Direct extraction of phase gradients from Fourier-transform and phase-step fringe patterns

An approach to computing pixel-by-pixel gradients of optical phase directly from digitally encoded Fourier-transform or phase-stepped fringe patterns is described. This approach can be classified as a phase unwrapping but is really a sine–cosine demodulation technique that finds its roots in the differential cross-multiplier phase-demodulation technique commonly used by the optical fiber sensor community. This technique is algorithmically simple, does not rely on a computation of the arctangent, and therefore is not subject to some of the limitations of the standard phase-unwrapping methodologies. The proposed phase-gradient technique is demonstrated by the calculation of strain fields from moire interferometric fringe patterns.