Intensity Fluctuations Beyond a One-dimensional Random Refracting Screen in the Short-wavelength Limit

Abstract

A plane monochromatic wave disturbed by passage through a refracting (phase changing) screen of irregular thickness develops intensity fluctuations beyond it. The distribution of intensity at an observation point depends on its distance from the screen, the wavelength and the randomness of the screen thickness. Here, the (exact) short wavelength limit of its moments <I ^m > are calculated in terms of these quantities. Attention is restricted to the two-dimensional problem where the screen is one dimensional or corrugated. The guiding principle is due to Berry [1]—that the moments in this geometrical limit are governed by multiple coalescences of ray paths, optical catastrophes, which directly determine the wavelength dependence (twinkling exponents) of <I ^m >. <I ^m is shown to be determined by the probability (suitably weighted) of observing a coalescence of n rays or apparent sources, where n is the integer part of ½(√ [16m − 7] − 1). The associated catastrophe A_n supplies, through its characteristic diffraction pattern, two numbers besides the twinkling exponent, which complete the description of <I ^m >. In the case of a stationary gaussian random screen the weighted coalescence probability is easily evaluated in terms of the screen correlation function.