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Correction of phase errors introduced by nonlinearity and specular reflection based on double N-step phase-shifting profilometry

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Abstract

The N-step phase-shifting profilometry (PSP) is widely used to calculate the wrapped phases of static objects. However, measurement accuracy and precision can be affected by nonlinear error caused by system nonlinearity, as well as phase error resulting from overexposed regions on objects with highly reflective surfaces. To address these two issues, the phase error due to system nonlinearity and the phase error due to intensity saturation region are analyzed separately in this paper. This paper proposes introducing an additional set of fringe sequences with a π/N phase shift on top of the N-step PSP by fusing the unwrapped phase of the original fringe sequences with that of the additional fringe sequences, i.e., double N-step PSP, in order to suppress the nonlinear error and the error in overexposed regions. The experimental results demonstrate that the double N-step PSP can suppress not only the nonlinear error within the system, but also the error caused by the overexposed regions of the objects with high reflective surfaces.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Acknowledgements

This work was funded by the Natural Science Foundation of Shandong Province (Contract No. ZR2021MF024 and ZR2020QF101) and National Natural Science Foundation of China (Contract No. 62273274).

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Authors and Affiliations

  1. School of Information and Control Engineering, Qingdao University of Technology, Qingdao, 266520, Shandong, China

    Wen Zhang, Shuo Shan, Ze Li, Peng Xu, Jintao Liu & Jianhua Wang

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  1. Wen Zhang
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  3. Ze Li
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Contributions

WZ Derived the relevant equations and wrote the body of the manuscript. SS and ZL assisted WZ in performing the experiments. PX and JTL prepared Figs. 1, 2, 3, 4, 5, 6, 7, 8. PX and JHW reviewed the manuscript

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Correspondence to Jianhua Wang.

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Zhang, W., Shan, S., Li, Z. et al. Correction of phase errors introduced by nonlinearity and specular reflection based on double N-step phase-shifting profilometry. Appl. Phys. B 130, 1 (2024). https://doi.org/10.1007/s00340-023-08142-4

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