Static and dynamic behavior of speckle patterns described by operator algebra

Together with a simplifying operator notation, concepts of linear systems analysis are applied to the description of the speckle pattern produced when laser light is scattered by a moving surface. The discussion is restricted to linear and deterministic optical systems, but the surface statistics are almost arbitrary. It is reported that: (1) a general expression for the intensity correlation function describing the speckle pattern was derived; (2) the translational speckle motion and the mean Doppler shift were found to be independent of the surface statistics; (3) the dependence of speckle size, shape, and lifetime on statistics and apertures was found explicitly; and (4) the results are shown to reduce the usually accepted relations only for very restricting assumptions.