A unified interpretation of interferometric and holographic fringe patterns in photoelasticity

Abstract

A unified interpretation of interferometric and holographic fringe patterns obtained from birefringent materials is presented by using physical concepts only. The two fundamental fringe systems, corresponding to the individual stress-optical retardations along the principal stress directions, are considered to recombine mechanically for the formation of isochromatic and isopachic fringe patterns. This mechanical interference is shown to be more pronounced only when certain conditions concerning the position and the spatial frequencies of the original systems are satisfied. It is shown that only one of the isochromatic and isopachic fringe patterns, corresponding to the shorter diagonals of the individual quadrangles, formed by the two initial fundamental fringe systems, is obtained under normal experimental conditions, and that it is possible to have in one region of the pattern one system and in another region the other. Both isochromatics and isopachics can be obtained only when special precautions are taken during the application of the particular experimental method. The factors influencing the formation of either the isochromatics or the isopachics, or both, are indicated and analysed. The existing confusion in the literature concerning the interpretation of holo-interferometric patterns is thoroughly discussed and clarified. Two simple examples—that is, the circular disc in diametral compression and the infinite plate with a circular hole in tension—are selected to show the main features in this interpretation.