  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.
