A New Theory for the Practical Interpretation of Holographic Interference Patterns Resulting from Static Surface Displacements

TLDR: In this paper, it is established that live holographic interference patterns are the result of the interference occurring between the wavefronts diffracted from corresponding points in the reconstructed image and the displaced real object.

Abstract: It is re-established, in a suitable form, that live holographic interference patterns are the result of the interference occurring between the wavefronts diffracted from corresponding points in the reconstructed image and the displaced real object. This result is employed to determine the path difference equations for the wavefront forming the interference pattern as observed in three orthogonal directions. A set of linear equations is derived which is shown to relate the components of a small general surface displacement to the fringe spacing and localization plane of the observed interference pattern. The practical application of the theory is then discussed. Numerical equations are derived for various geometries of interferometer and in particular the measurements of rigid-body translations and plane strain are dealt with. In addition it is shown how problems that arise in the measurement of complicated surface displacements may be considerably simplified.