Abstract

The statistical properties of speckle have been studied extensively, and the literature contains many photographs of speckle. However, contour plots of speckle patterns have not appeared. Determining such maps by measurement is very difficult, but they can be computed quite simply as follows. An array is formed of complex numbers exp(iA_kl), where the A_kl are random numbers varying from 0 to 2π. The shape of the nonzero portion of the array determines the range of angles contributing to the speckle pattern. The fast Fourier transform of this array gives the amplitude of the (scalar) speckle field that would be formed in the far field of the initial array. The square magnitude of the amplitude array is the irradiance. This corresponds to a physical arrangement in which a piece of ground glass located in the front focal plane of a lens is uniformly illuminated by monochromatic light. The ground glass is sampled by a mask in contact that is opaque except for a square array of identical pinholes. The resulting field is observed in the rear focal plane.

© 1985 Optical Society of America