Statistical Properties of Spatial Derivatives of the Amplitude and Intensity of Monochromatic Speckle Patterns

Abstract

The statistical properties of the amplitude and the intensity of a monochromatic speckle pattern as well as the behaviour of the spatial derivatives of these quantities are studied theoretically. Under the assumption of circular complex gaussian statistics general expressions are derived for the distribution density of the spatial derivative of the amplitude and the intensity of the speckle field. The spatial derivative of the real and the imaginary part of the amplitude is jointly gaussian distributed, whereas the distribution density of the spatial derivative of the intensity turns out to be of simple Laplacian form. Explicit formulas are given for speckle patterns produced by uniformly diffusing screens. Furthermore, the spatial density of level crossings of the intensity is investigated.