Complex ABCD-matrices: a general tool for analyzing arbitrary optical systems

摘要

In this paper, we describe a novel formulation of light beam propagation through any complex optical system that can be described by an ABCD ray-transfer matrix. Within the framework of complex ABC-optical systems, we then present novel speckle methods for analyzing linear and angular velocities and displacements. All methods rely on the dynamics of speckle patterns, produced by scattering of coherent light off solid surfaces undergoing angular and/or translational displacements. Coherent light scattered off a rough surface produces a granular diffraction pattern some distance away from the object. This pattern is referred to as speckles, and originates from elementary interference of the waves emanating from many microscopic areas on the surface within the illuminated region. If the illuminated object is in motion, the resulting speckle pattern also evolves with time, i.e., a dynamical speckle pattern results. The target motion or displacement is usually determined by calculating the space- or time-lagged covariance of the detector currents before and after object displacement, and then determine the position where the peak of the covariance attains its maximum.