The optical microscopy image plays an important role in scientific research through the direct visualization of the nanoworld, where the imaging mechanism is described as the convolution of the point spread function (PSF) and emitters. Based on a priori knowledge of the PSF or equivalent PSF, it is possible to achieve more precise exploration of the nanoworld. However, it is an outstanding challenge to directly extract the PSF from microscopy images. Here, with the help of self-supervised learning, we propose a physics-informed masked autoencoder (PiMAE) that enables a learnable estimation of the PSF and emitters directly from the raw microscopy images. We demonstrate our method in synthetic data and real-world experiments with significant accuracy and noise robustness. PiMAE outperforms DeepSTORM and the Richardson–Lucy algorithm in synthetic data tasks with an average improvement of 19.6% and 50.7% (35 tasks), respectively, as measured by the normalized root mean square error (NRMSE) metric. This is achieved without prior knowledge of the PSF, in contrast to the supervised approach used by DeepSTORM and the known PSF assumption in the Richardson–Lucy algorithm. Our method, PiMAE, provides a feasible scheme for achieving the hidden imaging mechanism in optical microscopy and has the potential to learn hidden mechanisms in many more systems.

The nonlinear fluorescence emission has been widely applied for high spatial resolution optical imaging. Here, we studied the fluorescence anomalous saturating effect of the nitrogen vacancy defect in diamond. The fluorescence reduction was observed with high power laser excitation. It increased the nonlinearity of the fluorescence emission, and changed the spatial frequency distribution of the fluorescence image. We used a differential excitation protocol to extract the high spatial frequency information. By modulating the excitation laser’s power, the spatial resolution of imaging was improved approximately 1.6 times in comparison with the confocal microscopy. Due to the simplicity of the experimental setup and data processing, we expect this method can be used for improving the spatial resolution of sensing and biological labeling with the defects in solids.