Intensity fluctuations due to a deep phase screen with a power-law spectrum

Abstract

The spatial frequency spectrum of intensity fluctuations arising in a plane wave after it traverses a one-dimensional screen which imposes large random fluctuations of phase is investigated in the case when the random phase of the screen has a modified power-law spectrum of the form (1 + L 2 q 2 ) –½ m , m = 2, 4, where q is the wavenumber and L determines the outer scale of the fluctuations. The case of a screen with an unmodified power-law phase spectrum, corresponding to a linear structure function of phase, is also investigated by letting L become very large for m = 2. It is shown that the unmodified power-law spectrum can only be used if the observer is so close to the screen that L , the outer scale of the irregular phase, cannot be seen. The intensity spectrum corresponding to m = 4 is considered and it is shown that its behaviour differs fundamentally from the previous case with m = 2. It is shown that for a more exact evaluation of the intensity spectrum the integral formulation must be extended to the complex plane and that an important contribution, partly responsible for a peak in the spectrum, comes from an hitherto unnoticed saddle point. Analytic forms for the spectrum are derived and curves for some typical spectra are given.