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In this tutorial, we aim to directly recreate some of our "aha" moments whenexploring the impact of heat diffusion on the spatial resolution limit ofphotothermal imaging. Our objective is also to communicate how this physicallimit can nevertheless be overcome and include some concrete technologicalapplications. Describing diffusion as a random walk, one insight is that such astochastic process involves not only a Gaussian spread of the mean values inspace, with the variance proportional to the diffusion time, but also temporaland spatial fluctuations around these mean values. All these fluctuationsstrongly influence the image reconstruction immediately after the short heatingpulse. The Gaussian spread of the mean values in space increases the entropy,while the fluctuations lead to a loss of information that blurs thereconstruction of the initial temperature distribution and can be describedmathematically by a spatial convolution with a Gaussian thermalpoint-spread-function (PSF). The information loss turns out to be equal to themean entropy increase and limits the spatial resolution proportional to thedepth of the imaged subsurface structures. This principal resolution limit canonly be overcome by including additional information such as sparsity orpositivity. Prior information can be also included by using a deep neuralnetwork with a finite degrees of freedom and trained on a specific class ofimage examples for image reconstruction.

Heat diffusion blurs photothermal images with increasing depth