Selection of fringe frequency sequence based on “2 + 1” phase-shifting algorithm

IF 2 3区物理与天体物理 Q3 OPTICS Applied Physics B Pub Date : 2025-02-21 DOI:10.1007/s00340-025-08411-4

Yixin Ji, Longxiang Zhang, Wei Wu, Jianhua Wang

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Abstract

The combination of the “2 + 1” phase-shifting algorithm with temporal phase unwrapping (TPU) not only facilitates the acquisition of phase information using fewer fringe patterns but also minimizes errors resulting from motion in the 3-step phase-shifting profilometry (PSP). By considering the influence of fringe frequency sequences on measurement accuracy, we derive the noise-induced wrapped phase error and its variance of the “2 + 1” phase-shifting algorithm and further analyze the phase unwrapping accuracy at each stage of the “2 + 1 + 2 + 2” algorithm. Consequently, a method for selecting the optimal fringe frequency sequence is introduced, ensuring that the phase unwrapping accuracy in both stages remains as consistent as possible, while the effectiveness of this method is experimentally validated. The experimental results demonstrate that the method for selecting the optimal fringe frequency is applicable to both hierarchical and heterodyne TPU and aligns well with theoretical analysis. Compared to two sets of non-optimal frequency sequences, the error rates of the optimal fringe frequency sequences are reduced by 33.41% and 72.53%, respectively.

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基于“2 + 1”移相算法的条纹频率序列选择

将“2 + 1”相移算法与时间相位展开（TPU）相结合，不仅可以使用更少的条纹模式获取相位信息，而且可以最大限度地减少三步相移轮廓术（PSP）中运动引起的误差。考虑条纹频率序列对测量精度的影响，推导了“2 + 1”移相算法的噪声包绕相位误差及其方差，并进一步分析了“2 + 1 + 2 + 2”移相算法各阶段的相位解包裹精度。在此基础上，提出了一种选择最优条纹频率序列的方法，以保证两阶段的相位展开精度尽可能一致，并通过实验验证了该方法的有效性。实验结果表明，该方法既适用于层次式TPU，也适用于外差式TPU，与理论分析结果吻合较好。与两组非最优频率序列相比，最优条纹频率序列的错误率分别降低了33.41%和72.53%。

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来源期刊

Applied Physics B 物理-光学

CiteScore

4.00

自引率

4.80%

发文量

202

审稿时长

3.0 months

期刊介绍： Features publication of experimental and theoretical investigations in applied physics Offers invited reviews in addition to regular papers Coverage includes laser physics, linear and nonlinear optics, ultrafast phenomena, photonic devices, optical and laser materials, quantum optics, laser spectroscopy of atoms, molecules and clusters, and more 94% of authors who answered a survey reported that they would definitely publish or probably publish in the journal again Publishing essential research results in two of the most important areas of applied physics, both Applied Physics sections figure among the top most cited journals in this field. In addition to regular papers Applied Physics B: Lasers and Optics features invited reviews. Fields of topical interest are covered by feature issues. The journal also includes a rapid communication section for the speedy publication of important and particularly interesting results.