We address the problem of image reconstruction from incomplete measurements, encompassing both upsampling and inpainting, within a learning-based framework. Conventional supervised approaches require fully sampled ground truth data, while self-supervised methods allow incomplete ground truth but typically rely on random sampling that, in expectation, covers the entire image. In contrast, we consider fixed, deterministic sampling patterns with inherently incomplete coverage, even in expectation. To overcome this limitation, we exploit multiple invariances of the underlying image distribution, which theoretically allows us to achieve the same reconstruction performance as fully supervised approaches. We validate our method on optical-resolution image upsampling in photoacoustic microscopy, demonstrating competitive or superior results while requiring substantially less ground truth data.

Infrared thermography nondestructive testing faces challenges due to the diffusive nature of heat, which causes increasing blurring with depth beneath the surface during the reconstruction of internal structures and affects the determination of thermal properties in multilayered materials. This article explores the contextual application of pulse compression and virtual wave methods in active thermography to address these challenges. Pulse compression enables extended, modulated heating of materials and compresses the resulting heat signatures in the time domain. The virtual wave method, on the other hand, transforms temperature signals into virtual propagating damped wave signals, facilitating the reconstruction of defects following the excitation. We analyzed thermal data before and after applying the virtual wave method, and our findings demonstrate enhanced signal-to-noise ratio and high linearity in defect characterization. Building on these insights, we propose a deep spatio-temporal fusion network trained to mimic the virtual wave transformation, thereby enabling efficient and physically guided tomographic reconstruction.

We have used the locally computed virtual waves from the measured diffusive surface signals for image reconstruc-tion using established time-of-flight methods from ultrasound or RADAR imaging. This improves the spatial resolution in thermography and compensates for the dispersion of quantum wave packets in atom probe tomography.

In this research work, photothermal reconstruction for imaging foreign object defects in curved orthotropic composite samples is demonstrated using the virtual wave concept. For this purpose, the virtual wave concept is extended for defect reconstruction in orthotropic samples with a surface curvature in one direction. Furthermore, it is discussed how the multidirectional heat flows due to the complex-shaped geometry influences the propagation of the virtual wave. For verification, photothermal experiments with single-pulse flash lamp excitation in the pulse-echo configuration are performed. In summary, this study underlines the capability of the reconstruction scheme for imaging defects in strongly curved composite components.

Acquiring a fully sampled high-resolution image in optical resolution photoacoustic microscopy (OR-PAM) and elsewhere is time-consuming and costly. To accelerate data acquisition and reduce costs, we decrease the number of data samples in combination with self-supervised learning. Key features of our proposal include a sparse-dense sampling strategy, where both fully sampled and sparsely sampled regions are collected, along with an alternating training strategy to extract relevant image structures. By extracting high-resolution information from the fully sampled regions and global information from the sparsely sampled regions, we can generate high-quality, fully sampled OR-PAM images with reduced acquisition time and cost. (c) 2025 The Author(s)

Bei der zerstörungsfreien Bildgebung breiten sich die Wellen von der abzubildenden Struktur zu einem Detektor aus, wo ihr Signal zur Rekonstruktion des Bildes verwendet wird. Wie bereits Ernst Abbe gezeigt hat, ist die räumliche Auflösung in optischen Mikroskopen durch die Wellenlänge beugungsbegrenzt. In der Akustik, z. B. bei der photoakustischen Bildgebung, wird die detektierbare Wellenlänge nicht nur durch technische Beschränkungen wie die Bandbreite des Akustikdetektors begrenzt, sondern auch durch die frequenzabhängige akustische Dämpfung während der Ausbreitung von der inneren Struktur zum Detektor auf der Probenoberfläche. In der Thermographie bestimmt die Wellenlänge der "Wärmewelle" die räumliche Auflösung. Höhere Frequenzkomponenten mit kleineren Wellenlängen ermöglichen eine bessere räumliche Auflösung. Die höhere Dämpfung von Wärmewellen im Vergleich zur Akustik führt jedoch zu starker Unschärfe und geringer räumlicher Auflösung bei der Abbildung tieferer Strukturen. Mandelis hat einen vereinheitlichenden Rahmen für die Behandlung verschiedener diffusionsbezogener periodischer Phänomene unter dem globalen mathematischen Begriff der Diffusionswellenfelder entwickelt, wie z.B. thermische Wellen aber auch modulierte Wirbelströme. Wellen, die der Wellengleichung genügen, bleiben auch dann gültig Lösung dieser Gleichung, wenn die Zeitrichtung umgekehrt wird, d. h. sie sind zeitinvariant. Diese Eigenschaft ist entscheidend für bildgebende Anwendungen. In der Praxis führen jedoch Phänomene wie Dissipation, Diffusion und Dispersion dazu, dass sich ein Wellenpaket während der Ausbreitung verbreitert. Diese Verbreiterung zerstört die Zeitinvarianz der Welle, was zu einer geringeren räumlichen Auflösung der rekonstruierten Bilder führt. Um dem entgegenzuwirken, wandeln wir diese Wellensignale für jeden Detektorpunkt lokal in „virtuelle Wellen“ um und können dadurch die räumliche Auflösung wesentlich verbessern.

This work presents one-dimensional photothermal results for estimating subsurface interface parameters using the virtual wave concept. The performed study demonstrates the capability of the virtual wave concept as a feature extraction method for estimating the depth position and thermal mismatch of subsurface interfaces within layered materials. The mathematical relationship between the reflection coefficient of the thermal wave and the signal of the virtual wave is demonstrated for exact one-dimensional solutions. For experimental validation, pulsed thermography in the pulse-echo configuration for different metallic specimens is applied. This method yields a very good estimation of the interfacial parameters for the analyzed samples. In summary, a feasible and fast one-dimensional photothermal evaluation of subsurface interfaces using the virtual wave concept is demonstrated.

In this study, we present an extension of the virtual wave concept to enable photothermal reconstruction from temporal non-uniform pulsed thermography data. Therefore, we introduce a generalized discrete transformation kernel, which allows to account for arbitrary temporal sampling strategies. First, we show the evidence of the proposed strategy for analytical temperature signals. Moreover, we demonstrate the advantages of the strategy for simulated temperature signals, obtained from an orthotropic sample with defect interfaces at various depth positions. For experimental verification, we apply pulsed thermography in the pulse-echo configuration for a carbon fiber-reinforced polymer sample with different embedded defects. It can be shown that efficient time sampling in the virtual wave concept allows a significant reduction in the number of data points compared to uniform sampling, without compromising the quality of the reconstruction results.

Many non-destructive optical testing methods are currently used for material research, providing various information about material parameters. At RECENDT, a multimodal experimental setup has been designed that combines terahertz (THz) spectroscopy, optical coherence tomography (OCT), infrared (IR), and Raman spectroscopy with a tensile test stage. This setup aims to gather material information such as crystallinity and optical parameters of high-density polyethylene (HDPE) during a tensile test. The setup compares common IR and Raman spectroscopy and the less common optical methods THz and OCT. Complementarity is achieved through different frequency ranges and measurement approaches, resulting in different measured optical material parameters and depths. During tensile testing, HDPE samples with varying crystallinity were analysed, and the determined optical parameters such as refractive index, birefringence, scattering coefficient of decay, and penetration depth can be correlated with the change in crystallinity. These findings demonstrate that the optical methods and their outcomes can be interconnected. With further optimization of the experimental setup, it would be possible to observe the alignment of fibres in fibre composite panels and the stress distribution of polymers effectively. This opens interesting possibilities for polymer characterization in the future, including quality control during moulding processes and material testing.

This study presents photothermal imaging results of subsurface material defects within fiber metal laminates utilizing the virtual wave concept. Therefore, we theoretically analyze the propagation of the virtual wave signal in a hybrid composite laminate via the method of images. For provoking local material damage, the hybrid composite sample is subjected to a defined impact loading. The results obtained from photothermal defect imaging, utilizing rectangular laser pulse excitation, are compared with results obtained from 3D x-ray computed tomography. To sum up, we demonstrate a fast, non-invasive, and easily interpretable reconstruction of defects within macroscopic hybrid composite laminates based on the virtual wave concept.

Significance:Compressed sensing (CS) uses special measurement designs combined with powerful mathematical algorithms to reduce the amount of data to be collected while maintaining image quality. This is relevant to almost any imaging modality, and in this paper we focus on CS in photoacoustic projection imaging (PAPI) with integrating line detectors (ILDs). Aim:Our previous research involved rather general CS measurements, where each ILD can contribute to any measurement. In the real world, however, the design of CS measurements is subject to practical constraints. In this research, we aim at a CS-PAPI system where each measurement involves only a subset of ILDs, and which can be implemented in a cost-effective manner. Approach:We extend the existing PAPI with a self-developed CS unit. The system provides structured CS matrices for which the existing recovery theory cannot be applied directly. A random search strategy is applied to select the CS measurement matrix within this class for which we obtain exact sparse recovery. Results:We implement a CS PAPI system for a compression factor of 4:3, where specific measurements are made on separate groups of 16 ILDs. We algorithmically design optimal CS measurements that have proven sparse CS capabilities. Numerical experiments are used to support our results. Conclusions:CS with proven sparse recovery capabilities can be integrated into PAPI, and numerical results support this setup. Future work will focus on applying it to experimental data and utilizing data-driven approaches to enhance the compression factor and generalize the signal class.

AbstractSurface‐enhanced Raman scattering (SERS) is a sensitive and fast technique for sensing applications such as chemical trace analysis. However, a successful, high‐throughput practical implementation necessitates the availability of simple‐to‐use and economical SERS substrates. In this work, we present a robust, reproducible, flexible and yet cost‐effective SERS substrate suited for the sensitive detection of analytes at near‐infrared (NIR) excitation wavelengths. The fabrication is based on a simple dropcast deposition of silver or gold nanomaterials on an aluminium foil support, making the design suitable for mass production. The fabricated SERS substrates can withstand very high average Raman laser power of up to 400 mW in the NIR wavelength range while maintaining a linear signal response of the analyte. This enables a combined high signal enhancement potential provided by (i) the field enhancement via the localized surface plasmon resonance introduced by the noble metal nanomaterials and (ii) additional enhancement proportional to an increase of the applicable Raman laser power without causing the thermal decomposition of the analyte. The application of the SERS substrates for the trace detection of melamine and rhodamine 6G is demonstrated, which shows limits of detection smaller than 0.1 ppm and analytical enhancement factors on the order of 104 as compared to bare aluminium foil.

The spatial resolution limit in photoacoustic/thermal imaging is derived from the irreversibility of attenuation of the pressure wave and of heat diffusion during propagation of the signals from the imaged subsurface structures to the sample surface, respectively. The acoustic or temperature signals are converted into so-called virtual waves, which are their reversible counterparts, and which can be used for image reconstruction by well-known ultrasound reconstruction methods, which is an ill-posed inverse problem. The resolution from entropy production is equal to the diffraction limit -which is noise limited. Incorporating sparsity and non-negativity in iterative regularization methods gives a significant resolution enhancement.

In this tutorial, we aim to directly recreate some of our "aha" moments when exploring the impact of heat diffusion on the spatial resolution limit of photothermal imaging. Our objective is also to communicate how this physical limit can nevertheless be overcome and include some concrete technological applications. Describing diffusion as a random walk, one insight is that such a stochastic process involves not only a Gaussian spread of the mean values in space, with the variance proportional to the diffusion time, but also temporal and spatial fluctuations around these mean values. All these fluctuations strongly influence the image reconstruction immediately after the short heating pulse. The Gaussian spread of the mean values in space increases the entropy, while the fluctuations lead to a loss of information that blurs the reconstruction of the initial temperature distribution and can be described mathematically by a spatial convolution with a Gaussian thermal point-spread-function (PSF). The information loss turns out to be equal to the mean entropy increase and limits the spatial resolution proportional to the depth of the imaged subsurface structures. This principal resolution limit can only be overcome by including additional information such as sparsity or positivity. Prior information can be also included by using a deep neural network with a finite degrees of freedom and trained on a specific class of image examples for image reconstruction.

Thermographic imaging is a fast and contactless way of inspecting material parts. Usually, with model-driven evaluation procedures, lateral heat flow is ignored, and, thus, 1D reconstruction is applied to detect defects. However, to correctly size defects, the lateral heat flow must be considered, which requires a full 3D reconstruction. The 3D thermal defect imaging is a major challenge because heat propagation is an irreversible process. The virtual wave concept (VWC) is a recently developed method that considers both lateral and axial heat flows and, therefore, allows multidimensional reconstruction at improved spatial resolution. This approach decomposes the problem into two steps; can be used for 1D, 2D, and 3D heat conduction problems; and provides new alternatives to using physical priors (e.g., nonnegativity and/or sparsity), all of which improve reconstruction accuracy at a relatively low computational cost.

In this work, we show the application of the virtual wave concept for 3D “pulse-echo” photothermal defect imaging in anisotropic materials. We consider a woven and a unidirectional carbon fiber reinforced material including flat bottom holes with varying diameter-to-depth ratios. We discuss the characteristics of the virtual wave signal due to disturbed heat diffusion caused by a defect and the resulting consequences for our defect reconstruction method regarding the incorporation of prior information. In addition, we optimize the virtual wave concept in terms of computation time by performing a parameter study and a physical-based derivation that suggest reasonable values for the temporal and spatial discretization, respectively. The paper presents a very fast, easily interpretable and efficient 3D reconstruction tool for active thermography testing of anisotropic materials.

The mandatory Non-Destructive Testing (NDT) by the aerospace industry for both present and future generation hybrid aircraft using thick composite structures poses many challenges for traditional inspection techniques. Laser Ultrasonic Testing (LUT) deployed by a robot for inspection of modern aerospace composite components shows good promise. It is a non-contact method offering the possibility of fast scan times without the need for couplant. This paper presents the latest work-in-progress for the design and development of the system developed by the ACCURATe consortium. ACCURATe is an ongoing H2020 Clean Sky 2 part funded project to develop a laser ultrasound based NDT system prototype for fast and contactless testing of large carbon fibre reinforced polymer (CFRP) aircraft structures. The approach is based on a non-contact laser generated and detected pulsed ultrasound technique with delivery of both the laser ultrasound excitation and detection pulses through flexible optical fibres. The backscattered light from the lasers is also collected into a fibre. The measurement head, which contains the two beam outputs and the light collection optics is raster scanned over the surface by a 6-axis robot arm. A balanced two wave mixing interferometer (B-TWM) is used for the demodulation of the ultrasonic waves. The system has recently been used to scan a reference panel, and a scrap panel of fuselage, the latest test results are presented and show promising progress against the project objectives.

In this paper, we present a 3D photothermal imaging tool to detect subsurface defects in anisotropic media using the virtual wave concept. In addition, we propose a novel approach to compute the temperature contrast using a virtual wave signal, which enables a temporal noise-free representation of the contrast temperature signal. The results obtained with the proposed imaging tool are compared with those obtained using computed tomography for a carbon fiber-reinforced polymer sample containing a delamination caused by a defined impact. To sum up, this work presents a fast, easily interpretable, and efficient 3D photothermal defect reconstruction and visualization tool.