GEOMETRIC VS. DIFFRACTION PREDICTION OF PROPERTIES OF A STAR IMAGE IN THE PRESENCE OF AN ISOTROPIC RANDOM WAVEFRONT DISTURBANCE

Abstract

A random perturbation in the wavefront transmitted through an optical system results in diffraction effects in the image which are describable in terms of the statistical measures of the wavefront perturbations, whereas the geometrical effects are determined only by the statistics of the gradient of the wavefront perturbation. By using a model in which the gradient statistics are held constant while the depth of perturbations is varied, differences between the geometrical and diffraction images are made apparent. For an rms depth Qw /A > 0.5, the diffraction and geometric images are statistically indistinguishable, but for smaller depths the diffraction image departs from the geometric image, separating in effect into an undisturbed core and a diffracted halo, between which the partition of the image power depends on the depth of the wavefront perturbations. Various proper- ties of the diffraction image as a function of the rms depth of the perturbations are discussed.