structure, , the thermal properties of the two layers effusivities and diffusivities, and the boundary conditions characterized by heat transfer coefficients ℎ.
Figure 9 presents the wide variety of contrast evolutions that can be encountered.ese data are the synthesis of simulation results taken from [15].All parameters are nondimensional and the graph is in log-log scales to conveniently show the various time scales.e possible domain in which the contrast may evolve, here lightly coloured in grey, is enormous, and it is obvious that to solve the inverse problem it is necessary to rely on a model taking into consideration all the aforementioned parameters.
A simple explicit expression relating the time of occurrence and the amplitude of the maximum relative contrast, a universally known and used approach, cannot be a priori T 2: In situ identi�ed thermal properties of two 3D C/C composites, taken from [10].F 7: Compared mean temperature time histories of the front-and rear faces in the case of the 3D C/C #3// and comparison to the calculated thermograms corresponding to the thermal properties of the bulk reinforcement (longitudinal properties), bulk equivalent matrix, and fully homogenised composite, taken from [14].

Identi�ed thermal parameters
satisfying when one considers the wide scatter existing on these two parameters.Nevertheless, the main lesson which can be drawn from this graph is the existence, at the origin, of a narrow tailshaped domain in which all curves merge, thus where a unique correlation between the relative contrast Cr and the defect Fourier number Fo  can be used for the identi�cation of the defect depth whatever is the thermal resistance and the other already mentioned parameters.
If we suppose that one can evaluate the occurrence time of a contrast of 1%, the maximum error on the identi�ed depth is ±7%.Of course an earlier identi�cation, based on a still lower contrast, leads to a more precise identi�ed depth.e aim to be reached is clear; the problem is in the way to practically achieve the required experimental accuracy.
is simple example illustrates the main virtue of the emerging contrast: the "universality" of its applicability.Another illustration of this universality is given by the following study of the characterization of a defect embedded at different depths in a slab of a homogeneous sample.Let us consider a slab of thickness , with a 1D defect located at the depth   and characterized by a thermal resistance   .For such a defect embedded in a semi-in�nite medium, the thermal contrast associated with the 1D defect is depending on two non dimensional parameters: the Fourier number related to the defect depth,   =  2   , and the non dimensional thermal resistance  * =   (  , the ratio of the defect thermal resistance to the one of the material layer in between the defect and the front-surface (see for instance [16,17].In these expressions,  and  are, respectively, the diffusivity and the thermal conductivity of the material in between the monitored surface and the defect.In the case of a slab, the situation is more complex as seen in Figure 10(a).is Figure presents the Fourier-evolution of the relative contrast for various values of the normalized defect depth,   , and for  * = 1.Similar (but different) nets would be obtained for other values of this last parameter.e shape of the contrast curves presents a maximum highly dependent on  * and    parameters.e in�uence of the rear face "echo" gains in importance with increasing    and drastically decreases the amplitude of the relative contrast when the defect is approaching from this rear face, making the detection more and more problematic.Like in Figure 9, the large spreading of the net is converging to a narrow "tail" in which all curves merge for early times when the contrast is emerging form the noise.us, considering the emerging contrast domain (  < 0.5 and Cr of a few percents), for identi�cation purpose, we can use the unique curve Cr (  ,  * = 1 corresponding to the case of the defect embedded in a semi-in�nite medium, for which there is no rear face re�ection (see Figure 10(b)).

�denti�cation Based on Emer�in� Contrast Needs Sim� pler Model than at Based on Maximum Contrast. Figure 10(b) presents the emerging contrast domain taken from
Figure 10(a) and compares the contrast curves net to the two grey dotted curves of relative contrast related to the defects of in�nite thermal resistance and  * = 1 in a semi-in�nite medium, curves taken from [19,20].We see that this second curve remains near of the curves of the net for contrast of a few percents when    is smaller than 0.8.is means that we can use the semi-in�nite medium solution Cr (  ,  *  for identifying the depth and thermal resistance of a defect in this early time domain, instead of using a Cr (  ,  * ,   ) function.

Early Detection and Characterization Lead to Less
Blurred �ma�es and More Accurate �denti�ed Defect �aram� eters.Both Figures 9 and 10 show that the gain in precociousness of the identi�cation when going from maximum contrasts to emerging contrasts can be very important (up to one order of magnitude).is gain is important since less time is given to 3D internal heat diffusion effects.is means from a qualitative point of view that the defect images will be less blurred, an important quality that increases the detectivity of the method, and quantitatively this produces a gain in accuracy for the identi�ed parameters.is has been demonstrated in [19,20].

Rapid Survey of the Early Detection and Characterization
Approach in the NDE Literature.At the beginning of the 90's, the attention of several authors was drawn to the fact that it would be better to consider the contrast at its beginning to achieve an early detection.
e idea of an early identi�cation of the defect depth,   , from the emerging contrast time was �rst formulated by Bontaz [21,22] who proposed the following empirical relation: where  0 is the origin time of the contrast, called by the authors the "divergence" time.is relation can be formulated using the defect Fourier number e weakness of this approach was double: (i) the relation between defect depth and divergence time was totally empirical and no precise procedure was proposed since the emergence had to be localized by the simple examination of the contrast curve without any indication given concerning the relative contrast value to consider for this determination of  0 ; (ii) for the thermal resistance,   , the identi�cation was similar to the temporal moment approach already proposed for diffusivity identi�cation by Degiovanni [6], and for defect characterization by Balageas et al. [23], and was based on the use of the time integral of the full contrast from its origin to its extinction, then comprising data related to high Fourier numbers and consequently corrupted by 3D conduction effects.
Finally, Krapez et al. [18,24,25] kept the idea of performing the identi�cation as early as possible with the emerging contrast, but developed a precise methodology contrast, for   / < 0.9 In the region the semiinfinite medium model can be used for the relative F 9: e virtues of the emerging contrast: universality, precociousness, and simple modeling.Comparison to the maximum contrast.
for the identi�cation leading to propose explicit analytical formulas for identifying both depth and thermal resistance of a defect expressions in which Cr() is the relative contrast measured at time , and   and   are, respectively, the thermal conductivity and thermal diffusivity of the material between the monitored surface and the defect.e identi�cation was achieved in two steps.e �rst relation was used for relative contrasts near of 1 to 3% and once the defect depth identi�ed, the second formula was used for identifying the thermal resistance for slightly larger contrast (3 to 6%).In parallel to this research, another way to perform early detection was explored.Almond et al. [26,27] found from numerical simulations and from experiments on a sample with arti�cial defects of same thermal resistance, located at the same depth, but with different sizes, that the "thermal contrast slope at the beginning" was independent of the size of the defect and just related to the defect depth.He suggested that the "short-time slope" of the contrast-time curve can be used to assess the defect depth rather than the peak time (time of the maximum contrast).omas, Favro and coll [28][29][30], and Ringermacher et al. [31] proposed to use the time of occurrence of the "peak slope" of the contrast to identify the Recently, Sun [32] studied quantitatively the relation between the contrast slope peak time,  ps , and the defect depth using a normalized time  def =  2  def =  2  ps / 2 def.�is study, limited to the case of an in�nite defect thermal resistance (case of a hole machined in a slab), shows that the maximum slope is reached for a  def = 0.368, which allows to identify the defect depth

Advances in Optical Technologies
Nevertheless, this relation is only valid when the relative depth (ratio of the defect depth to the total sample thickness) is lower than 0.5.For higher values, the characteristic Fourier number is a strong function of the normalized defect depth, decreasing continuously down to 0.25 for a defect approaching the sample rear face.is approach, although constituting a progress compared to the use of the occurrence time of the maximum contrast, is not as interesting as the early detection from the emerging contrast because the contrast slope peak occurs later than the emergence of the contrast ( def = 0.368 instead of  def = 0.159 for the Bontaz method, see ( 7)).

Recent Developments in Early Detection and
Characterization of Defects 4.3.1.Improvement of the Emerging Contrast Technique by Linear Extrapolation to Nill Contrast.Balageas [19,20] recently reworked the method developed in the 90's [18,24,25], following rigorously the early detection procedure described in Section 2 and using the identi�cation formulas (8).In particular, he proposed and experimentally validated the extrapolation to zero contrast of the law of the identi�ed defect depth as a function of the contrast.By this way, the most accurate estimate of the defect depth is obtained.A relation between the error on the so-identi�ed defect depth and the value of the defect thermal resistance is found, allowing to correct the �rst estimate of the defect depth once estimated the thermal resistance, which improves the accuracy of the method.e early detection approach using the described procedure allows to reach the optimum accuracy on both the depth and the thermal resistance of defects: between 0.1% and 10% for the depth, and less than 30% for the thermal resistance (see Figure 11).e values of accuracy here given are intrinsic to the method and do not include the in�uence of the experimental noise and the 3D heat transfer effect linked to the limited extent of defects.e experimental noise can be reduced with the modern thermographic cameras characterized by an NETD of 20 mK or less, and by the use of a preprocessing technique of the thermograms such as the TSR method (see following Section).

Improvement of the Emerging Contrast Technique by the Combined Use of the ermographic Signal Reconstruction
Technique (TSR).e TSR method [33][34][35][36][37], well known and largely used in pulse thermographic NDE, consists in the �tting of the experimental log-log plot thermogram by a logarithmic polynomial ln (Δ) =  0 +  1 ln () +  2 [ln ()] 2 ⋯ +   [ln ()]  , (10) and the use for NDE purpose of the 1st and 2nd logarithmic derivatives of the thermogram, the derivation being achieved directly on the polynomial, then with a limited increase of the temporal noise.
e advantages of the �tting are as follows: (i) a noticeable noise reduction; (ii) the replacement of the sequence of temperature rise images, Δ(, , ), by the series of ( + 1) images of the polynomial coefficients, F 11: Simulation results: (a) identi�cation of the depth pro�le of a circular defect (  /  = 1.5 and   * =     /  = 1) using the early detection/characterization with extrapolation to zero contrast and comparison to the results obtained with the maximum and half maximum contrast techniques (simulation results taken from Krapez and Balageas [18]), revisited using a linear extrapolation [19,20]; (b) identi�cation of the thermal resistance pro�le, taken from [20].
0 ( )     ( ), which allows a drastic reduction of the data amount; (iii) the possibility of reconstructing a full thermographic sequence (from which the name of the method follows).e logarithmic derivations are interesting too, because they produce a remarkable increase of detectivity and a "precession" of the detection [19,20], which improve the precociousness of the defect detection.
So, it is easy to understand that both methods (early detection by emerging contrast and TSR) pursue identical purposes, and that consequently coupling them is bene�cial.e increase of signal-to-noise ratio (SNR) given by the logarithmic �tting is particularly welcome since experimental crude thermal contrasts may have weak SNR, especially when deep defects are considered.In this case, the TSR technique is used as a preprocessing tool before application of the early detection process.An example of such a coupling is shown in [20].
A deeper coupling could be used, consisting in considering the emerging contrast of the 1st or 2nd logarithmic derivatives instead of the emerging contrast of the thermogram itself for the characterisation of the defect.Such an early detection method, which remains until now to be established regarding the quantitative identi�cation of the defect parameters, is better than the one based on the half-rise time of the �rst derivative or the time of the maximum of the second derivative.Nevertheless, if the sole qualitative aspect is considered (detection of defects from thermographic images), the use of early images of the �rst and second logarithmic derivatives produces sharper defect images, a noticeable improvement compared to traditional maximum contrast images.Figure 12, taken from [19], demonstrates the ability of this approach to produce images with good SNR and high sharpness, making the pulse thermographic NDE technique comparable to the better-established techniques, in particular ultrasonics.

Application of the Early Detection and Characterization of Defects to
Step-Heating ermography.e early detection and characterization approach based on the emerging contrast has been extended to step-heating thermography, leading to comparable improvements.e theory is given in [38], leading to identi�cation formulas for defect depth and thermal resistance analogous to the ones found for pulse heating experiments (8).

Conclusion and Perspectives
A review of the literature of the early time detection approach in the �eld of thermophysical properties measurements and NDE has been made.is approach has been built progressively and never presented as a well-de�ned general procedure.is is due to the fact that the applications of the method were spread in time (3 decades) and pertaining to di�erent �elds.�utting these works in perspective, it has been possible to describe and formalize the general procedure here called "the early detection and characterization." In the �eld of thermophysical properties measurements, two examples of �ash di�usivity identi�cation using rear face thermograms have been presented.ey illustrate the philosophy of the approach and are well suited to thermography.is paper demonstrates that in NDE by pulse-stimulated thermography, the generally followed attitude that consists in taking into account the sole signal-to-noise ratio when optimizing an identi�cation process is an error.e optimization The artificial defect Unexpected defects must consider with the same weight the signal-to-noise ratio and the precociousness for both qualitative and quantitative purposes.
A way to conciliate both signal-to-noise ratio and precociousness is now more easily feasible by combining the early detection/characterization and the thermographic signal reconstruction (TSR) technique.Presently, this combination has given rise to recent developments in the �eld of NDE, increasing the attractiveness of time-resolved thermography.

F 5 :
In situ characterization of a 1D PDRC.Principle of the early time and later time identi�cations (a), followed by spatial extrapolations to zero and in�nite sample thicknesses (b).
Normalizied rear-face temperature increase, Δ/Δ lim Time,  (s) Homogeneous medium with diffusivity  1-D directional reinforced composite equivalent to the 3-D C/C with the identified parameters:   ,   and  F 6: Normalized experimental pulse diffusivity rear face thermograms (mean temperature) obtained with a series of 3D C/C coupons of different thicknesses.Comparison to the homogeneous medium solution with the identi�ed homogenized diffusivity, , and to the 1D directional reinforcement composite equivalent to the 3D C/C using the identi�ed parameters: axial thermal diffusivity of the reinforcement,   , diffusivity of the matrix,   , and thermal contact resistance of the reinforcement/matrix interface, .Taken from [10, 13].

F 8 :
Principle of the detection of the emerging contrast.

F 10 :
On the le�: In�uence of the normalized defect depth,   /, on the relative contrast generated by a defect of normalized thermal resistance  * = 1 in a slab of thickness .On the right: Comparison in the emerging contrast domain between the contrasts generated by the same defect in a semi-in�nite medium (solution used for the depth and thermal resistance identi�cation by the early detection technique) and in a slab of thickness .defect depth.is proposal remained qualitative, no explicit relation relating the defect depth to this time being proposed by these authors.

F 12 :
Comparison between the best images obtained by the TSR method coupled with an early detection approach and an ultrasonic D-scan: (a) ermograms, Δ at 2.20 s� (b) 2nd derivative at 0.20 s� (c) 1st derivative at 0.6 s� (d) ultrasonic absorption image.e arti�cial defect to detect is located at the center of the sample.Une�pected defects were discovered in the near vicinity of the arti�cial defect.e chosen times of observation have not been optimized for imaging the 3 peripheral inner inserts that are sound regions.
T 1: Present method result and comparison to Parker's and Degiovanni's methods.