The computation and statistical analysis of aberrational diffraction patterns in holographic optical elements

Abstract

Three numerical methods for calculating the point spread function for holographic optical elements in the presence of aberrations are analyzed. The starting point for the analytical formulation of the diffraction theory of aberrations for holographic optical elements is the Fresnel-Kirchhoff diffraction integral. To calculate the diffraction integral, the exit pupil of the element is broken up into subdomains each with the same area, using both cartesian and polar coordinates. A statistical analysis of the point spread function is introduced by defining a set of irradiance distribution moments. These moments can be used to characterize the imaging properties and aberrations of the holographic optical element. The minimum number of area subdomains needed on the exit pupil of the element to obtain the correct point spread function is obtained by optimizing the statistical moments of the irradiance distribution.