Self-calibration Algorithm of Systematic Errors For Interferometer

간섭계에 있어서의 계통 오차의 자율 교정 알고리즘

  • Published : 2005.05.01

Abstract

When an almost flat surface under test is measured by an interferometer, the measurement result is largely influenced by systematic errors that include geometrical errors of a reference flat surface. To determine the systematic errors of the interferometer by the conventional method that is called the three flat method, we must take the reference flat surface out from the interferometer and measure it. Because of difficulties to set the reference flat surface to the interferometer exactly and quickly, this method is not practical. On the other hand, the method that measures a surface under test with some shifts in the direction being perpendicular to the optical axis of the interferometer is studied. However, the parasitic pitching, rolling and up-down movement caused by the above shifts brings serious error to the measurement result, and the algorithm by which the influences can be eliminated is not still established. In this paper, we propose the self-calibration algorithm for determining the systematic errors that include geometrical errors of a reference flat surface by several rotation shifts and a linear shift of general surface under test, and verify by a numerical experiment that this algorithm is useful for determining the systematic errors.

Keywords

References

  1. Oreb.Bozenko, F., 'Calibration of a 300-mm-aperture phase-shifting Fizeau interferometer,' Appl. Opt., Vol. 39, No. 28, pp. 5161-5171, 2000 https://doi.org/10.1364/AO.39.005161
  2. Takatsuji, T., Ueki N., Hibino, K., Kurosawa T., 'Japanese Ultimate flatness Interferometer and its preliminary experiment,' Proc. of SPIE, May 2001
  3. Schulz, G.. and Schwider, J., 'Precise Measurement of Planeness,' Appl. Opt. 6, pp. 1077-1084, 1967 https://doi.org/10.1364/AO.6.001077
  4. Fritz, B. S., 'Absolute calibration of optical flat,' Optical engineering, 23-4, pp. 379-383, 1984
  5. Hariharan, P., 'Interferometoric measurements of devi ations from flatness: some new techniques,' SPIE Vol. 3479, pp. 1-13, 1998
  6. Mercier, R., Lamare, M., Picart, P., Marioge, J. P., 'Two-flat method for bi-dimensional measurement of absolute departure from the best sphere,' Pure. Appl. Opt., 6, pp. 117-126, 1997 https://doi.org/10.1088/0963-9659/6/1/013
  7. Kiyono, S., Gao, W., Seio, H., 'Theoritical Study on Abosolute Measurement Method of Surface Shape by Interferogram,' Journal of Jpn. Soc. Prec. Eng., 64, pp. 1137-1145, 1998 https://doi.org/10.2493/jjspe.64.1137
  8. Sonosaki, A., Iwata, K., Iwasaki, Y., 'Profile Mearuement with No Standard,' Journal of Jpn. Soc. Prec. Eng., 63, pp. 129-133, 1999
  9. Ito, T., Hinaji, T., Horiuchi, O.,'High precision Flatness Measurement by Combing Two-Orientation method and Radial Shift Method,'Jounal of Jpn. Soc. Prec. Eng., 58, pp. 883-886, 1992 https://doi.org/10.2493/jjspe.58.883
  10. Fujimoto, I.,'One Idea on the Reduction of Systematic Errors with Interferometer,' Proc. of National Conf. of JSPE, pp. 89, 2000