Discerning holographic and shearographic carrier fringes using the hyperboloids in holodiagrams

Abstract

The carrier fringe is frequently used together with conventional double-exposure holography and shearography. The pattern of the carrier fringes to be used is affected by the pattern of the deformation fringes, for instance, parallel fringe-lines will not be useful for beam bending problems and concentric circular carrier fringes will be unsuitable for circular plates under axisymmetrical loading. The formation of holographic fringe patterns has been explained using the moire fringes that are generated by optically differentiating the ellipsoids of holodiagrams. This paper describes a new method based on the hyperboloids instead of ellipsoids. With this method, the hyperboloids directly depict holographic carrier fringe patterns; to understand the formation of shearographic patterns, only one optical differentiation is made on the hyperboloids. This therefore will allow easy understanding of how the light source should be shifted in generating the appropriate carrier fringe patterns.