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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 13 — Jun. 21, 2010
  • pp: 13431–13443

Algorithm and experiment of whole-aperture wavefront reconstruction from annular subaperture Hartmann–Shack gradient data

Hongyan Xu, Hao Xian, and Yudong Zhang  »View Author Affiliations

Optics Express, Vol. 18, Issue 13, pp. 13431-13443 (2010)

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Abstract: A new method is proposed for testing a rotationally symmetric aspheric surface with several annular subapertures based on a Hartmann–Shack sensor. In consideration of the limited sampling of Hartmann–Shack subapertures in the matching annular subaperture, a new algorithm for whole-aperture wavefront reconstruction from annular subaperture Hartmann–Shack gradient data is established. The algorithm separates the tip, tilt, and defocus misalignments for each annular subaperture by introducing annular Zernike polynomials. The performance of the algorithm is evaluated for different annular subaperture configurations, and the sensitivity of the algorithm to the detector error of the wavefront gradient is analyzed. The algorithm is verified by the experimental results.

© 2010 OSA

OCIS Codes
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
(220.1250) Optical design and fabrication : Aspherics
(220.4840) Optical design and fabrication : Testing

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: March 8, 2010
Revised Manuscript: May 19, 2010
Manuscript Accepted: May 23, 2010
Published: June 8, 2010

Hongyan Xu, Hao Xian, and Yudong Zhang, "Algorithm and experiment of whole-aperture wavefront reconstruction from annular subaperture Hartmann–Shack gradient data," Opt. Express 18, 13431-13443 (2010)

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  1. C. J. Kim, “Polynomial fit of interferograms,” Appl. Opt. 21(24), 4521–4525 (1982). [CrossRef] [PubMed]
  2. J. G. Thunen and O. Y. Kwon, “Full aperture testing with subaperture test optics,” Proc. SPIE 351, 19–27 (1982).
  3. W. W. Chow and G. N. Lawrence, “Method for subaperture testing interferogram reduction,” Opt. Lett. 8(9), 468–470 (1983). [CrossRef] [PubMed]
  4. T. W. Stuhlinger, “Subaperture optical testing: experimental verification,” Proc. SPIE 656, 118–127 (1986).
  5. Y.-M. Liu, G. N. Lawrance, and C. L. Koliopoulos, “Subaperture testing of aspheres with annular zones,” Appl. Opt. 27(21), 4504–4513 (1988). [CrossRef] [PubMed]
  6. X. Hou, F. Wu, L. Yang, S. B. Wu, and Q. Chen, “Full-aperture wavefront reconstruction from annular subaperture interferometric data by use of Zernike annular polynomials and a matrix method for testing large aspheric surfaces,” Appl. Opt. 45(15), 3442–3455 (2006). [CrossRef] [PubMed]
  7. X. Hou, F. Wu, L. Yang, and Q. Chen, “Experimental study on measurement of aspheric surface shape with complementary annular subaperture interferometric method,” Opt. Express 15(20), 12890–12899 (2007). [CrossRef] [PubMed]
  8. M. Melozzi, L. Pezzati, and A. Mazzoni, “Testing aspheric surfaces using multiple annular interferograms,” Opt. Eng. 32(5), 1073–1079 (1993). [CrossRef]
  9. D. Malacara, M. Servin, A. Morales, and Z. Maracara, “Aspherical wavefront testing with several defusing steps,” in International Conference on Optical Fabrication and Testing, T. Kasai,ed., Proc.SPIE 2576,190–192 (1995).
  10. M. J. Tronolone, J. F. Fleig, C. Huang, and J. H. Bruning, “Method of testing aspherical optical surfaces with an interferometer,” US Patent 5416586 (May.16, 1995).
  11. F. Granados-Agustín, J. F. Escobar-Romero, and A. Cornejo-Rodríguez, “Testing parabolic surfaces with annular subaperture interferograms,” Opt. Rev. 11, 82–86 (2004). [CrossRef]
  12. M. Otsubo, K. Okada, and J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994). [CrossRef]
  13. P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photon. News 14(5), 38–43 (2003). [CrossRef]
  14. P. Murphy, G. Devries, C. Brophy, and G. Forbes, “Stitching of near-nulled subaperture measurements,” US Patent 2009/0251702 A1 (October 8, 2009).
  15. S. Y. Chen, S. Y. Li, Y. F. Dai, L. Y. Ding, and S. Y. Zeng, “Experimental study on subaperture testing with iterative stitching algorithm,” Opt. Express 16(7), 4760–4765 (2008). [CrossRef] [PubMed]
  16. D. R. Neal, R. R. Rammage, D. J. Armstrong, W. T. Turner, and J. D. Mansell, “Apparatus and method for evaluating a target larger than a measuring aperture of a sensor,” US Patent 6184974 B1 (February 6, 2001).
  17. T. D. Raymond, D. R. Neal, D. M. Topa, and T. L. Schmitz, “High-speed noninterferometric nanotopographic characterization of Si wafer surfaces,” Proc. SPIE 4809, 208–216 (2002). [CrossRef]
  18. V. N. Mahajan, “Zernike annular polynomials for imaging systems with annular pupils,” J. Opt. Soc. Am. 71(1), 75–85 (1981). [CrossRef]
  19. X. Hou, F. Wu, L. Yang, and Q. Chen, “Comparison of annular wavefront interpretation with Zernike circle polynomials and annular polynomials,” Appl. Opt. 45(35), 8893–8901 (2006). [CrossRef] [PubMed]

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