Local frequency estimation for the fringe pattern with a spatial carrier: principle and applications

A local frequency estimation approach for the fringe pattern with a spatial carrier by which the 2D spatial frequencies at a certain pixel are estimated from its neighborhood is presented. The applications of this approach in the fringe pattern analyses are also introduced. First, a 2D spatial carrier phase-shifting algorithm is derived. With it the detuning errors induced by frequency mismatching are avoided, and the stronger phase deformations can be successfully coped with. Second, a novel aperture extrapolation method is developed by which the phase accuracies of the Fourier-transform method at the aperture boundaries are effectively improved.