In this work, it is shown that image reconstruction methods from ultrasonic imaging can be employed for thermographic signals. Before using these imaging methods, a virtual signal is calculated by applying a local transformation to the temperature evolution measured on a sample surface. The introduced transformation describes all the irreversibility of the heat diffusion process and can be used for every sample shape. To date, one-dimensional methods have been primarily used in thermographic imaging. The proposed two-stage algorithm enables reconstruction in two and three dimensions. The feasibility of this approach is demonstrated through simulations and experiments. For the latter, small steel beads embedded in an epoxy resin are imaged. The resolution limit is found to be proportional to the depth of the structures and to be inversely proportional to the logarithm of the signal-to-noise ratio. Limited-view artefacts can arise if the measurement is performed on a single planar detection surface. These artifacts can be reduced by measuring the thermographic signals from multiple planes, which is demonstrated by numerical simulations and by experiments performed on an epoxy cube.

Using an infrared camera for thermographic imaging allows the contactless temperature measurement of many surface pixels simultaneously. From the measured surface data, the structure below the surface, embedded inside a sample or tissue, can be reconstructed and imaged, if heated by an excitation light pulse. The main drawback in active thermographic imaging is the degradation of the spatial resolution with the imaging depth, which results in blurred images for deeper lying structures. We circumvent this degradation by using blind structured illumination combined with a non-linear joint sparsity reconstruction algorithm. We demonstrate imaging of a line pattern and a star-shaped structure through a 3 mm thick steel sheet with a resolution four times better than the width of the thermal point-spread-function. The structured illumination is realized by parallel slits cut in an aluminum foil, where the excitation coming from a flashlight can penetrate. This realization of super-resolution thermographic imaging demonstrates that blind structured illumination allows thermographic imaging without high degradation of the spatial resolution for deeper lying structures. The groundbreaking concept of super-resolution can be transferred from optics to diffusive imaging by defining a thermal point-spread-function, which gives the principle resolution limit for a certain signal-to-noise ratio, similar to the Abbe limit for a certain optical wavelength. In future work, the unknown illumination pattern could be the speckle pattern generated by a short laser pulse inside a light scattering sample or tissue.

In this paper, we investigate two deep learning approaches to recovering initial temperature profiles from thermographic images in non-destructive material testing. First, we trained a deep neural network (DNN) in an end-to-end fashion by directly feeding the surface temperature measurements to the DNN. Second, we turned the surface temperature measurements into virtual waves (a recently developed concept in thermography), which we then fed to the DNN. To demonstrate the effectiveness of these methods, we implemented a data generator and created a dataset comprising a total of 100 000 simulated temperature measurement images. With the objective of determining a suitable baseline, we investigated several state-of-the-art model-based reconstruction methods, including Abel transformation, curvelet denoising, and time- and frequency-domain synthetic aperture focusing techniques. Additionally, a physical phantom was created to support evaluation on completely unseen real-world data. The results of several experiments suggest that both the end-to-end and the hybrid approach outperformed the baseline in terms of reconstruction accuracy. The end-to-end approach required the least amount of domain knowledge and was the most computationally efficient one. The hybrid approach required extensive domain knowledge and was more computationally expensive than the end-to-end approach. However, the virtual waves served as meaningful features that convert the complex task of the end-to-end reconstruction into a less demanding undertaking. This in turn yielded better reconstructions with the same number of training samples compared to the end-to-end approach. Additionally, it allowed more compact network architectures and use of prior knowledge, such as sparsity and non-negativity. The proposed method is suitable for non-destructive testing (NDT) in 2D where the amplitudes along the objects are considered to be constant (e.g., for metallic wires). To encourage the development of other deep-learning-based reconstruction techniques, we release both the synthetic and the real-world datasets along with the implementation of the deep learning methods to the research community.

In this Tutorial, we combine the different scientific fields of information theory, thermodynamics, regularization theory, and non-destructive imaging, especially for photoacoustic and photothermal imaging. The goal is to get a better understanding of how information gaining for subsurface imaging works and how the spatial resolution limit can be overcome by using additional information. Here, the resolution limit in photoacoustic and photothermal imaging is derived from the irreversibility of attenuation of the pressure wave and of heat diffusion during the 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. The conversion into virtual waves is an ill-posed inverse problem, which needs regularization. The reason for that is the information loss during signal propagation to the sample surface, which turns out to be equal to the entropy production. As the entropy production from acoustic attenuation is usually small compared to the entropy production from heat diffusion, the spatial resolution in acoustic imaging is higher than in thermal imaging. Therefore, it is especially necessary to overcome this resolution limit for thermographic imaging by using additional information. Incorporating sparsity and non-negativity in iterative regularization methods gives a significant resolution enhancement, which was experimentally demonstrated by one-dimensional imaging of thin layers with varying depth or by three-dimensional imaging, either from a single detection plane or from three perpendicular detection planes on the surface of a sample cube.