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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 18 — Jun. 20, 2011
  • pp: 2815–2822

Method for designing phase-calculation algorithms for two-dimensional grating phase-shifting interferometry

Yucong Zhu, Satoru Odate, Ayako Sugaya, Katsura Otaki, Katsumi Sugisaki, Chiaki Koike, Tetsuya Koike, and Kiyoshi Uchikawa  »View Author Affiliations

Applied Optics, Vol. 50, Issue 18, pp. 2815-2822 (2011)

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We propose a design method of phase-analysis algorithms based on two-dimensional grating phase shifting for Talbot interferometry, Talbot-Lau imaging, or the Ronchi test. These algorithms are designed to separate the two orthogonal shearing wavefronts and eliminate error effects of unwanted diffraction orders, simultaneously. Taking the effect of multidiffraction into account, moving the two-dimensional grating along a certain pass leads to a series of phase-shifted interfrograms, from which two orthogonal shearing wavefronts are derived, for the tested wavefront to be retrieved. The designing process is demonstrated, and the residual errors are analyzed via simulation works and experimental comparison.

© 2011 Optical Society of America

OCIS Codes
(050.5080) Diffraction and gratings : Phase shift
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: January 19, 2011
Revised Manuscript: April 13, 2011
Manuscript Accepted: April 14, 2011
Published: June 10, 2011

Yucong Zhu, Satoru Odate, Ayako Sugaya, Katsura Otaki, Katsumi Sugisaki, Chiaki Koike, Tetsuya Koike, and Kiyoshi Uchikawa, "Method for designing phase-calculation algorithms for two-dimensional grating phase-shifting interferometry," Appl. Opt. 50, 2815-2822 (2011)

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  1. M. Takeda and S. Kobayashi, “Lateral aberration measurements with a digital Talbot interferometer,” Appl. Opt. 23, 1760–1764 (1984). [CrossRef] [PubMed]
  2. A. Momose, “Phase-sensitive imaging and phase tomography using X-ray interferometers,” Opt. Express 11, 2303–2314(2003). [CrossRef] [PubMed]
  3. K. A. Goldberg, P. Naulleau, S. Rekawa, P. Denham, J. A. Liddle, E. Anderson, K. Jackson, J. Bokor, and D. Attwood, “At-wavelength interferometry of high-NA diffraction-limited EUV Optics,” AIP Conf. Proc. 705, 855–860 (2004). [CrossRef]
  4. K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266. [CrossRef]
  5. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974). [CrossRef] [PubMed]
  6. A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45, 5254–5262(2006). [CrossRef]
  7. M. L. Cruz, A. Castro, and V. Arrizon, “Phase shifting digital holography implemented with a twisted-nematic liquid-crystal display,” Appl. Opt. 48, 6907–6912 (2009). [CrossRef] [PubMed]
  8. W. Zhao, X. Su, Q. Zhang, and L. Xiang, “Wavefront reconstruction method using the intensity image of phase-shift grating,” Opt. Lasers Eng. 48, 600–604 (2010). [CrossRef]
  9. M. Visser, M. Dekker, P. Hegeman, and J. Braat, “Extended-source interferometry for at-wavelength testing of EUV optics,” Proc. SPIE 3676, 253–263 (1999). [CrossRef]
  10. Y. Zhu, K. Sugisaki, M. Okada, K. Otaki, Z. Liu, J. Kawakami, M. Ishii, J. Saito, K. Murakami, M. Hasegawa, C. Ouchi, S. Kato, T. Hasegawa, A. Suzuki, H. Yokoda, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt. 46, 6783–6792 (2007). [CrossRef] [PubMed]
  11. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982). [CrossRef]
  12. K. A. Goldberg and J. Boker, “Fourier-transform method of phase-shift determination,” Appl. Opt. 40, 2886–2894 (2001). [CrossRef]
  13. J. Braat and A. J. E. M. Janssen, “Improved Ronchi test with extended source,” J. Opt. Soc. Am. A 16, 131–140 (1999). [CrossRef]
  14. M. Atlan, M. Gross, and E. Absil, “Accurate phase-shifting digital interferometry,” Opt. Lett. 32, 1456–1458 (2007). [CrossRef] [PubMed]
  15. S. Lai, B. King, and M. A. Nerfeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000). [CrossRef]
  16. W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805(2009). [CrossRef]
  17. M. P. Rimmer, “Method of evaluating lateral shearing interferograms,” Appl. Opt. 13, 623–629 (1974). [CrossRef] [PubMed]
  18. G. Harbers, P. J. Kunst, and G. W. R. Leibbrandt, “Analysis of lateral shearing interferograms by use of Zernike polynomials,” Appl. Opt. 35, 6162–6172 (1996). [CrossRef] [PubMed]
  19. CODE V 10.3 Reference Manual, Appendix C Zernike Polynomials, Fringe Zernike Polynomials, C-8.
  20. D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007), pp. 568–596.

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