Frequency modulation interpretation of fringes and computation of strains

Phase modulation is a traditional model for the interpretation of fringe patterns that provide displacement information, moire, holographic interferometry, and speckle techniques. An alternative interpretation of the fringes is to consider them as frequency modulated signals. This change of interpretation has profound practical consequences if the space-frequency representation of signals is applied. The utilization of the energy representation of a signal in the coordinates-frequency space provides powerful procedures to retrieve strains distributions directly from fringe patterns without resorting to differentiation of the displacements. This approach also simplifies the determination of displacements replacing unwrapping procedures by integration of the strains, a robust operation in the presence of noise. The Gabor transform, wavelet transforms, and quadratic representations of the energy of signals are tools that are available to carry out the practical implementation of this approach to fringe processing. This paper extends to two dimensions the methodology developed for one dimension in a previous paper.