Linear Revolution-Invariance: Modeling and Deblurring Spatially-Varying Imaging Systems

We develop theory and algorithms for modeling and deblurring imaging systems that are composed of rotationally-symmetric optics. Such systems have point spread functions (PSFs) which are spatially-varying, but only vary radially, a property we call linear revolution-invariance (LRI). From the LRI property we develop an exact theory for linear imaging with radially-varying optics, including an analog of the Fourier Convolution Theorem. This theory, in tandem with a calibration procedure using Seidel aberration coefficients, yields an efficient forward model and deblurring algorithm which requires only a single calibration image -- one that is easier to measure than a single PSF. We test these methods in simulation and experimentally on images of resolution targets, rabbit liver tissue, and live tardigrades obtained using the UCLA Miniscope v3. We find that the LRI forward model generates accurate radially-varying blur, and LRI deblurring improves resolution, especially near the edges of the field-of-view. These methods are available for use as a Python package at https://github.com/apsk14/lri.