The basic problem in holographic interferometry, in the case of a deformed opaque body, concerns the determination of displacements, rotations, and especially surface strains from the fringes that can be observed when reconstructing the image. However, in industrial application, large deformations often occur, so that fringes would not be visible. Several approaches were proposed previously to overcome this problem by a sort of compensation. In most cases, fringes can be recovered and analyzed by such a modification. The same problem of recovering fringes can also come up in the case of a strong spatial change of index of refraction, for instance, in a gas with a high temperature gradient. After the process of modification, three conditions must be fulfilled: (a) small areas around each pair of aberrated image points of the undeformed and the deformed object surface must overlap; (b) the expected fringes must become sufficiently spaced; and (c) they must have a sufficient contrast. The authors establish here the basic concept of aberrated images and modified fringe formation leading to two fundamental equations by means of a differential form of the relevant optical path difference. In order to show how to use these equations, a development, in combination with image processing, is given in the case of moderate rotation of the order (mu) << 1 and small strains of the order (mu) 2.