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Applied Optics

Applied Optics


  • Vol. 39, Iss. 28 — Oct. 1, 2000
  • pp: 5179–5186

High-precision analysis of a lateral shearing interferogram by use of the integration method and polynomials

Seiichi Okuda, Takashi Nomura, Kazuhide Kamiya, Hiroshi Miyashiro, Kazuo Yoshikawa, and Hatsuzo Tashiro  »View Author Affiliations

Applied Optics, Vol. 39, Issue 28, pp. 5179-5186 (2000)

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Interferograms obtained with ordinary interferometers, such as the Fizeau interferometer or the Twyman–Green interferometer, show the contour maps of a wave front under test. On the other hand, lateral shearing interferograms show the difference between a wave front under test and a sheared wave front, that is, the inclination of the wave front. Therefore the shape of the wave front under test is reconstructed by means of analyzing the difference. To reconstruct the wave front, many methods have been proposed. An integration method is usually used to reconstruct the wave front under test rapidly. However, this method has two disadvantages: The analysis accuracy of the method is low, and part of the wave front cannot be measured. To overcome these two problems, a new, to our knowledge, integration method, improved by use of polynomials, is proposed. The validity of the proposed method is evaluated by computer simulations. In the simulations the analysis accuracy achieved by the proposed method is compared with the analysis accuracy of the ordinary integration method and that of the method proposed by Rimmer and Wyant. The results of the simulations show that the analysis accuracy of the newly proposed method is better than that of the integration method and that of the Rimmer–Wyant method.

© 2000 Optical Society of America

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry

Original Manuscript: February 4, 2000
Revised Manuscript: June 22, 2000
Published: October 1, 2000

Seiichi Okuda, Takashi Nomura, Kazuhide Kamiya, Hiroshi Miyashiro, Kazuo Yoshikawa, and Hatsuzo Tashiro, "High-precision analysis of a lateral shearing interferogram by use of the integration method and polynomials," Appl. Opt. 39, 5179-5186 (2000)

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  1. R. N. Smartt, “Zone plates interferometer,” Appl. Opt. 13, 1093–1099 (1974). [CrossRef] [PubMed]
  2. G. Harbers, P. J. Kunst, G. W. R. Leibbrandt, “Analysis of lateral shearing interferograms by use of Zernike polynomials,” Appl. Opt. 35, 6162–6172 (1996). [CrossRef] [PubMed]
  3. M. Servin, D. Malacara, J. L. Marroquin, “Wave-front recovery from two orthogonal sheared interferograms,” Appl. Opt. 35, 4343–4348 (1996). [CrossRef] [PubMed]
  4. W. Shen, M. W. Chang, D. S. Wan, “Zernike polynomial fitting of lateral shearing interferometry,” Opt. Eng. 36, 905–913 (1997). [CrossRef]
  5. C. Elster, I. Weingartner, “Solution to the shearing problem,” Appl. Opt. 38, 5024–5031 (1999). [CrossRef]
  6. H. Schreiber, J. Schwider, “Lateral shearing interferometer based on two Ronchi phase gratings in series,” Appl. Opt. 36, 5321–5324 (1997). [CrossRef] [PubMed]
  7. M. P. Rimmer, J. C. Wyant, “Evaluation of large aberration using a lateral-shear interferometer having variable shear,” Appl. Opt. 14, 142–150 (1975). [CrossRef] [PubMed]
  8. T. Yatagai, T. Kanou, “Aspherical surface testing with shearing interferometer using the fringe scanning detection method,” Opt. Eng. 23, 357–360 (1997).
  9. F. M. Dickey, T. M. Harder, “Shearing plate optical alignment,” Opt. Eng. 17, 295–298 (1978). [CrossRef]
  10. T. Nomura, K. Kamiya, S. Okuda, H. Miyashiro, K. Yoshikawa, H. Tashiro, “Shape measurements of mirror surfaces with a lateral-shearing interferometer during machine running,” Precis. Eng. 22, 185–189 (1998). [CrossRef]
  11. D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992), pp. 461–466.

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