The influence of spatially random wavefronts on coherent diffraction imagery

Abstract

The averaged diffraction image of a coherently illuminated object viewed through an optical system with a circular exit pupil in the presence of a spatially random wavefront is derived. The final expression for the averaged diffraction image is given by a fourfold integral which contains the covariance function of the random wavefront. It is shown that when the covariance function is very narrow compared with the radius of the exit pupil, the averaged diffraction image decomposes into the sum of a slowly varying background term and the diffraction image of the object (in the absence of the random wavefront) modulated by the exponential of the variance of the random wavefront. The special, but important, case of line objects is considered in detail along with representative numerical calculations.