A NOVEL ANALYTICAL SPACE-VARIANT POINT SPREAD FUNCTION MODEL FOR UNDERCORRECTED OPTICAL SYSTEMS

Abstract

An analytical model is developed for the space-variant (SV) point-spread-function (PSF) of an undercorrected optical system with a rectangular aperture. The model accommodates broadening and shifting of the central lobe, as well as sidelobe asymmetry of the PSF, as field angle increases. These effects are exhibited by diffraction-based PSF models. The proposed model uses eight parameters for any specific field position, compared to ~ 210 parameters required for direct sampling of an individual PSF. The model is adapted to PSFs developed from diffraction theory using an adaptive system with gradient descent parameter adjustment. Consequently, the model is useful for applying certain SV digital image restoration methods because it significantly reduces the memory required to store PSF sample functions. In addition, the model does not require samples of the PSF or a DFT operation to obtain samples of the optical transfer function (OTF). Thus, the efficiency of SV restoration methods applied in the frequency domain, such as sectioning approaches, is further improved. Data presented confirms the accuracy and the computational advantage of the model by quantifying its adaptation to a physical PSF over a range of field angles.