Few-fringe-based phase-shifting profilometry employing hilbert transform.

In optical measurement techniques, when the projector works at a constant projection rate, reducing the number of projected fringe patterns is an effective way to reduce the projection time. In this paper, we propose a few-fringe-based phase-shifting profilometry employing Hilbert transform. We project only two fringe patterns for each frequency of fringes, with the phase shift between the fringes designed to be π. The Hilbert transform makes these two captured fringes phase shifted by π /2, thus transforming the original two fringes into four, and the wrapped phase can be obtained through these four fringes with a phase difference of π /2. To improve the accuracy and robustness of the method, we adopt three frequencies of fringes for phase unwrapping. Further, since different phase unwrapping methods can be used for the different frequencies of the fringes, we propose a heterodyne 2H+2 M+2 L method and a hierarchical 2H+2 M+2 L respectively. Multiple experimental results have confirmed the feasibility and effectiveness of the two 2H+2 M+2 L methods, and the different characteristics of the reconstructed shapes obtained by the two 2H+2 M+2 L methods are compared to provide useful guidance in the selection of the required method for different application scenarios. The experimental results demonstrate that when using the heterodyne and hierarchical methods for phase unwrapping, the RMSE of the 2H+2 M+2 L method is only higher than that of the three-frequency four-step phase-shifting method by 0.0056 and 0.0024 respectively, but this 2H+2 M+2 L method improves the efficiency of the three-frequency four-step phase-shifting method by 50%. • Our proposed method requires only two fringes to calculate the wrapped phase for each frequency fringe. • We analyzed the phase error of our proposed two-fringe method and found it comparable to the wrapped phase error of the 4-step phase-shifting method. • We experimentally analyzed the transformation results of fringes with different frequencies using the Hilbert transform. • We provide the fringe generation and wrapped phase calculation formulas for the commonly used heterodyne and hierarchical methods in temporal phase unwrapping. [ABSTRACT FROM AUTHOR]