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Error-immune Algorithm for Absolute Testing of Rotationally Asymmetric Surface Deviation

  • Zhang, Yanwei (State Key Laboratory of Applied Optics, Changchun Institute of Optic, Fine Mechanics and Physics, Chinese Academy of Sciences) ;
  • Su, Dongqi (State Key Laboratory of Applied Optics, Changchun Institute of Optic, Fine Mechanics and Physics, Chinese Academy of Sciences) ;
  • Li, Le (State Key Laboratory of Applied Optics, Changchun Institute of Optic, Fine Mechanics and Physics, Chinese Academy of Sciences) ;
  • Sui, Yongxin (State Key Laboratory of Applied Optics, Changchun Institute of Optic, Fine Mechanics and Physics, Chinese Academy of Sciences) ;
  • Yang, Huaijiang (State Key Laboratory of Applied Optics, Changchun Institute of Optic, Fine Mechanics and Physics, Chinese Academy of Sciences)
  • Received : 2014.05.09
  • Accepted : 2014.07.02
  • Published : 2014.08.25

Abstract

Based on Zernike polynomial fitting, we propose an algorithm believed to be new for interferometric measurements of rotationally asymmetric surface deviation of optics. This method tests and calculates each angular surface by choosing specified rotation angles with lowest error. The entire figure can be obtained by superimposing these sub-surfaces. Simulation and experiment studies for verifying the proposed algorithm are presented. The results show that the accuracy of the proposed method is higher than single-rotation algorithm and almost comparable to the rotation-averaging algorithm with fewer rotation measurements. The new algorithm can achieve a balance between the efficiency and accuracy.

Keywords

References

  1. R. E. Park, "Removal of test optics errors," 22nd Annual Technical Symposium, International Society for Optics and Photonics (1978).
  2. B. S. Fritz, "Absolute calibration of an optical flat," Opt. Eng. 23, 234379 (1984). https://doi.org/10.1117/12.7973304
  3. V. Greco, R. Tronconi, C. D. Vecchio, M. Trivi, and G. Molesini, "Absolute measurement of planarity with Fritz's method: Uncertainty evaluation," Appl. Opt. 38, 2018-2027 (1999). https://doi.org/10.1364/AO.38.002018
  4. C. J. Evans and R. N. Kestner, "Test optics error removal," Appl. Opt. 35, 1015-1021 (1996). https://doi.org/10.1364/AO.35.001015
  5. R. E. Parks, L. Shao, and C. J. Evans, "Pixel-based absolute topography test for three flats," Appl. Opt. 37, 5951-5956 (1998). https://doi.org/10.1364/AO.37.005951
  6. R. Freimann, B. Dorband, and F. Holler, "Absolute measurement of non-comatic aspheric surface errors," Opt. Commun. 161, 106-114 (1999). https://doi.org/10.1016/S0030-4018(99)00006-1
  7. W. Otto, "Method for the interferometric measurement of non-rotationally symmetric wavefront errors," U.S. Patent No. 6,839,143 (2005).
  8. W. Otto and S. Guenther, "Method for the interferometric measurement of non-rotationally symmetric wavefront errors," U.S. Patent No. 7,277,186 (2007).
  9. S. W. Kim and H. G. Rhee, "Self-calibration of high frequency errors of test optics by arbitrary N-step rotation," Int. J. Korean Soc. Precision Eng. 1, 115-123 (2000).
  10. H. G. Rhee, Y. W. Lee, and S. W. Kim, "Azimuthal position error correction algorithm for absolute test of large optical surfaces," Opt. Express 14, 9169-9177 (2006). https://doi.org/10.1364/OE.14.009169
  11. W. Song, F. Wu, and X. Hou, "Method to test rotationally asymmetric surface deviation with high accuracy," Appl. Opt. 51, 5567-5572 (2012). https://doi.org/10.1364/AO.51.005567
  12. S. K. Gil, "2-step quadrature phase-shifting digital holographic optical encryption using orthogonal polari zation and error analysis," J. Opt. Soc. Korea 16, 354-364 (2012). https://doi.org/10.3807/JOSK.2012.16.4.354
  13. W. D. Joo, "Wavefront sensitivity analysis using global wavefront aberration in an unobscured optical system," J. Opt. Soc. Korea 16, 228-235 (2012). https://doi.org/10.3807/JOSK.2012.16.3.228

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