On the Concept of Homologous Rays in Holographic Interferometry of Diffusely Reflecting Surfaces

In holographic interferometry of diffusely reflecting surfaces the two interfering fields observed are homologous, provided certain observation conditions and idealizations are satisfied. The physical content of this statement, as it is given here, is that the complex amplitude of field one, in a small volume about a point P of observation, is identical (or proportional) to the complex amplitude of field two in a similar volume about a point P′, close to P. The conditions for homology are given, and a proof is outlined with reference to a more detailed investigation carried out elsewhere. A principal ray, and the locus of points satisfying homology of field two with respect to points along the principal ray in field one, constitute a pair of homologous rays. The concept of homologous rays was introduced by Viénot et al. [1] for surface movements coplanar with the illumination and observation directions. Its validity is extended here to more general movements, including strain and shear. It is shown how points of intersection or crossing of homologous rays may be used to compute and visualize fringe localization. It is further shown how the interspace and inclination of straight-line fringes are influenced by the distance between the object surface and the entrance pupil, and how this influence can be interpreted in terms of observation data and in terms of the mutual separation of the homologous rays at the pupil.