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Improved Iterative Method for Wavefront Reconstruction from Derivatives in Grid Geometry

  • Nguyen, Vu-Hai-Linh (Department of Science of measurement, University of Science and Technology) ;
  • Rhee, Hyug-Gyo (Department of Science of measurement, University of Science and Technology) ;
  • Ghim, Young-Sik (Department of Science of measurement, University of Science and Technology)
  • Received : 2021.09.03
  • Accepted : 2021.11.02
  • Published : 2022.02.25

Abstract

This paper proposes a robust, simple zonal wavefront-estimation method in a grid sampling model. More slopes are added to the integral equation of the algorithm to improve the accuracy and convergence rate of this approach, especially for higher-order optical aberrations. The Taylor theorem is applied to clarify the mathematical description of the remaining error in the proposed method. Several numerical simulations are conducted to ensure the performance and improvement in comparison to the Southwell and previous algorithm. An experiment is also conducted according to deflectometry output and the results are verified using a reference measured with a stylus system.

Keywords

Acknowledgement

This study was supported by the Commercialization Promotion Agency for R&D Outcomes (COMPA), "Real-time 3D surface measurement for aspheric and freeform lens", funded by the Ministry of Science and ICT(MSIT).

References

  1. J. H. Lee, S. E. Lee, and Y. J. Kong, "Performance prediction of a laser-guide star adaptive optics system for a 1.6 m telescope," Curr. Opt. Photonics 2, 269-279 (2018). https://doi.org/10.3807/COPP.2018.2.3.269
  2. J. H. Lee, S. Shin, G. N. Park, H.-G. Rhee, and H.-S. Yang, "Atmospheric turbulence simulator for adaptive optics evaluation on an optical test bench," Curr. Opt. Photonics 1, 107-112 (2017). https://doi.org/10.3807/COPP.2017.1.2.107
  3. K. Ahn, S.-H. Lee, I.-K. Park, and H.-S. Yang, "Simulation of a laser tomography adaptive optics with Rayleigh laser guide stars for the satellite imaging system," Curr. Opt. Photonics 5, 101-113 (2021). https://doi.org/10.3807/COPP.2021.5.2.101
  4. Y.-S. Ghim, H.-G. Rhee, A. Davies, H.-S. Yang, and Y.-W. Lee, "3D surface mapping of freeform optics using wavelength scanning lateral shearing interferometry," Opt. Express 22, 5098-5105 (2014). https://doi.org/10.1364/OE.22.005098
  5. M. T. Nguyen, Y.-S. Ghim, and H.-G. Rhee, "Single-shot deflectometry for dynamic 3D surface profile measurement by modified spatial-carrier frequency phase-shifting method," Sci. Rep. 9, 3157 (2019). https://doi.org/10.1038/s41598-019-39514-6
  6. M. P. Rimmer, "Method for evaluating lateral shearing interferograms," Appl. Opt. 13, 623-629 (1974). https://doi.org/10.1364/AO.13.000623
  7. J. Herrmann, "Least-squares wave front errors of minimum norm," J. Opt. Soc. Am. 70, 28-35 (1980). https://doi.org/10.1364/JOSA.70.000028
  8. E. P. Wallner, "Optimal wave-front correction using slope measurements," J. Opt. Soc. Am. 73, 1771-1776 (1983). https://doi.org/10.1364/JOSA.73.001771
  9. L. Huang and A. Asundi, "Improvement of least-squares integration method with iterative compensations in fringe reflectometry," Appl. Opt. 51, 7459-7465 (2012). https://doi.org/10.1364/AO.51.007459
  10. K. R. Freischlad and C. L. Koliopoulos, "Modal estimation of a wave front from difference measurements using the discrete Fourier transform," J. Opt. Soc. Am. A 3, 1852-1861 (1986). https://doi.org/10.1364/JOSAA.3.001852
  11. W. H. Southwell, "Wave-front estimation from wave-front slope measurements," J. Opt. Soc. Am. 70, 998-1006 (1980). https://doi.org/10.1364/JOSA.70.000998
  12. R. Cubalchini, "Modal wave-front estimation from phase derivative measurements," J. Opt. Soc. Am. 69, 972-977 (1979). https://doi.org/10.1364/JOSA.69.000972
  13. R. H. Hudgin, "Wave-front reconstruction for compensated imaging," J. Opt. Soc. Am. 67, 375-378 (1977). https://doi.org/10.1364/JOSA.67.000375
  14. D. L. Fried, "Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements," J. Opt. Soc. Am. 67, 370-375 (1977). https://doi.org/10.1364/JOSA.67.000370
  15. W. Zou and J. P. Rolland, "Quantifications of error propagation in slope-based wavefront estimations," J. Opt. Soc. Am. A 23, 2629-2638 (2006). https://doi.org/10.1364/JOSAA.23.002629
  16. G. Li, Y. Li, K. Liu, X. Ma, and H. Wang, "Improving wavefront reconstruction accuracy by using integration equations with higher-order truncation errors in the Southwell geometry," J. Opt. Soc. Am. A 30, 1448-1459 (2013). https://doi.org/10.1364/JOSAA.30.001448
  17. B. Pathak and B. R. Boruah, "Improved wavefront reconstruction algorithm for Shack-Hartmann type wavefront sensors," J. Opt. 16, 055403 (2014). https://doi.org/10.1088/2040-8986/16/5/055403
  18. P. H. Phuc, N. T. Manh, H.-G. Rhee, Y.-S. Ghim, H.-S. Yang, and Y.-W. Lee, "Improved wavefront reconstruction algorithm from slope measurements," J. Korean Phys. Soc. 70, 469-474 (2017). https://doi.org/10.3938/jkps.70.469
  19. Y. Saad and H. A. van der Vorst, "Iterative solution of linear systems in the 20th century," J. Comput. Appl. Math. 123, 1-33 (2000). https://doi.org/10.1016/S0377-0427(00)00412-X
  20. C. Canuto and A. Tabacco, "Taylor expansions and applications BT," in Mathematical Analysis I, C. Canuto and A. Tabacco, Eds., 2nd ed. (Springer International Publishing, Charm, Germany. 2015), pp. 225-257.
  21. B. Pathak and B. R. Boruah, "Improvement in error propagation in the Shack-Hartmann-type zonal wavefront sensors," J. Opt. Soc. Am. A 34, 2194-2202 (2017). https://doi.org/10.1364/JOSAA.34.002194
  22. R. J. Noll, "Zernike polynomials and atmospheric turbulence," J. Opt. Soc. Am. 66, 207-211 (1976). https://doi.org/10.1364/JOSA.66.000207
  23. V. Lakshminarayanan and A. Fleck, "Zernike polynomials: a guide," J. Mod. Opt. 58, 545-561 (2011). https://doi.org/10.1080/09500340.2011.554896
  24. M. T. Nguyen, P. Kang, Y.-S. Ghim, and H.-G. Rhee, "Nonlinearity response correction in phase-shifting deflectometry," Meas. Sci. Technol. 29, 045012 (2018). https://doi.org/10.1088/0957-0233/29/4/045012