Three-dimensional speckles: Static and dynamic properties

A discussion of the static and dynamic three-dimensional (3D) behaviour of a speckle pattern is given. The discussion is based on general theoretical results, which are valid within the paraxial approximation for a general optical system using the concept of complex ABCD-matrices. Especially, we examine the three-dimensional nature of speckles, which are formed in free-space, in Fourier transform geometry and in imaging systems. The dynamic evolution of these speckles is derived from the space/time-lagged intensity covariance that results from an in-plane translation of a diffuse scattering object, which is illuminated by a Gaussian shaped laser beam in a back-scattering configuration. In particular, the origin of speckle decorrelation will be investigated. Speckles are commonly analysed in a plane where decorrelation can arise either from true speckle decorrelation or due to a frozen three-dimensional speckle pattern being translated through the plane of observation, i.e. subjective speckle decorrelation. The presentation will be concluded with illustrative experimental results. The implications of the three-dimensional dynamic properties for measurement systems based on speckle correlation will be considered.