Phase error compensation for three-dimensional shape measurement with projector defocusing

Abstract

This paper analyzes the phase error for a three-dimensional (3D) shape measurement system that utilizes our recently proposed projector defocusing technique. This technique generates seemingly sinusoidal structured patterns by defocusing binary structured patterns and then uses these patterns to perform 3D shape measurement by fringe analysis. However, significant errors may still exist if an object is within a certain depth range, where the defocused fringe patterns retain binary structure. In this research, we experimentally studied a large depth range of defocused fringe patterns, from near-binary to near-sinusoidal, and analyzed the associated phase errors. We established a mathematical phase error function in terms of the wrapped phase and the depth z. Finally, we calibrated and used the mathematical function to compensate for the phase error at arbitrary depth ranges within the calibration volume. Experimental results will be presented to demonstrate the success of this proposed technique. Disciplines Computer-Aided Engineering and Design | Mechanical Engineering CommentsThis article is from Applied Optics 50 (2011) This paper analyzes the phase error for a three-dimensional (3D) shape measurement system that utilizes our recently proposed projector defocusing technique. This technique generates seemingly sinusoidal structured patterns by defocusing binary structured patterns and then uses these patterns to perform 3D shape measurement by fringe analysis. However, significant errors may still exist if an object is within a certain depth range, where the defocused fringe patterns retain binary structure. In this research, we experimentally studied a large depth range of defocused fringe patterns, from near-binary to near-sinusoidal, and analyzed the associated phase errors. We established a mathematical phase error function in terms of the wrapped phase and the depth z. Finally, we calibrated and used the mathematical function to compensate for the phase error at arbitrary depth ranges within the calibration volume. Experimental results will be presented to demonstrate the success of this proposed technique.

Three-dimensional profilometry with nearly focused binary phase-shifting algorithms

“…Similar to the method of Su et al using a Ronchi grating [3], this approach strives to generate ideal sinusoidal fringe patterns by defocusing binary structured ones. However, compared to the conventional sinusoidal fringe generation technique, this technique has two major shortcomings: a smaller depthmeasurement range [4] and the difficulty of calibrating the defocused projector [2].…”

“…It clearly shows binary structures. The phase errors of the different algorithms, computed as in [4], are plotted in Figure 2 shows the measurement results. This experiment indicates that, when the projector is nearly focused, the seven-and nine-step algorithms yield the most accurate results, while the four-step algorithm yields the least accurate results.…”

Three-dimensional shape measurement with binary dithered patterns

“…The narrower phase maps are unwrapped with the assistance of the phase from the largest fringe period using a temporal phaseunwrapping algorithm. To convert the unwrapped phase to depth, we used a simple phase-to-height conversion algorithm described in [14]. It is well known that when fringe stripes are wide, the random noise is very large, and with the fringe period decreasing, the quality of the 3D results becomes better.…”

Optimal fringe angle selection for digital fringe projection technique

“…For a simple reference-plane-based calibration method, the relationship between the depth z and the phase difference is z z 0 c × ΔΦ [12]; here, z 0 is the constant shift and c is the calibration constant. Therefore, the depth error caused by system noise is approximately Δz e c × δΦ e .…”

“…4(e) clearly shows the highly detailed features on the difference map when the fringe patterns use the optimal fringe angle. We further convert phase difference maps to depth maps using the simple phaseto-height conversion algorithm discussed in [12]. The depth scaling coefficient was obtained using the optimal fringe angle, and applied to both phase difference maps.…”