Natural Demodulation of 2D Fringe Patterns

For almost two decades one of the most successful methods of demodulating fringe patterns was based on the Fourier transform implementation of the 1-D Hilbert transform /1/ . Recently, however, a method of fringe analysis based on an isotropic 2-D Hilbert transform has been proposed /2/ . An isotropic Hilbert transform had been previously considered topologically impossible by many researchers. The new method has been called the "vortex transform" for brevity. The vortex transform [VT] is based on the approximate quadrature relationship of a spiral phase Fourier operator. The approximation is asymptotic /3/ with high accuracy predicted for any meaningful fringes; fringes which have a radius of curvature larger than the fringe spacing. An important aspect of the VT is the orientation phase factor required to obtain the final demodulated pattern's phase and amplitude. In this paper I shall concentrate on the remarkable simplification in fringe analysis made possible by the VT utilising orientation phase unwrapping.