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Die laserbasierte aktive thermografische Prüfung als berührungslose Methode der zerstörungsfreien Werkstoffprüfung (NDT) basiert auf der aktiven Erwärmung des Testobjekts (OuT) und Messung des resultierenden Temperaturanstiegs mit einer Infrarotkamera. Dadurch bedingt können systematische Abweichungen vom vorhergesagten Erwärmungsverhalten Aufschluss über dessen innere Struktur geben. Jedoch ist das Auflösungsvermögen für innenliegende Defekte durch die diffusive Natur der Wärmeleitung in Festkörpern begrenzt. Thermografische Super-Resolution (SR)-Methoden zielen darauf ab, diese Limitation durch die Kombination mehrerer Messungen mit jeweils unterschiedlicher strukturierter Erwärmung und mathematischer Optimierungsmethoden zu überwinden.
Zur Rekonstruktion innerer Defekte mithilfe thermografischer SR-Rekonstruktionsmethodik wird für die Gesamtheit mehrerer Messungen ein schlecht gestelltes und stark regularisiertes inverses mathematisches Problem gelöst, was in einer dünnbesetzten Karte der internen Defektstruktur des OuTs resultiert.
Der vorliegende Vortrag gibt einen Überblick über die geleisteten Arbeiten in diesem Gebiet im Rahmen der hier mit dem Wissenschaftspreis der DGZfP 2024 prämierten Arbeit.
In infrared thermography, the interaction of the heat flow with the internal geometry or inhomogeneities in a sample and their effect on the transient temperature distribution is used, e.g., to detect defects non-destructively. An equivalent way of describing this is the propagation of thermal waves inside the sample. Although thermography is suitable for a wide range of inhomogeneities and materials, the fundamental limitation is the diffuse nature of thermal waves and the need to measure their effect radiometrically at the sample surface only. The crucial difference between diffuse thermal waves and propagating waves, as they occur, e.g., in ultrasound, is the rapid degradation of spatial resolution with increasing defect depth. This degradation usually limits the applicability of thermography for finding small defects on and below the surface.
A promising approach to improve the spatial resolution and thus the detection sensitivity and reconstruction quality of the thermographic technique lies in the shaping of these diffuse thermal wave fields using structured laser thermography.
Some examples are:
• Narrow crack-like defects below the surface can be detected with high sensitivity by superimposing several interfering thermal wave fields,
• Defects very close to each other can be separated by multiple measurements with varying heating structures,
• Defects at different depths can be distinguished by an optimized temporal shaping of the thermal excitation function,
• Narrow cracks on the surface can be found by robotic scanning with focused laser spots.
We present the latest results of this technology obtained with high-power laser systems and modern numerical methods.
Thermographic NDT is based on the interaction of thermal waves with inhomogeneities. The propagation of thermal waves from the heat source to the inhomogeneity and to the detection surface according to the thermal diffusion equation leads to the fact that two closely spaced defects can be incorrectly detected as one defect in the measured thermogram. In order to break this spatial resolution limit (super resolution), the combination of spatially structured heating and numerical methods of compressed sensing can be used.
The improvement of the spatial resolution for defect detection then depends in the classical sense directly on the number of measurements. Current practical implementations of this super resolution detection still suffer from long measurement times, since not only the achievable resolution depends on performing multiple measurements, but due to the use of single spot laser sources or laser arrays with low pixel count, also the scanning process itself is quite slow. With the application of most recent high-power digital micromirror device (DMD) based laser projector technology this issue can now be overcome.
Our studies deal with the application of fully 2D-structured DMD-based excitation and subsequent super-resolution-based defect reconstruction. We analyze the influence of different testing parameters, like the number of measurements or the white content of the excitation pattern. Furthermore, we have dealt with the choice of parameters in the reconstruction that have an influence on the underlying minimization problem in terms of compressed sensing. Finally, the results of the super resolution reconstruction are compared with the results based on conventional thermographic testing methods.
Laser-based active thermography is a contactless non-destructive testing method to detect material defects by heating the object and measuring its temperature increase with an infrared camera. Systematic deviations from predicted behavior provide insight into the inner structure of the object. However, its resolution in resolving internal structures is limited due to the diffusive nature of heat diffusion. Thermographic super resolution (SR) methods aim to overcome this limitation by combining multiple thermographic measurements and mathematical optimization algorithms to improve the defect reconstruction.
Thermographic SR reconstruction methods involve measuring the temperature change in an object under test (OuT) heated with multiple different spatially structured illuminations. Subsequently, these measurements are inputted into a severely ill-posed and heavily regularized inverse problem, producing a sparse map of the OuT’s internal defect structure. Solving this inverse problem relies on limited priors, such as defect-sparsity, and iterative numerical minimization techniques. Previously mostly experimentally limited to one-dimensional regions of interest (ROIs), this thesis aims to extend the method to the reconstruction of twodimensional ROIs with arbitrary defect distributions while maintaining reasonable experimental complexity. Ultimately, the goal of this thesis is to make the method suitable for a technology transfer to industrial applications by advancing its technology readiness level (TRL).
In order to achieve the aforementioned goal, this thesis discusses the numerical expansion of a thermographic SR reconstruction method and introduces two novel algorithms to invert the underlying inverse problem. Furthermore, a forward solution to the inverse problem in terms of the applied SR reconstruction model is set up. In conjunction with an additionally proposed
algorithm for the automated determination of a set of (optimal) regularization parameters, both create the possibility to conduct analytical simulations to characterize the influence of the experimental parameters on the achievable reconstruction quality. On the experimental side, the method is upgraded to deal with two-dimensional ROIs, and multiple measurement campaigns are performed to validate the proposed inversion algorithms, forward solution
and two exemplary analytical studies. For the experimental implementation of the method, the use of a laser-coupled DLP-projector is introduced, which allows projecting binary pixel patterns that cover the whole ROI, reducing the number of necessary measurements per ROI significantly (up to 20x).
Finally, the achieved reconstruction of the internal defect structure of a purpose-made OuT is qualitatively and qualitatively benchmarked against well-established thermographic testing methods based on homogeneous illumination of the ROI. Here, the background-noise-free twodimensional photothermal SR reconstruction results show to outclass all defect reconstructions by the considered reference methods.
The achievable spatial resolution of active thermographic testing is inherently limited by the diffusive nature of heat conduction in solids. This degradation of the achievable spatial resolution for a semi-infinite body acting on a defect signal can be approximated by spatial convolution with the Green’s function of the heat PDE. As the degradation in spatial resolution is dependent on the depth 𝐿, a common rule of thumb specifies that for proper detection, any defect should feature a spatial extension greater or equal to the depth it is located at. However, as the exact shape of a defect can have a large impact on its severity, at best a proper reconstruction of the defect shape should be performed, which therefore must also deal with the aforementioned adverse effects of heat conduction. One recent method to overcome the spatial resolution limit of thermographic testing is the photothermal super resolution reconstruction method. It is based on performing multiple active thermographic measurements on the same region of interest (ROI) with varying spatially structured heating and subsequent numerical reconstruction of the measured defect signals by solving a severely ill-posed inverse reconstruction problem relying on heavy regularization. By extending the experimental implementation of the method to make use of random-pixel patterns projected onto the ROI using a laser-coupled DLP-projector, defect reconstructions can now be performed within a reasonable time frame (~15 min per ROI) at high accuracy. Compared to conventional thermographic testing methods, the photothermal super resolution reconstruction stands out by resulting in a sparse representation of the defect structure of the ROI, making it especially well-suited to further automatic defect classification and quality assurance measures in an Industry 4.0 context.
Due to the diffusive nature of heat propagation in solids, the detection and resolution of internal defects with active thermography based non-destructive testing is commonly limited to a defect-depth-to-defect-size ratio greater than or equal to one. In the more recent past, we have already demonstrated that this limitation can be overcome by using a spatially modulated illumination source and photothermal super resolution-based reconstruction. Furthermore, by relying on compressed sensing and computational imaging methods we were able to significantly reduce the experimental complexity to make the method viable for investigating larger regions of interest. In this work we share our progress on improving the defect/inhomogeneity characterization using fully 2D spatially structured illumination patterns instead of scanning with a single laser spot. The experimental approach is based on the repeated blind pseudo-random illumination using modern projector technology and a high-power laser. In the subsequent post-processing, several measurements are then combined by taking advantage of the joint sparsity of the defects within the sample applying 2D-photothermal super resolution reconstruction. Here, enhanced nonlinear convex optimization techniques are utilized for solving the underlying ill-determined inverse problem for typical simple defect geometries. As a result, a higher resolution defect/inhomogeneity map can be obtained at a fraction of the measurement time previously needed.
In this work, we report on our progress for investigating a new experimental approach for thermographic detection of internal defects by performing 2D photothermal super resolution reconstruction. We use modern high-power laser projector technology to repeatedly excite the sample surface photothermally with varying spatially structured 2D pixel patterns. In the subsequent (blind) numerical reconstruction, multiple measurements are combined by exploiting the joint-sparse nature of the defects within the specimen using nonlinear convex optimization methods. As a result, a 2D-sparse defect/inhomogeneity map can be obtained. Using such spatially structured heating combined with compressed sensing and computational imaging methods allows to significantly reduce the experimental complexity and to study larger test surfaces as compared to the one-dimensional approach reported earlier.
Due to the diffusive nature of heat propagation in solids, the detection and resolution of internal defects with active thermography based non-destructive testing is commonly limited to a defect-depth-to-defect-size ratio greater than or equal to one. In the more recent past, we have already demonstrated that this limitation can be overcome by using a spatially modulated illumination source and photothermal super resolution-based reconstruction. Furthermore, by relying on compressed sensing and computational imaging methods we were able to significantly reduce the experimental complexity to make the method viable for investigating larger regions of interest. In this work we share our progress on improving the defect/inhomogeneity characterization using fully 2D spatially structured illumination patterns instead of scanning with a single laser spot. The experimental approach is based on the repeated blind pseudo-random illumination using modern projector technology and a high-power laser. In the subsequent post-processing, several measurements are then combined by taking advantage of the joint sparsity of the defects within the sample applying 2D-photothermal super resolution reconstruction. Here, enhanced nonlinear convex optimization techniques are utilized for solving the underlying ill-determined inverse problem for typical simple defect geometries. As a result, a higher resolution defect/inhomogeneity map can be obtained at a fraction of the measurement time previously needed.