Numerical Models for Speckle Fields

A speckle field is a random interference pattern that is produced when coherent laser light is reflected from a rough surface or scattered in a volume diffuser. It was soon recognized that this phenomenon could have significant application in non-contact industrial metrology applications such as for measuring deformations in a test structure or the displacement and rotation of a surface. It was therefore important to develop a theoretical model describing these scattering properties. A common approach, taken by Goodman [1976] is to assume that the speckle field is fully developed and can be modeled using Gaussian random variables; and that the auto-correlation of the field “just after” the rough surface is “delta correlated”. This analytical model leads to theoretical predictions that match experimental observations. The “delta” correlated model is difficult to simulate numerically because of sampling. Here we examine a variety of different numerical models to describe optically rough surfaces and examine the statistical characteristics of the intensity in a displaced optical plane.