• Acta Optica Sinica
  • Vol. 45, Issue 10, 1011001 (2025)
Yu Han, Zhoujie Wu, and Qican Zhang*
Author Affiliations
  • College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, Sichuan , China
  • show less
    DOI: 10.3788/AOS250553 Cite this Article Set citation alerts
    Yu Han, Zhoujie Wu, Qican Zhang. Temporal Phase Unwrapping Algorithm Based on Multi-Frequency Phase Binarization[J]. Acta Optica Sinica, 2025, 45(10): 1011001 Copy Citation Text show less

    Abstract

    Objective

    In temporal phase unwrapping algorithms for fringe projection measurement technology, the accuracy of phase order decoding plays a decisive role in the successful recovery of the object’s height. The methods for obtaining phase orders are mainly divided into two categories. One approach involves projecting multi-frequency phase-shifted fringes, calculating the wrapped phases corresponding to fringes with different periods, and then solving the phase order according to the periodic relationship between the projected fringes. The other approach involves projecting a series of multi-level gray fringes or black-and-white binary fringes, encoding the period information of phase-shifted fringes at a single frequency, and obtaining the phase order after decoding according to established rules. Inspired by the above two methods, we propose directly dividing the wrapped phase values, calculated from multi-frequency phase-shifted fringes, into binary values according to different thresholds, and then obtaining different coding words, which are used to mark the orders of the phase-shifted fringes to reconstruct the continuous phase. Existing methods proposed by researchers, which rely on a single threshold for binarizing the wrapped phase to extract phase orders, are prone to errors in phase order jump areas. In this paper, corresponding threshold division results for the two methods are proposed to meet the complementary Gray code coding and decoding strategy, which can effectively avoid the error problem at the order jump, obtain correct phase order information, and flexibly realize different algorithms for phase unwrapping.

    Methods

    Different binary patterns can be obtained by dividing the wrapped phase values obtained from multi-frequency fringes with different thresholds. Considering that the Gray code encoding methods are complementary at the coding word transitions, and offer higher fault tolerance and stronger anti-noise performance, the idea of Gray code is introduced. By adjusting the threshold of the wrapped phase, a pattern sequence that meets the coding and decoding strategy of the complementary Gray code method can be directly constructed. This sequence can effectively avoid jump errors and provide correct order information after decoding. To reduce the number of multi-frequency phase-shifted fringes that need to be projected in one measurement, we further propose a method of projecting only bi-frequency phase-shifted fringes. The single-period phase-shifted fringes are used to generate the pattern corresponding to the complementary Gray code method, thus enabling accurate reconstruction of the three-dimensional surface shape. This method significantly reduces the number of projected patterns and greatly improves the efficiency and usability of the temporal phase unwrapping algorithm based on multi-frequency phase binarization.

    Results and Discussions

    In this paper, we propose two new methods successively: the bi-threshold binarization for multi-frequency fringes method (MFBT) and the multi-threshold binarization for bi-frequency fringes method (BFMT). Both methods acquire Gray code sequence patterns and calculate the fringe orders through decoding based on the complementary Gray code method, thus avoiding errors in fringe order jumps in principle. Among them, the BFMT offers more advantages in terms of phase unwrapping efficiency and performance, with the following specific manifestations. In terms of efficiency, compared with the MFBT also proposed in this paper, the number of fringes required to recover the accurate phase is significantly reduced. Furthermore, compared with the traditional complementary Gray code method, it still has an advantage in the number of projected fringes under certain specific conditions. In terms of robustness, compared with the phase unwrapping algorithm in which the Gray code pattern assists phase shifting, the BFMT only requires projecting a single type of phase-shifted fringe pattern to achieve phase unwrapping with the assistance of binary-coded patterns. This effectively solves the problem of inconsistent defocus requirements in the projection system, which is common in the traditional Gray code method. Compared with the traditional bi-frequency phase unwrapping method, the BFMT adopts the encoding and decoding strategy of the complementary Gray code method. When the frequency difference between the bi-frequency fringes is large, the Gray code patterns are less sensitive to frequency changes and exhibit stronger anti-noise performance. Therefore, for the same number of projected patterns, the BFMT shows stronger robustness.

    Conclusions

    Combining the two categories of methods for calculating phase orders in temporal phase unwrapping algorithms, we propose two temporal phase unwrapping algorithms based on multi-frequency phase binarization: MFBT and BFMT. Both methods adopt the idea of complementary Gray code, which can effectively avoid the jump errors caused by using the single-threshold binarization method previously proposed by researchers. Both simulation and actual experiments verify the effectiveness of the proposed methods, enhancing the practicality of multi-frequency fringe projection three-dimensional measurement technology. In addition, the BFMT has an advantage in unwrapping efficiency and offers higher practical value.