Temporal frame-to-frame noise in multipattern structured light projection can significantly corrupt depth measurement repeatability. We present a rigorous stochastic analysis of phase-measuring-profilometry temporal noise as a function of the pattern parameters and the reconstruction coefficients. The analysis is used to optimize the two-frequency phase measurement technique. In phase-measuring profilometry, a sequence of phase-shifted sine-wave patterns is projected onto a surface. In two-frequency phase measurement, two sets of pattern sequences are used. The first, low-frequency set establishes a nonambiguous depth estimate, and the second, high-frequency set is unwrapped, based on the low-frequency estimate, to obtain an accurate depth estimate. If the second frequency is too low, then depth error is caused directly by temporal noise in the phase measurement. If the second frequency is too high, temporal noise triggers ambiguous unwrapping, resulting in depth measurement error. We present a solution for finding the second frequency, where intensity noise variance is at its minimum.
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