Theory and application of robust linear phase-shift algorithm for phase-shift deflectometry method

Based on the polynomial theory, the error propagation characteristics of the widely used N-step discrete Fourier transform (N-DFT) phase-shift algorithm were analyzed via theoretical analysis, under the effect of Gamma distortion and phase detuning. The results showed that the N-DFT algorithm could...

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Bibliographic Details
Published in:Scientific reports 2024-08, Vol.14 (1), p.18424-21, Article 18424
Main Authors: Yang, Song, Zhu, Xianyong, Cao, Zhirui, Zhao, Jiali, Xiao, Xiong, Lv, Changchun, Du, Yang, Wang, Ruiqing, Wu, Peng, Wang, Zheyuan
Format: Article
Language:English
Subjects:
639/166/988
639/624/1111/1116
Algorithms
Detuning error
Fourier transforms
Gamma distortion
Humanities and Social Sciences
multidisciplinary
Phase shift algorithm
Phase-shift deflectometry
Science
Science (multidisciplinary)
Simulation analysis
Theoretical analysis
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Summary:Based on the polynomial theory, the error propagation characteristics of the widely used N-step discrete Fourier transform (N-DFT) phase-shift algorithm were analyzed via theoretical analysis, under the effect of Gamma distortion and phase detuning. The results showed that the N-DFT algorithm could not simultaneously suppress both types of error. A robust linear phase-shift (RLPS) algorithm was designed, the performance of the RLPS and 8-DFT algorithms in terms of spectral response, detuning robustness, and G S / N was briefly analysis by Manuel Servin method. The Simulation analysis and comparison of the results show that the RLPS algorithm could suppress both types of error simultaneously, which exhibited better stability and accuracy than N-DFT and exponential algorithms, particularly in gradient measurement stability, peak-to-valley (PV) and root-mean-square (RMS) error suppression. Moreover, a physical experiment apparatus was built to test unidirectionally inclined plane mirror and concave mirror using the RLPS, N-DFT, and exponential algorithms. The results showed that the RLPS algorithm could significantly improve the measurement stability and accuracy in the presence of detuning and without screen Gamma calibration.
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-024-69264-z