Starting with the basic equation of holographic interferometry for arbitrary deformations, a generalization of the real-time technique with modification in the case of large deformations is laid out. Ultimately, the problem of recovering previously invisible fringes when reconstructing and the following fringe analysis is discussed. In the past, necessary equations derived from two first derivatives have been established to ensure a proper spacing and a sufticient contrast of these fringes, by a careful choice of the modification parameters at least locally around some point for such a general setup. To make the fringes visible not only locally but also in a larger domain, further equations resulting from the second derivatives of the optical path difference must be considered; in other words, the remaining modification parameters must be determined in such a way that the optical path difference becomes quasi-stationary in an extended domain. This second derivative reveals a particular relation to the aberration theory of the holographic image. It is composed of a mechanical deformation term containing the curvature change of the object surface, a completely dual term of the virtual optical deformation because of the modification, also implying the astigmatism of the image points, and finally a mixed term that is dual to itself. Two illustrative examples of the application of this second-derivative expression are discussed. First, with a small shift of the reference source but no object deformation, a previous result is confirmed, which also shows explicitly how to alter the fringe curvature. Second, the standard case of small isometric object surface deformation without modification reveals a result which allows the determination of the curvature change of Kolter-Sanders of the object surface.