  The most ubiquitous form of computational aberration correction for
microscopy is deconvolution. However, deconvolution relies on the assumption
that the point spread function is the same across the entire field-of-view. It
is well recognized that this assumption is often inadequate, but space-variant
deblurring techniques generally require impractical amounts of calibration and
computation. We present a new imaging pipeline, ring deconvolution microscopy
(RDM), that leverages the rotational symmetry of most optical systems to
provide simple and fast spatially-varying aberration correction. We formally
derive theory and algorithms for exact image recovery and additionally propose
a neural network based on Seidel coefficients as a fast alternative. We
showcase significant enhancements both visually and quantitatively compared to
standard deconvolution and existing spatially-varying deconvolution across a
diverse range of microscope modalities, including miniature microscopy,
multicolor fluorescence microscopy, and point-scanning multimode fiber
micro-endoscopy. Our approach enables near-isotropic, subcellular resolution in
each of these applications.
