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

An analytical model is presented that accurately represents 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 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 describes a SV PSF over a range of field angles with only four parameters for any specific 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. An example is also presented that demonstrates the use of the model for restoration of a SV image formed by a single-lens optical system, resulting in a 7.5 dB improvement in normalized error energy (NEE)