Advertisement

Applied Physics B

, 125:45 | Cite as

Virtual wavefront calibration method based on ray tracing for alignment error compensation in the interferometric bearing ball measurement system

  • Weina Hao
  • Zhigang LiuEmail author
  • Shaowei Gu
  • Fengchao Ling
  • Jun Hong
Article
  • 47 Downloads

Abstract

The accuracy of laser interferometry for measuring bearing balls is limited because it is challenging to realize null positioning of the ball being assessed. Even a slight alignment error causes the reflected wavefront to carry an uncertain aberration, which results in the surface error being obscured by the wavefront aberration. To effectively separate the surface error from the reflected wavefront, a virtual wavefront calibration method of ray tracing for alignment error compensation in the interferometric bearing ball measurement system is proposed. A virtual wavefront measurement model with variable alignment vector of the system is established based on the ray tracing principle and coordinate transform theory. According to the virtual wavefront, a calibration process is achieved in the virtual model with a known regularization and optimization method; as a result, no accurate adjustment mechanism is required to adjust the position of the bearing ball in the actual measurement system. Simulation and experiment results indicate that the proposed method is effective, and the repeatability of this measurement system is better than λ/40 peak–valley value. The final results may promote the application of this method in other fields of optical measurement.

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) (Grant numbers 51635010, 51875447).

References

  1. 1.
    T.W. Ng, Optical inspection of ball bearing defects. Meas. Sci. Technol. 18, N73–N76 (2007)ADSCrossRefGoogle Scholar
  2. 2.
    J. Schmit, S. Han, E. Novak, Ball bearing measurement with white light interferometry. Proc. SPIE 7389, 73890P–73890P–73812 (2009)ADSCrossRefGoogle Scholar
  3. 3.
    J.A. Lipa, G.J. Siddall, High precision measurement of gyro rotor sphericity. Precis. Eng. 2, 123–128 (1980)CrossRefGoogle Scholar
  4. 4.
    B. Kimbrough, J. Millerd, J. Wyant, J. Hayes, Low-coherence vibration insensitive Fizeau interferometer. Proc. SPIE 6292, 62920F (2006)CrossRefGoogle Scholar
  5. 5.
    M.V. Mantravadi, D. Malacara. In: D. Malacara Optical Shop Testing (eds) Newton, Fizeau, and Haidinger Interferometers, 3rd edn. (Wiley, Hoboken, 2007)Google Scholar
  6. 6.
    J. Peng, Y. Shen, K. Wang, D. Wang, Error impact analysis and experimental research for absolute testing of spherical surfaces. Infrar. Laser. Eng. 41, 1345–1350 (2012)Google Scholar
  7. 7.
    Y.-Y. Cheng, J.C. Wyant, Two-wavelength phase shifting interferometry. Appl. Opt. 23(24), 4539 (1984)ADSCrossRefGoogle Scholar
  8. 8.
    D. Mo, R. Wang, G. Li, N. Wang, K. Zhang, Y. Wu, Double-sideband frequency scanning interferometry for long-distance dynamic absolute measurement. Appl. Phys. B-Lasers O 11, 123 (2017)Google Scholar
  9. 9.
    H. Wu, F. Zhang, T. Liu, P. Balling, X. Qu, Absolute distance measurement by multi-heterodyne interferometry using a frequency comb and a cavity-stabilized tunable laser. Appl. Opt. 55, 4210–4218 (2016)ADSCrossRefGoogle Scholar
  10. 10.
    G. Baer, Automated surface positioning for a non-null test interferometer. Opt. Eng. 49, 095602 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    B. Li, B. Li, B. Liu, T. Jiang, An improved calibration method for structured light projection measurement system. Proc. SPIE 8791, 879116 (2013)CrossRefGoogle Scholar
  12. 12.
    E.D. Kim, M.S. Kang, S.C. Choi, Y.W. Choi, Reverse-optimization alignment algorithm using Zernike sensitivity. J. Opt. Soc. Korea 9, 68–73 (2005)CrossRefGoogle Scholar
  13. 13.
    L. Zhang, D. Liu, T. Shi, Y. Yang, Y. Shen, Practical and accurate method for aspheric misalignment aberrations calibration in non-null interferometric testing. Appl. Opt. 52, 8501–8511 (2013)ADSCrossRefGoogle Scholar
  14. 14.
    X. Hou, F. Wu, L. Yang, Q. Chen, Experimental study on measurement of aspheric surface shape with complementary annular subaperture interferometric method. Opt. Exp. 15, 12890–12899 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    R. Kulkarni, P. Rastogi, Direct unwrapped phase estimation in phase shifting interferometry using Levenberg–Marquardt algorithm. J. Opt. 19, 015608 (2017)ADSCrossRefGoogle Scholar
  16. 16.
    S.S. Lee, J.H. Kim, E.S. Choi, Phase shifting interferometry based on a vibration sensor—feasibility study on elimination of the depth degeneracy. J. Korean Phys. Soc. 70, 687–692 (2017)ADSCrossRefGoogle Scholar
  17. 17.
    Y. Zhang, Z. Pang, X. Fan, Z. Ma, Q. Chen, L. Xiang, S. To, The computer-aided alignment study of three-mirror off-axis field bias optical system. Proc. SPIE 8417, 84170L (2012)ADSCrossRefGoogle Scholar
  18. 18.
    J. Li, H. Shen, R. Zhu, Method of alignment error control in free-form surface metrology with the tilted-wave-interferometer. Opt. Eng. 55, 044101 (2016)ADSCrossRefGoogle Scholar
  19. 19.
    W.A. Ramadan, H.H. Wahba, Simulated Fizeau ring fringes in transmission through spherical and plane reflected surfaces. Appl. Phys. B-Lasers O 1, 124 (2017)Google Scholar
  20. 20.
    Q. Hao, S. Wang, Y. Hu, H. Cheng, M. Chen, T. Li, Virtual interferometer calibration method of a non-null interferometer for freeform surface measurements. Appl. Opt. 55, 9992–10001 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    G. Baer, J. Schindler, C. Pruss, J. Siepmann, W. Osten, Calibration of a non-null test interferometer for the measurement of aspheres and free-form surfaces. Opt. Exp. 22, 31200 (2014)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Weina Hao
    • 1
  • Zhigang Liu
    • 1
    Email author
  • Shaowei Gu
    • 1
  • Fengchao Ling
    • 1
  • Jun Hong
    • 1
  1. 1.Key Laboratory of Education Ministry for Modern Design and Rotor-Bearing SystemXi’an Jiaotong UniversityXi’anChina

Personalised recommendations