Current Optics and Photonics

Optical Society of Korea (한국광학회)
권호 표지
DOI QR코드

DOI QR Code

High-order Reduced Radial Zernike Polynomials for Modal Reconstruction of Wavefront Aberrations in Radial Shearing Interferometers

  • Tien Dung Vu (Department of Mechanical System Design Engineering, Seoul National University of Science and Technology) ;
  • Quang Huy Vu (Department of Mechanical System Design Engineering, Seoul National University of Science and Technology) ;
  • Joohyung Lee (Department of Mechanical System Design Engineering, Seoul National University of Science and Technology)
  • Received : 2023.09.06
  • Accepted : 2023.11.13
  • Published : 2023.12.25
Download PDF
⟨ Previous Next ⟩

Abstract

We present a method for improving the accuracy of the modal wavefront reconstruction in the radial shearing interferometers (RSIs). Our approach involves expanding the reduced radial terms of Zernike polynomials to high-order, which enables more precise reconstruction of the wavefront aberrations with high-spatial frequency. We expanded the reduced polynomials up to infinite order with symbolic variables of the radius, shearing amount, and transformation matrix elements. For the simulation of the modal wavefront reconstruction, we generated a target wavefront subsequently, magnified and measured wavefronts were generated. To validate the effectiveness of the high-order Zernike polynomials, we applied both low- and high-order polynomials to the wavefront reconstruction process. Consequently, the peak-to-valley (PV) and RMS errors notably decreased with values of 0.011λ and 0.001λ, respectively, as the order of the radial Zernike polynomial increased.

Keywords

Acknowledgement

National Research Foundation of Korea (Grant no. NRF-2021R1A4A1031660), Ministry of Trade, Industry and Energy (Grant no. MOTIE-20014784, 20018441), KOITA grant funded by MSIT (Grant no. 1711199141), and Hanoi University of Science and Technology (Grant no. HUST, T2022-PC-021).

References

  1. E. Donath and W. Carlough, "Radial shearing interferometer," J. Opt. Soc. Am. 53, 395-395 (1963). https://doi.org/10.1364/JOSA.53.000395
  2. N. Gu, B. Yao, L. Huang, and C. Rao, "Compact single-shot radial shearing interferometer with random phase shift," Opt. Lett. 42, 3622-3625 (2017). https://doi.org/10.1364/OL.42.003622
  3. H. M. Park, D. W. Kim, C. E. Guthery, and K-N. Joo, "Radial shearing dynamic wavefront sensor based on a geometric phase lens pair," Opt. Lett. 47, 549-552 (2022). https://doi.org/10.1364/OL.447505
  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. K.-N. Joo and H. M. Park, "Shearing Interferometry: Recent research trends and applications," Curr. Opt. Photonics 7, 325-336 (2023).
  6. Y. Guo, H. Chen, J. Xu, and J. Ding, "Two-dimensional wavefront reconstruction from lateral multi-shear interferograms," Opt. Express 20, 15723-15733 (2012). https://doi.org/10.1364/OE.20.015723
  7. H.-H. Lee, J.-H. You, and S.-H. Park, "Phase-shifting lateral shearing interferometer with two pairs of wedge plates," Opt. Lett. 28, 2243-2245 (2003). https://doi.org/10.1364/OL.28.002243
  8. J. E. Greivenkamp, "Sub-Nyquist interferometry," Appl. Opt. 26, 5245-5258 (1987). https://doi.org/10.1364/AO.26.005245
  9. D. Malacara, Optical Shop Testing, 3rd ed. (John Wiley & Sons, USA, 2007), pp. 187-202.
  10. N. Gu, L. Huang, Z. Yang, and C. Rao, "A single-shot common-path phase-stepping radial shearing interferometer for wavefront measurements," Opt. Express 19, 4703-4713 (2011). https://doi.org/10.1364/OE.19.004703
  11. J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, "Pixelated phase-mask dynamic interferometer," Proc. SPIE 5531, 305 (2004).
  12. J. C. Wyant, "Dynamic interferometry," Opt. Photonics News 14, 36-41 (2003). https://doi.org/10.1364/OPN.14.4.000036
  13. Y. B. Seo, H. B. Jeong, H.-G. Rhee, Y.-S. Ghim, and K.-N. Joo, "Single-shot freeform surface profiler," Opt. Express 28, 3401-3409 (2020). https://doi.org/10.1364/OE.380305
  14. D. Bian, D. Kim, B. Kim, L. Yu, K.-N. Joo, and S. W. Kim, "Diverging cyclic radial shearing interferometry for single-shot wavefront sensing," Appl. Opt. 59, 9067-9074 (2020). https://doi.org/10.1364/AO.402903
  15. 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
  16. L. J. Li, W. B. Jing, W. Shen, Y. Weng, B. K. Huang, and X. Feng, "Improving the capture-range problem in phase-diversity phase retrieval for laser-wavefront measurement using geometrical-optics initial estimates," Curr. Opt. Photonics 6, 473-478 (2022).
  17. 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
  18. Z. Ji, X. Zhang, Z. Zheng, Y. Li, and J. Chang, "Algorithm based on the optimal block zonal strategy for fast wavefront reconstruction," Appl. Opt. 59, 1383-1396 (2020). https://doi.org/10.1364/AO.380999
  19. V.-H.-L. Nguyen, H.-G. Rhee, and Y.-S. Ghim, "Improved iterative method for wavefront reconstruction from derivatives in grid geometry," Curr. Opt. Photonics 6, 1-9 (2022).
  20. I. Mochi and K. A. Goldberg, "Modal wavefront reconstruction from its gradient," Appl. Opt. 54, 3780-3785 (2015). https://doi.org/10.1364/AO.54.003780
  21. N. Gu, L. Huang, Z. Yang, Q. Luo, and C. Rao, "Modal wavefront reconstruction for radial shearing interferometer with lateral shear," Opt. Lett. 36, 3693-3695 (2011). https://doi.org/10.1364/OL.36.003693
  22. C. Tian, X. Chen, and S. Liu, "Modal wavefront reconstruction in radial shearing interferometry with general aperture shapes," Opt. Express 24, 3572-3583 (2016). https://doi.org/10.1364/OE.24.003572
  23. Y. Zhang, D. Su, L. Li, Y. Sui, and H. Yang, "Error-immune algorithm for absolute testing of rotationally asymmetric surface deviation," J. Opt. Soc. Korea 18, 335-340 (2014). https://doi.org/10.3807/JOSK.2014.18.4.335
  24. D.T. Nguyen, K. C. T. Nguyen, B. X. Cao, V. T. Tran, T. D. Vu, and N. T. Bui, "Modal reconstruction based on arbitrary high-order zernike polynomials for deflectometry," Mathematics 11, 3915 (2023).
  25. T. M. Jeong, D.-K. Ko, and J. Lee, "Method of reconstructing wavefront aberrations by use of Zernike polynomials in radial shearing interferometers," Opt. Lett. 32, 232-234 (2007). https://doi.org/10.1364/OL.32.000232
  26. V. Lakshminarayanana and A. Fleck, "Zernike polynomials: a guide," J. Mod. Opt. 58, 545-561 (2011). https://doi.org/10.1080/09500340.2011.554896
  27. K. Niu and C. Tian, "Zernike polynomials and their applications," J. Opt. 24, 123001 (2022).
  28. H. van Brug, "Efficient Cartesian representation of Zernike polynomials in computer memory," Proc. SPIE 3190, 382-392 (1997).