A novel dual-frequency pattern is developed which combines a high-frequency sinusoid component with a unit-frequency sinusoid component, where the high-frequency component is used to generate robust phase information, and the unit-frequency component is used to reduce phase unwrapping ambiguities. With our proposed pattern scheme, phase unwrapping can overcome the major shortcomings of conventional spatial phase unwrapping: phase jumping and discontinuities. Compared with conventional temporal phase unwrapped approaches, the proposed pattern scheme can achieve higher quality phase data using a less number of patterns. To process data in real time, we also propose and develop look-up table based fast and accurate algorithms for phase generation and 3-D reconstruction. Those fast algorithms can be applied to our pattern scheme as well as traditional phase measuring profilometry. For a 640 x 480 video stream, we can generate phase data at 1063.8 frames per second and full 3-D coordinate point clouds at 8.3 frames per second. These achievements are 25 and 10 times faster than previously reported studies.

Several performance criteria are described to enable a fair comparison among the various correlation filter designs: signal-to-noise ratio, peak sharpness, peak location, light efficiency, discriminability, and distortion invariance. The trade-offs resulting between some of these criteria are illustrated with the help of a new family of filters called fractional power filters (FPFs). The classical matched filter, phase-only filter (POF), and inverse filter are special cases of FPFs. Using examples, we show that the POF appears to provide a good compromise between noise tolerance and peak sharpness.

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.

Phase measuring profilometry is a method of structured light illumination whose three-dimensional reconstructions are susceptible to error from nonunitary gamma in the associated optical devices. While the effects of this distortion diminish with an increasing number of employed phase-shifted patterns, gamma distortion may be unavoidable in real-time systems where the number of projected patterns is limited by the presence of target motion. A mathematical model is developed for predicting the effects of nonunitary gamma on phase measuring profilometry, while also introducing an accurate gamma calibration method and two strategies for minimizing gamma's effect on phase determination. These phase correction strategies include phase corrections with and without gamma calibration. With the reduction in noise, for three-step phase measuring profilometry, analysis of the root mean squared error of the corrected phase will show a 60x reduction in phase error when the proposed gamma calibration is performed versus 33x reduction without calibration.

Based on recent discoveries, we introduce a method to project a single structured pattern onto an object and then reconstruct the three-dimensional range from the distortions in the reflected and captured image. Traditional structured light methods require several different patterns to recover the depth, without ambiguity or albedo sensitivity, and are corrupted by object movement during the projection/ capture process. Our method efficiently combines multiple patterns into a single composite pattern projection allowing for real-time implementations. Because structured light techniques require standard image capture and projection technology, unlike time of arrival techniques, they are relatively low cost.