Skip to main content
SpringerLink
Log in

Self-correction of fringe order jump error induced by system nonlinearity based on phase-coding method

  • Regular Paper
  • Published:
Optical Review Aims and scope Submit manuscript

Abstract

Temporal phase unwrapping based on phase-encoding is a technique widely used in 3D measurement for its high-speed advantage. However, eliminating fringe order jump error induced by the system’s luminance nonlinearity is still a key challenge. We propose a fringe order jump error self-correction method to address this issue. First, we encode the shifting phase and stair phase separately and combine them into the same pattern based on four-step phase shifting. This allows us to calculate the fringe order and wrapped phase simultaneously and avoid the overlapping of two set phases. Then, we add auxiliary patterns to obtain information on the order-located period’s odd-evenness characteristic. Theoretically, we demonstrate that under the influence of the nonlinear effect, the order calculation value for a particular period fluctuates between the ideal values of two adjacent orders. Thus, the correct order value can be directly determined by acquiring the period characteristic information, without the need for complex error compensation. Simulations demonstrate that the method performs good robustness where random noise and luminance saturation exist simultaneously in addition to system nonlinearity. Our experiments confirm the effectiveness of this method for high-accurate and fast fringe order determination.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Data availability

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

References

  1. Xu, J., Zhang, S.: Status, challenges, and future perspectives of fringe projection profilometry. Opt. Lasers Eng. 135, 106193 (2020)

    Article  Google Scholar 

  2. Liang, R.: Short wavelength and polarized phase shifting fringe projection imaging of translucent objects. Opt. Eng. 53, 014104 (2014)

    Article  ADS  Google Scholar 

  3. Gorthi, S.S., Rastogi, P.: Fringe projection techniques: Whither we are? Opt. Lasers Eng. 48, 133–140 (2010)

    Article  Google Scholar 

  4. Jeong, M.S., Kim, S.W.: Color grating projection moire with time-integral fringe capturing for high-speed 3-D imaging. Opt. Eng. 41, 1912–1917 (2002)

    Article  ADS  Google Scholar 

  5. Song, L., Dong, X., Xi, J., Yu, Y., Yang, C.: A new phase unwrapping algorithm based on Three Wavelength Phase Shift Profilometry method. Opt. Laser Technol. 45, 319–329 (2013)

    Article  ADS  Google Scholar 

  6. Zuo, C., Huang, L., Zhang, M., Chen, Q., Asundi, A.: Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review. Opt. Lasers Eng. 85, 84–103 (2016)

    Article  Google Scholar 

  7. Zuo, C., Feng, S., Huang, L., Tao, T., Yin, W., Chen, Q.: Phase shifting algorithms for fringe projection profilometry: A review. Opt. Lasers Eng. 109, 23–59 (2018)

    Article  Google Scholar 

  8. Yang, F., He, X.: Two-step phase-shifting fringe projection profilometry: intensity derivative approach. Appl. Optics 46, 7172–7178 (2007)

    Article  ADS  Google Scholar 

  9. Chen, X., Wu, J., Fan, R., Liu, Q., Xiao, Y., Wang, Y., Wang, Y.: Two-Digit Phase-Coding Strategy for Fringe Projection Profilometry. IEEE Trans. Instrum. Meas. 70, 7001309 (2021)

    ADS  Google Scholar 

  10. He, X., Kemao, Q.: A comparison of n-ary simple code and n-ary gray code phase unwrapping in high-speed fringe projection profilometry. Opt. Lasers Eng. 128, 106046 (2020)

    Article  Google Scholar 

  11. Li, E.B., Peng, X., Xi, J., Chicharo, J.F., Yao, J.Q., Zhang, D.W.: Multi-frequency and multiple phase-shift sinusoidal fringe projection for 3D profilometry. Opt. Express 13, 1561–1569 (2005)

    Article  ADS  Google Scholar 

  12. Zhu, H., Guo, H.: Alternate Iterative Least-Squares Algorithm Based on Nonuniform Phase Shifting for Suppressing Nonlinearity Errors in Fringe Projection Profilometry. IEEE Trans. Instrum. Meas. 71, 1–13 (2022)

    Article  Google Scholar 

  13. Yu, X., Lai, S., Liu, Y., Chen, W., Xue, J., Zhang, Q.: Generic nonlinear error compensation algorithm for phase measuring profilometry. Chin. Opt. Lett. 19, 101201 (2021)

    Article  ADS  Google Scholar 

  14. Luo, J., Wang, Y., Yang, X., Chen, X., Wu, Z.: Modified five-step phase-shift algorithm for 3D profile measurement. Optik 162, 237–243 (2018)

    Article  ADS  Google Scholar 

  15. Wu, G., Wu, Y., Li, L., Liu, F.: High-resolution few-pattern method for 3D optical measurement. Opt. Lett. 44, 3602–3605 (2019)

    Article  ADS  Google Scholar 

  16. Shiyang, T., Yanjun, F., Jiannan, G., Baiheng, M., Zhanjun, Y.: A novel fast 3D measurement method based on phase-coded fringe projection. Opt. Rev. 29, 215–224 (2022)

    Article  Google Scholar 

  17. Zou, Z., Zhu, Y., Qin, G., Wang, D.: Three-dimensional shape measurement method based on composite cyclic phase coding. Appl. Optics 62, 246–254 (2023)

    Article  ADS  Google Scholar 

  18. Ma, M., Yao, P., Deng, J., Deng, H., Zhang, J., Zhong, X.: A morphology phase unwrapping method with one code grating. Rev. Sci. Instrum. 89, 073112 (2018)

    Article  ADS  Google Scholar 

  19. Wu, J., Zhou, Z., Liu, Q., Wang, Y., Wang, Y., Gu, Y., Chen, X.: Two-wavelength phase-shifting method with four patterns for three-dimensional shape measurement. Opt. Eng. 59, 024107 (2020)

    Article  ADS  Google Scholar 

  20. Chen, X., Wang, Y., Wang, Y., Ma, M., Zeng, C.: Quantized phase coding and connected region labeling for absolute phase retrieval. Opt. Express 24, 28613–28624 (2016)

    Article  ADS  Google Scholar 

  21. Xing, S., Guo, H.: Directly recognizing and removing the projector nonlinearity errors from a phase map in phase-shifting fringe projection profilometry. Opt. Commun. 435, 212–220 (2019)

    Article  ADS  Google Scholar 

  22. Xing, S., Guo, H.: Correction of projector nonlinearity in multi-frequency phase-shifting fringe projection profilometry. Opt. Express 26, 16277–16291 (2018)

    Article  ADS  Google Scholar 

  23. Hoang, T., Pan, B., Nguyen, D., Wang, Z.: Generic gamma correction for accuracy enhancement in fringe-projection profilometry. Opt. Lett. 35, 1992–1994 (2010)

    Article  ADS  Google Scholar 

  24. Wang, Y., Zhang, S.: Novel phase-coding method for absolute phase retrieval. Opt. Lett. 37, 2067–2069 (2012)

    Article  ADS  Google Scholar 

  25. Jiang, C., Xing, S., Guo, H.: Fringe harmonics elimination in multi-frequency phase-shifting fringe projection profilometry. Opt. Express 28, 2838–2856 (2020)

    Article  ADS  Google Scholar 

  26. Pan, B., Kemao, Q., Huang, L., Asundil, A.: Phase error analysis and compensation for nonsinusoidal waveforms in phase-shifting digital fringe projection profilometry. Opt. Lett. 34, 416–418 (2009)

    Article  ADS  Google Scholar 

  27. Ri, S., Wang, Q., Xia, P., Tsuda, H.: Spatiotemporal phase-shifting method for accurate phase analysis of fringe pattern. J. Opt. 21, 095702 (2019)

    Article  ADS  Google Scholar 

  28. Yao, J., Xiong, C., Zhou, Y., Miao, H., Chen, J.: Phase error elimination considering gamma nonlinearity, system vibration, and noise for fringe projection profilometry. Opt. Eng. 53, 094102 (2014)

    Article  ADS  Google Scholar 

  29. Liu, K., Wang, Y., Lau, D. L., Hao, Q., Hassebrook, L. G.: Gamma model and its analysis for phase measuring profilometry. J. Opt. Soc. Am. A-Opt. Image Sci. Vis. 27, 553–562 (2010)

Download references

Funding

The Joint Funds of the National Natural Science Foundation of China (No. 51975374).

Author information

Authors and Affiliations

  1. School of Sensing Science and Engineering, Shanghai Jiao Tong University, Shanghai, China

    Ze-Bo Wu, Wei Tao, Na Lv & Hui Zhao

Authors
  1. Ze-Bo Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Tao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Na Lv
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hui Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hui Zhao.

Ethics declarations

Conflict of interest

The authors declare no conflicts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, ZB., Tao, W., Lv, N. et al. Self-correction of fringe order jump error induced by system nonlinearity based on phase-coding method. Opt Rev 30, 436–453 (2023). https://doi.org/10.1007/s10043-023-00825-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10043-023-00825-9

Keywords

Search

Navigation