Image synthesis using a physics-informed diffusion model for crack detection with laser flying spot thermography

In non-destructive testing for metallic materials, 'Flying-spot' thermography is a method for detecting cracks based on the infrared scanning of samples by a local laser heat source. However, identifying a crack from other surface artefacts such as air ducts or non-planar shapes on the material surface can be challenging. That is why a recent series of works has proposed the use of deep learning techniques, which can exploit contextual information but require a significant amount of data. Some of these works use a diffusion model to increase the amount of data available to train the defect detection model. However, the diffusion model only imitates the training images it was fed and therefore, there is no physical meaning enforced to the images it generates. This can cause some synthetic images to exhibit temperature fields that do not comply with the diffusion law, or even contain obvious inconsistencies. In this paper, we propose the implementation of a physics-informed diffusion model to generate synthetic thermal images with a real physical meaning. In the literature, the integration of physical information is achieved using a partial differential equation (PDE). In contrast, we propose to directly incorporate the solution of the equation for a semi-infinite homogeneous solid (i.e. a defect-free material). To evaluate the benefits of such a model, several metrics are measured such as the Fréchet Inception Distance, the physical error and the speed of convergence, but also the performance on a downstream anomaly detection task.