Optimized two-frequency phase-measuring-profilometry light-sensor temporal-noise sensitivity

Abstract

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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“…The procedure is illustrated in Figure 2(c). According to [11], the phase error σϕ of the phase map should be…”

Ultra High-speed 3-dimensional Profilometry Using a Laser Grating Projection System

“…2 shows such images. Since we adopted the two-wavelength phase unwrapping method [18,19], there are two images present having grating pitches different from each other. Note that the 'wavelength' does not mean the optical wavelength, but the pitch of the grating.…”

“…If the pitch difference is too small, however, the noise in the process of pattern projection and image capturing makes it difficult to achieve the accurate profile of the object. Generally the two-wavelength phase-unwrapping method is advantageous for high-speed 3D profilometry [18,19].…”

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“…A well designed projection pattern can achieve significant accuracy and precision (Li et al, 2003). However, due to the difficulties involved in encoding each pixel uniquely, many of the most effective pattern types require more than one projection/capture instance in order to reconstruct the subject surface.…”