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Fast calculation of phase in spatial n-point phase-shifting techniques

The n-point technique (also called the spatial carrier phase-shifting technique) is one of a few fringe pattern analysis techniques. We present modified algorithms for the n-point technique from which the phase modulo 2(pi) can be calculated in a much shorter time versus conventional algorithms. The algorithms are based on spatial synchronous detection techniques, and by analogy to those techniques, the modified algorithms are named low-pass algorithms, as opposed to the convention 'high-pass' algorithms in the n-point technique.