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.

翻译：在本教程中，我们旨在直接再现探索热扩散对光热成像空间分辨率极限影响时的若干“顿悟”时刻。我们的目标还包括阐明这一物理极限如何能够被突破，并介绍一些具体的技术应用。将扩散描述为随机游走时，一个关键见解是：这一随机过程不仅涉及均值在空间上的高斯扩散（其方差与扩散时间成正比），还包含围绕这些均值的时间与空间涨落。所有这些涨落都会显著影响短加热脉冲后的即时图像重建。均值在空间上的高斯扩散增加了熵，而涨落则导致信息损失，从而使初始温度分布的重建变得模糊，可数学描述为与高斯热点扩散函数（PSF）的空间卷积。结果表明，信息损失等于平均熵增，并限制了空间分辨率，使其与成像地下结构深度成反比。这一基本分辨率极限只能通过引入稀疏性或正定性等额外信息来突破。先验信息也可通过使用具有有限自由度的深度神经网络来纳入，该网络需针对特定类别的图像示例进行训练以完成图像重建。