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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 two-dimensionalROIs 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 two-dimensional photothermal SR reconstruction results show to outclass all defect reconstructions by the considered reference 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.
For a long time, the rule of thumb for active thermography as a non-destructive testing method was that the resolution of internal defects/inhomogeneities is limited to a ratio of defect depth/defect size ≤ 1. This is due to the diffusive nature of thermal conduction in solids. So-called super resolution approaches have recently allowed this physical limit to be overcome many times over. This offers the attractive possibility of developing thermography from a purely near surface-sensitive testing method to one with improved depth range. How far this development can be pushed is the subject of current research.
We have already been able to show that this classical limitation for one- and two-dimensional defect geometries can be overcome by illuminating the test object sequentially in a structured manner with individual laser spots and thus subsequently calculating a defect map from the resulting measurement data by applying photothermal super resolution reconstruction, which allows significantly improved separation of individual closely spaced defects. As a result, this method benefits strongly from the combination of sequential spatially structured illumination and modern numerical optimization methods, which come at the expense of higher experimental complexity. This leads to long measurement times, large data sets, and tedious numerical analysis, in contrast to the application of established standard thermographic methods with homogeneous illumination.
In this work, we report on the application of full-area spatially structured two-dimensional illumination patterns, which, by applying state-of-the-art laser projector technology in conjunction with a high-power laser, makes it possible to achieve an efficient implementation of photothermal super-resolution reconstruction even for larger test areas in the first place.
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.
In this work, the limits of using spatially structured heating combined with subsequent photothermal super resolution reconstruction for the thermographic detection and resolution of internal defects are investigated. The approach is based on the application of modern high-power laser projector technology, which is used to repeatedly project varying spatially structured 2D pixel patterns to photothermally heat the object under test. After processing the generated thermographic data using nonlinear convex optimisation in conjunction with exploiting the joint-sparse nature of the defect signals within the individual measurements, a high-resolution 2D-sparse defect/inhomogeneity map is obtained. The main focus of the investigation is set on the influence of the number of individual measurements on the achievable reconstruction quality. Using numerical simulations based on an analytical representation of the forward solution to the underlying inverse problem, the convergence rate over performed measurements of the achievable reconstruction quality is determined. Finally, all findings are experimentally validated by reconstructing a set of internal defects in an additively manufactured sample. In this work, it is shown that for a variety of different defect separation distances, the projection of 50 different pixel patterns allows for a good trade-off between experimental complexity and reconstruction quality.
In this work, we present a novel approach to photothermal super resolution based thermographic resolution of internal defects using two-dimensional pixel pattern-based active photothermal laser heating in conjunction with subsequent numerical reconstruction to achieve a high-resolution reconstruction of internal defect structures. With the proposed adoption of pixelated patterns generated using laser coupled high-power DLP projector technology the complexity for achieving true two-dimensional super resolution can be dramatically reduced taking a crucial step forward towards widespread practical viability. Furthermore, based on the latest developments in high-power DLP projectors, we present their first application for structured pulsed thermographic inspection of macroscopic metal samples. In addition, a forward solution to the underlying inverse problem is proposed along with an appropriate heuristic to find the regularization parameters necessary for the numerical inversion in a laboratory setting. This allows the generation of synthetic measurement data, opening the door for the application of machine learning based methods for future improvements towards full automation of the method. Finally, the proposed method is experimentally validated and shown to outperform several established conventional thermographic testing techniques while conservatively improving the required measurement times by a factor of 8 compared to currently available photothermal super resolution techniques.
Für die aktive Thermografie als zerstörungsfreie Prüfmethode galt lange Zeit die Faustformel, dass die Auflösung interner Defekte/Inhomogenitäten auf ein Verhältnis von Defekttiefe/Defektgröße ≤ 1 beschränkt ist. Die Ursache hierfür liegt in der diffusiven Natur der Wärmeleitung in Festkörpern. Sogenannte Super-Resolution-Ansätze erlauben seit Kurzem die Überwindung dieser physikalischen Grenze um ein Vielfaches. Damit ergibt sich die attraktive Möglichkeit die Thermografie von einem rein oberflächensensitiven Prüfverfahren hin zu einem Verfahren mit verbesserter Tiefenreichweite zu entwickeln. Wie weit diese Entwicklung getrieben werden kann, ist Gegenstand aktueller Forschung. Wir konnten bereits zeigen, dass diese klassische Einschränkung für ein- und zweidimensionale Defektgeometrien überwunden werden kann, indem das Prüfobjekt mit einzelnen Laserspots sequenziell strukturiert beleuchtet wird und damit anschließend aus den resultierenden Messdaten durch Anwendung photothermischer Super-ResolutionRekonstruktion eine Defektkarte berechnet werden kann, welche eine deutlich verbesserte Trennung einzelner naheliegender Defekte erlaubt. Dieses Verfahren profitiert dabei im Ergebnis stark von der Kombination von sequenzieller räumlich strukturierter Beleuchtung und modernen numerischen Optimierungsverfahren, was jedoch in Summe stark auf Kosten der experimentellen Komplexität geht. Dies führt im Gegensatz zur Anwendung von etablierten thermografischen Standardverfahren mit vollflächiger Beleuchtung zu langen Messzeiten, großen Datensätzen und langwieriger numerischer Auswertung. In dieser Arbeit berichten wir über die Anwendung vollflächig räumlichstrukturierter zweidimensionaler Beleuchtungsmuster, welche es durch den Einsatz modernster Laserprojektortechnik in Verbindung mit einem Hochleistungslaser überhaupt erst erlaubt, eine effiziente Umsetzung von photothermischer Super-ResolutionRekonstruktion auch für größere Prüfflächen zu erreichen.
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.
Thermographic non-destructive testing 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.