Asymmetric, space-variant point spread function model for a spherical lens optical system

Abstract

An asymmetric analytical model is presented for the space variant (SV) point-spread-function (PSF) of an optical system consisting of a single spherical lens with a rectangular aperture. The model is an improvement over a prior model in that additional parameters allow shifting of the central lobe and asymmetry of the sidelobes. Both of these effects are seen in diffraction-based PSF models as field angle is increased. The model is useful for applying certain SV restoration methods to digital images formed by simple optical systems, since it significantly reduces the memory required to store PSF sample functions. The proposed model uses eight parameters for any specific field position. The model is adapted to PSFs developed from diffraction theory, using an adaptive system with gradient descent parameter adjustment. Data is presented that characterizes the accuracy of the adapted model to a physical PSF as a function of field angle.