Some Effects of Temporal Coherence on the First Order Statistics of Speckle

Moments and the first order probability density function of the intensity in a speckle pattern are considered as a function of the spectral bandwidth of the incident light. It is shown that the standard deviation of the intensity generally depends on the surface roughness of the diffuser, and on the position of measurement in the far field. Numerical results are given for a diffuser with a Gaussian distribution of surface height limited by a circular aperture. Exact and approximate forms of the probability density function are discussed. The analysis applies when the fluctuations in optical path are greater than the maximum wavelength incident.