Temporal phase unwrapping towards high-accuracy and high-speed fringe projection profilometry

• Main Author: He, Xiaoyu
• Other Authors: Qian Kemao
• Format: Thesis-Doctor of Philosophy
• Language: English
• Published: Nanyang Technological University 2021
• Subjects: Engineering::Computer science and engineering
• Online Access: https://hdl.handle.net/10356/150663
• Institution: Nanyang Technological University

Optical three-dimensional (3D) measurement technologies, mainly including photogrammetry, interferometry, time of flight, and speckle/fringe projection profilometry, have been widely used in industrial inspection, motion capture, virtual/augmented reality, and heritage preservation. Compared with the other technologies, the fringe projection profilometry (FPP) has many inherent advantages, such as low cost, high resolution, and relatively high speed. In FPP, a continuous phase map is extracted from the captured fringe patterns and then converted to the profile of the object. To obtain the continuous phase map, spatial and temporal phase unwrapping techniques are developed. Compared with the spatial phase unwrapping, the temporal phase unwrapping (TPU) avoids the interference from the physical discontinuities on the measured objects by the pixel-by-pixel manner, thus has more applications. However, there are still some issues unclear in TPU for high-accuracy and high-speed FPP: (i) the limited measurement speed of gray code phase unwrapping by the number of codes; (ii) the impact of the different orders of codes in the gray code and simple code phase unwrapping methods; (iii) the comparison between different TPU methods with different coding strategies. Therefore, in this thesis, a systematic study of TPU methods towards high-speed and high-accuracy FPP is proposed to address the above issues. First, to enhance the speed of gray code phase unwrapping, I propose a novel quaternary gray code method under a binary defocusing FPP system. A weighted optimization algorithm is presented for the design of special binary code patterns. The designed binary patterns are projected on the object with a defocused projector, and interestingly become quaternary patterns which are more expressive gray codes. After the distorted code patterns are captured by a camera, they will undergo the proposed normalization-denoising-clustering process to recover the desired gray codes, which are then used to recover the phase orders for phase unwrapping. Compared with the traditional binary/ternary gray code methods, the proposed method obtains the unwrapped phase with similar accuracy but fewer patterns, thus the measurement speed is enhanced. Second, I comprehensively compare the simple code and gray code methods with the consideration of various factors, including the strategies for error removal, the numbers of codes, the step heights and invalid regions on the measured objects, defocusing level and noise level of the system. From simulations and experiments, I conclude that (i) in general, simple code with a proposed identification and binary classification method has a similar result as gray code; (ii) when accuracy is critical, binary simple code and binary gray code methods are recommended; (iii) when speed is critical, quaternary simple code method with continuity/geometry constraints is recommended. Third, I compare three popular TPU methods using different coding strategies, two-frequency, phase coding, and gray code methods, in which three situations are considered: the traditional 8-bit focused FPP (bFPP), the high-speed binary defocused FPP (bFPP), and the geometry/continuity constrained binary defocused FPP (cFPP). In all three methods, two types of phase unwrapping errors result from the system noise: uniformly distributed errors (E^U) all over the phase map and non-uniformly distributed errors (E^N) only around particular regions. The E^U and E^N of the three methods are compared qualitatively and quantitatively, from which I find that (i) In aFPP, E^U is more noticeable in TF and PC than GC when the fringe frequency is high (f≥16), and E^N is around left and right image borders in TF, while it is around 2π phase jumps in PC and GC; GC shows the best performance; (ii) In bFPP, the overall performances of the three methods are similar to those in aFPP, but there are more E^N in PC and GC than aFPP due to defocusing; TF becomes more comparable to GC; (iii) In cFPP, compared with bFPP, E^U in TF and PC is reduced greatly and E^N in TF is removed, thus TF shows the best performance. Based on these new findings, a quick guide for TPU selection is provided. In summary, this thesis has the following contributions for TPU in high-accuracy and high-speed FPP: (i) a framework for gray code phase unwrapping to enhance the measurement speed; (ii) the comparison of TPU methods with different orders of codes, and (iii) the comparison of TPU methods with different coding strategies. These contributions enable researchers and engineers to understand the state-of-the-art TPU methods and select the “best” TPU method for their applications.