The Optical Signal Analysis (OSA) method to process fringe patterns containing displacement information

In preceding publications, the authors have analyzed different aspects of the recovery of displacement information encoded in scalar fields of gray levels. The signals that contain displacement information can be generated by different optical methods or can be computer generated, for example, in the images of the magnetic resonance method (MRI). This paper merges ideas of the authors' previous developments, included in the manuscript references, with new developments. These developments simplify fundamental basic steps of the process of retrieving displacement information. They also extend the applicability of basic algorithms to a very diverse variety of patterns, including patterns that contain displacement singularities. Singularities in displacement fields indicate departures of the standard continuity conditions assumed in the mathematical model of Continuum Mechanics, these discontinuities can be local or can divide the field into piecewise continuous regions. To illustrate the practical aspect of these derivations the proposed methodology is applied to very complex patterns. The analysis of these patterns with standard techniques will require complex and time-consuming pattern processing procedures. In the approach presented in this paper, the same task can be accomplished by a much simpler and general scheme.