A Simplified Theory of the Scattering Geometries, Topologies and Vector Fields of Speckle Photography and Holographic Interferometry

Abstract

In many applications of speckle photography or holographic interferometry to surface or structure distortion measurement some general understanding of the theory and optics of coherent light scattering from rough surfaces is important. In order to apply a simplified heuristic solution to the different flow patterns which occur with moving speckle patterns a geometrical optics method of diffraction, using diffractive rays, has been used. A modified initial model of this concept has associated the speckle movements with either (1) linear displacement of mirror facet sets on the scatter surface, or (2) rotations of tangent planes on the surface. A surface tangent free vector and cotangent axial vector system is developed, together with various lens and surface scattering geometries, and these are applied to the distorting surface using vector topology. Two topological flows are described, one for the surface in-plane free vector displacements, and the other for the axial vector rotations of the scatter surface; these speckle vector topologies are shown to be closely connected to the topographic scalar pathlength fringes of holographic interferometry.