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This article presents deep unfolding neural networks to handle inverse problems in photothermal radiometry enabling super-resolution (SR) imaging. The photothermal SR approach is a well-known technique to overcome the spatial resolution limitation in photothermal imaging by extracting high-frequency spatial components based on the deconvolution with the thermal point spread function (PSF). However, stable deconvolution can only be achieved by using the sparse structure of defect patterns, which often requires tedious, handcrafted tuning of hyperparameters and results in computationally intensive algorithms. On this account, this article proposes Photothermal-SR-Net, which performs deconvolution by deep unfolding considering the underlying physics. Since defects appear sparsely in materials, our approach includes trained block-sparsity thresholding in each convolutional layer. This enables to super-resolve 2-D thermal images for nondestructive testing (NDT) with a substantially improved convergence rate compared to classic approaches. The performance of the proposed approach is evaluated on various deep unfolding and thresholding approaches. Furthermore, we explored how to increase the reconstruction quality and the computational performance. Thereby, it was found that the computing time for creating high-resolution images could be significantly reduced without decreasing the reconstruction quality by using pixel binning as a preprocessing step.
The work to be presented focuses on our most recent studies to laser excited super resolution (SR) thermography. The goal of nondestructive testing with SR is to facilitate the separation of closely spaced defects. Photothermal SR can be realized by performing structured illumination measurements in com-bination with the use of deconvolution algorithms in post-processing. We explain that stepwise as well as continuous scanning techniques are applicable to generate structured illumination measurements. Finally, we discuss the effect of experimental parameters and image processing techniques to find the optimal SR technique which leads to the highest reconstruction quality within laser thermography.
Thermographic super-resolution techniques allow the resolution of defects/inhomogeneities beyond the classical limit, which is governed by the diffusion properties of thermal wave propagation. Photothermal super-resolution is based on a combination of an experimental scanning strategy and a numerical optimization which has been proven to be superior to standard thermographic methods in the case of 1D linear defects. In this contribution, we report on the extension of this approach towards a full frame 2D photothermal super-resolution technique. The experimental approach is based on a repeated spatially structured heating using high power lasers. In a second post-processing step, several measurements are coherently combined using mathematical optimization and taking advantage of the (joint) sparsity of the defects in the sample. In our work we extend the possibilities of the method to efficiently detect and resolve defect cross sections with a fully 2D-structured blind illumination.
Active thermography as a nondestructive testing modality suffers greatly from the limitations imposed by the diffusive nature of heat conduction in solids. As a rule of thumb, the detection and resolution of internal defects/inhomogeneities is limited to a defect depth to defect size ratio greater than or equal to one. Earlier, we demonstrated that this classical limit can be overcome for 1D and 2D defect geometries by using photothermal laser-scanning super resolution. In this work we report a new experimental approach using 2D spatially structured illumination patterns in conjunction with compressed sensing and computational imaging methods to significantly decrease the experimental complexity and make the method viable for investigating larger regions of interest.
Thermographic super resolution techniques allow the spatial resolution of defects/inhomogeneities below the classical limit, which is governed by the diffusion properties of thermal wave propagation. In this work, we report on the extension of this approach towards a full frame 2D super resolution technique. The approach is based on a repeated spatially structured heating using high power lasers. In a second post-processing step, several measurements are coherently combined using mathematical optimization and taking advantage of the (joint) sparsity of the defects in the sample
Die thermografische ZfP basiert auf der Wechselwirkung von thermischen Wellen mit Inhomogenitäten. Die Ausbreitung von thermischen Wellen von der Wärmequelle zur Inhomogenität und zur Detektionsoberfläche entsprechend der thermischen Diffusionsgleichung führt dazu, dass zwei eng beieinander liegende Defekte fälschlicherweise als ein Defekt im gemessenen Thermogramm erkannt werden können. Um diese räumliche Auflösungsgrenze zu durchbrechen, also eine Super Resolution zu realisieren, kann die Kombination von räumlich strukturierter Erwärmung und numerischen Verfahren des Compressed Sensings verwendet werden.
Für unsere Arbeiten benutzen wir Hochleistungs-Laser im Kilowatt-Bereich um die Probe entweder hochaufgelöst entlang einer Linie (1D) abzurastern oder strukturiert zu erwärmen. Die Verbesserung des räumlichen Auflösungsvermögens zur Defekterkennung hängt dann im klassischen Sinne direkt von der Anzahl der Messungen ab. Mithilfe des Compressed Sensings und Vorkenntnissen über das System ist es jedoch möglich die Anzahl der Messungen zu reduzieren und trotzdem Super Resolution zu erzielen. Wie viele Messungen notwendig sind und wie groß der Auflösungsgewinn gegenüber der konventionellen thermografischen Prüfung mit flächiger Erwärmung ist, hängt von einer Reihe von Messparametern, der Messstrategie, Probeneigenschaften und den verwendeten Rekonstruktionsalgorithmen ab.
Unsere Studien befassen sich mit dem Einfluss der experimentellen Parameter, wie z.B. der Pulslänge der Laserbeleuchtung und der Größe des Laserspots. Weiterhin haben wir uns mit der Wahl der Parameter in der Rekonstruktion auseinandergesetzt, die einen Einfluss auf das im Compressed Sensing zugrundeliegende Minimierungsproblem haben. Für jeden getesteten Parametersatz wurde eine Rekonstruktionsqualität berechnet. Schließlich wurden die Defektrekonstruktionen basierend auf den Parameternsätzen verglichen, sodass eine Parameterwahl für hohe Rekonstruktionsqualitäten mit thermografischer Super Resolution
empfohlen werden kann.
The work to be presented focuses on our most recent studies to laser excited super resolution (SR) thermography. The goal of nondestructive testing with SR is to facilitate the separation of closely spaced defects. Photothermal SR can be realized by performing structured illumination measurements in com-bination with the use of deconvolution algorithms in post-processing. We explain that stepwise as well as continuous scanning techniques are applicable to generate structured illumination measurements. Finally, we discuss the effect of experimental parameters and image processing techniques to find the optimal SR technique which leads to the highest reconstruction quality within laser thermography.
This paper presents different super resolution reconstruction techniques to overcome the spatial resolution limits in thermography. Pseudo-random blind structured illumination from a onedimensional laser array is used as heat source for super resolution thermography. Pulsed thermography measurements using an infrared camera with a high frame rate sampling lead to a huge amount of data. To handle this large data set, thermographic reconstruction techniques are an essential step of the overall reconstruction process. Four different thermographic reconstruction techniques are analyzed based on the Fourier transform amplitude, principal component analysis, virtual wave reconstruction and the maximum thermogram. The application of those methods results in a sparse basis representation of the measured data and serves as input for a compressed sensing based algorithm called iterative joint sparsity (IJOSP). Since the thermographic reconstruction techniques have a high influence on the result of the IJOSP algorithm, this paper Highlights their Advantages and disadvantages.
In this work we focus on our most recent studies to super resolution (SR) laser thermography. The goal of SR nondestructive testing methods is to facilitate the separation of closely spaced defects. We explain how to combine laser scanning with SR techniques. It can be shown that stepwise as well as continuous scanning techniques are applicable. Finally, we discuss the effect of experimental parameters and im-age processing techniques to find the optimal SR technique which leads to the highest reconstruction quality within laser thermography.
Using spatial and temporal shaping of laser-induced diffuse thermal wave fields in thermography
(2020)
The diffuse nature of thermal waves is a fun-damental limitation in thermographic nonde-structive testing. In our studies we investigated different approaches by shaping the thermal wave fields which result from heating. We have used high-power laser sources to heat metallic samples. Using these spatial and temporal shaping techniques leads to a higher detection sensitivity in our measurements with the infra-red camera. In this contribution we show our implementation of shaping laser-induced diffuse thermal wave fields and the effect on the defect reconstruction quality.
Photothermal radiometry with an infrared camera allows the contactless temperature measurement of multiple surface pixels simultaneously. A short light pulse heats the sample. The heat propagates through the sample by diffusion and the corresponding temperature evolution is measured at the sample’s surface by an infrared camera. The main drawback in radiometric imaging is the loss of the spatial resolution with increasing depth due to heat diffusion, which results in blurred images for deeper lying structures. We circumvent this information loss due to the diffusion process by using blind structured illumination, combined with a non-linear joint sparsity reconstruction algorithm. The structured illumination is realized by parallel laser lines from a vertical-cavity surface-emitting laser (VCSEL) array controlled by a random binary pattern generator. By using 150 different patterns of structured illumination and our iterative joint sparsity algorithm, it was possible to resolve 1 mm thick lines at a distance down to 0.5 mm, which results in a resolution enhancement of approximately a factor of four compared to the resolution of 5.9 mm for homogenous illuminated thermographic reconstruction.
The separation of two closely spaced defects in fields of Thermographic NDE is very challenging. The diffusive nature of thermal waves leads to a fundamental limitation in spatial resolution. Therefore, super resolution image reconstruction can be used. A new concerted ansatz based on spatially structured heating and joint sparsity of the signal ensemble allows for an improved reconstruction of closely spaced defects. This new technique has been studied using a 1D laser array with randomly chosen illumination pattern.
This paper presents the results after applying super resolution algorithms, such as the iterative joint sparsity (IJOSP) algorithm, to our processed measurement data. Different data processing techniques before applying the IJOSP algorithm as well as the influence of regularization parameters in the data processing techniques are discussed. Moreover, the degradation of super resolution reconstruction goodness by the choice of experimental parameters such as laser line width or number of measurements is shown.
The application of the super resolution results in a spatial resolution enhancement of approximately a factor of four which leads to a better separation of two closely spaced defects.
The separation of two closely located defects in fields of Thermographic NDE is very challenging. The diffusive nature of thermal waves leads to a fundamental limitation in spatial resolution. Therefore, super resolution image reconstruction can be used. A new concerted ansatz based on spatially structured heating and joint sparsity of the signal ensemble allows an improved reconstruction of closely located defects. This new technique has also been studied using 1D laser arrays in active thermography.
The post-processing can be roughly described by two steps: 1. Finding a sparse basis representation using a reconstruction algorithm such as the Fourier transform, 2. Application of an iterative joint sparsity (IJOSP) method to the firstly reconstructed data. For this reason, different methods in post-processing can be compared using the same measured data set.
The focus in this work was the variation of reconstruction algorithms in step 1 and its influence on the results from step 2. More precise, the measured thermal waves can be transformed to virtual (ultrasound) waves that can be processed by applying ultrasound reconstruction algorithms and finally the super resolution algorithm. Otherwise, it is also possible to make use of a Fourier transform with a subsequent super resolution routine. These super resolution thermographic image reconstruction techniques in post-processing are discussed and evaluated regarding performance, accuracy and repeatability.
The diffusive nature of heat propagation complicates the separation of two closely spaced defects. This results in a fundamental limitation in spatial resolution. Therefore, super resolution (SR) image reconstruction can be used. SR processing techniques based on spatially structured heating and joint sparsity of the signal ensemble allows for an improved reconstruction of closely spaced defects. This new technique has been studied using a 1D laser array with randomly chosen illumination pattern.
This paper presents the results after applying SR algorithms such as the iterative joint sparsity (IJOSP) algorithm, to our processed measurement data. Two different data processing strategies are evaluated and discussed regarding their influence on the reconstruction goodness as well as their complexity. Moreover, the degradation of the SR reconstruction by the choice of regularization parameters in data processing is discussed.
The application of both SR techniques that are evaluated in this paper results in a spatial resolution enhancement of approximately a factor of four which leads to a better separation of two closely spaced defects. The fundamental difference between both SR techniques is their complexity.
The separation of two closely located defects in fields of Thermographic NDE is very challenging. The diffusive nature of thermal waves leads to a fundamental limitation in spatial resolution. Therefore, super resolution image reconstruction can be used.
The measured thermal waves can be transformed to virtual (ultrasound) waves that can be processed by applying ultrasound reconstruction algorithms and finally the super resolution algorithm. Otherwise, it is also possible to make use of a Fourier transform with a subsequent super resolution routine.
These super resolution thermographic image reconstruction techniques in post-processing are discussed and evaluated regarding performance, accuracy and repeatability.
Thermographic nondestructive evaluation (NDE) is based on the interaction of thermal waves with inhomogeneities. These inhomogeneities are related to sample geometry or material composition. Although thermography is suitable for a wide range of inhomogeneities and materials, the fundamental limitation is the diffusive nature of thermal waves and the need to measure their effect radiometrically at the sample surface only. The propagation of the thermal waves from the heat source to the inhomogeneity and to the detection surface results in a degradation in the spatial resolution of the technique. A new concerted ansatz based on a spatially structured heating and a joint sparsity of the signal ensemble allows an improved reconstruction of inhomogeneities. As a first step to establish an improved thermographic NDE method, an experimental setup was built based on structured 1D illumination using a flash lamp behind a mechanical aperture. As a follow-up to this approach, we now use direct structured illumination using a 1D laser array. The individual emitter cells are driven by a pseudo-random binary pattern and are additionally shifted by fractions of the cell period. The repeated measurement of these different configurations enables to illuminate each spot of the sample surface in lateral direction. This allows for a reconstruction that makes use of joint sparsity.
The measured data set is processed using super resolution image reconstruction algorithms such as the iterative joint sparsity (IJOSP) algorithm. Using this reconstruction technique and 150 different illumination patterns results in a spatial resolution enhancement of approximately a factor of four compared to the resolution of 5.9 mm for homogenously illuminated thermographic reconstruction.
Further, new data processing techniques have been studied before applying the IJOSP algorithm that are more performant or less prone to errors regarding image reconstruction. The choice of regularization parameters in data processing as well as experimental parameters such as the illumination pattern as a variable heat flux density (i.e., the Neumann boundary condition for convolution with the constant Green's function) have a big influence on the reconstruction goodness. With analytical-numerical modelling and numerical FEM simulations, we studied the influence of the experimental parameters on the result of the non-linear IJOSP reconstruction. This has also been investigated experimentally e.g. using different laser line widths or more measurements per position. These studies are used to derive optimal conditions for a certain measurement image reconstruction technique.
The separation of two closely spaced defects in fields of Thermographic NDE is very challenging. The diffusive nature of thermal waves leads to a fundamental limitation in spatial resolution. Therefore, super resolution image reconstruction can be used. A new concerted ansatz based on spatially structured heating and joint sparsity of the signal ensemble allows for an improved reconstruction of closely spaced defects. This new technique has been studied using a 1D laser array with randomly chosen illumination pattern.
This paper presents the results after applying super resolution algorithms, such as the iterative joint sparsity (IJOSP) algorithm, to our processed measurement data. Different data processing techniques before applying the IJOSP algorithm as well as the influence of regularization parameters in the data processing techniques are discussed. Moreover, the degradation of super resolution reconstruction goodness by the choice of experimental parameters such as laser line width or number of measurements is shown.
The application of the super resolution results in a spatial resolution enhancement of approximately a factor of four which leads to a better separation of two closely spaced defects.
Thermographic NDE is based on the interaction of thermal waves with inhomogeneities. These inhomogeneities are related to sample geometry or material composition. Although thermography is suitable for a wide range of inhomogeneities and materials, the fundamental limitation is the diffusive nature of thermal waves and the need to measure their effect radiometrically at the sample surface only. The propagation of the thermal waves from the heat source to the inhomogeneity and to the detection surface results in a degradation in the spatial resolution of the technique. A new concerted ansatz based on a spatially structured heating and a joint sparsity of the signal ensemble allows an improved reconstruction of inhomogeneities. As a first step to establish an improved thermographic NDE method, an experimental setup was built based on structured 1D illumination using a flash lamp behind a mechanical aperture. As a follow-up to this approach, we now use direct structured illumination using a 1D laser array. The individual emitter cells are driven by a random binary pattern and additionally shifted by fractions of the cell period. The repeated measurement of these different configurations with simultaneously constant inhomogeneity allows for a reconstruction that makes use of joint sparsity. With analytical-numerical modelling or numerical FEM simulations, we study the influence of the parameters on the result of non-linear reconstruction. For example, the influence of the illumination pattern as a variable heat flux density and Neumann boundary condition for convolution with the constant Green's function can be studied. These studies can be used to derive optimal conditions for a measurement technique.
Thermal waves are solutions of the heat diffusion equation for periodic boundary conditions and can be seen analogously to strongly damped waves. Although the underlying differential equation differs from the wave equation, the essential property for analogy between both equations is linearity such that superposition applies. This linearity is maintained even after a linear transformation, such as the Fourier transform from time to frequency domain. It follows that the temporal superposition principle is already used in active thermography, e.g. in pulsed thermography, as a superposition of many individual frequencies. However, the systematic spatial superposition has not yet been fully exploited, mainly due to a lack of suitable energy sources.
As a first step, we are investigating how thermal wave fields of arbitrary space-time structures can be engineered using structured laser illumination. The proof of principle was shown using a laser coupled projector. Unfortunately, the available optical output power was limited due to the thermal stress limit of the device. That is why we are working towards a more sophisticated moving 1D array of high-power diode lasers. We characterized the novel light source and believe that apart from the benefit of spatial and temporal illumination it can combine the temporal regimes of impulse and lock-in thermography.
In a second step, we investigate moving and oscillating line sources with different line shapes. We use a Green’s Function ansatz to analytically model the thermal wave propagation of structured 1D laser illumination in isotropic materials. Furthermore, we show some methods how they can be implemented. With this technique, we were able to accelerate our detection method firstly presented in for vertical narrow defects by factor three. Generally, we believe that this technique opens up similar opportunities than in other NDE methods. High-resolution ultrasound, for example, is also based on the superposition of single emitters and a recent concept suggests an option to deal with the diffusion wave character of the thermal waves.