Speckle: statistics and interferometric decorrelation effects in complex ABCD optical systems

Abstract

The mean, the variance, and the correlation function of the intensity pattern resulting from an incoherent source that has propagated through a complex ABCD optical system are derived. The number of speckle correlation cells (or modes, N) within an effective measurement area is presented and discussed. Optical field decorrelation effects with respect to secondary fringe formation in phase-shifting speckle interferometry are discussed. In particular, the correlation coefficient resulting from load-induced object tilt, in-plane translations, and displacements parallel to the optic axis as a function of the number of modes propagating through the optical system is derived and discussed. In contrast to previous research, in which the calculation of speckle interferometric decorrelation effects was restricted to direct imaging systems and the special case where N → ∞, the correlation coefficients that we derive are valid for arbitrary complex ABCD systems (i.e., nonimaging configurations) and for all finite values of N ≥ 1.