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In common industrial environment, large deformation measurements of opaque bodies by means of holographic interferometry are often related to the problem of decreasing fringe spacing and contrast, causing the loss of the interference fringe pattern, which contains the whole information on the corresponding deformation. Therefore, the only way to determine the surface strain, rotation and displacement components of a structure element under load relatively to the unloaded state is first to recover the interference fringes--at least locally--and then to use the correct adequate relations to process the recovered fringe pattern properly. This paper explicitly the quantitatively presents the general equation system for a systematic fringe recovery procedure in the general case of a large unknown object deformation. The relations for the quantitative evaluation of the recovered fringes, i.e. the optical path difference and the exact fringe vector of the modified interference pattern, are also explicitly presented. All needed relations are first introduced in form of general vector and tensor equations. Then, equations for fringe recovery are written in cartesian components and used within a quantitative experiment to demonstrate the reliability of the theory. Some important points still should be considered in order to enable fringe recovery for general geometrical cases: (1) the holographic setup should allow a geometrical and/or an optical modification to adequately compensate the unknown mechanical deformation and the optical image aberrations; (2) the holographic method should be one of the type belonging either the real-time technique or the double exposure technique on two holograms (because not all holographic methods are suitable for this purpose); (3) the holographic images of the deformed and undeformed body must sufficiently overlap so that the fringe spacing must be large enough and the fringe visibility must have sufficient quality to be analyzed properly. The relations considered are general and may also be used in other application fields (with their related problems) of holographic interferometry, when the loss of fringe spacing and contrast should be compensated.
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