OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 40, Iss. 17 — Jun. 10, 2001
  • pp: 2886–2894

Fourier-Transform Method of Phase-Shift Determination

Kenneth A. Goldberg and Jeffrey Bokor  »View Author Affiliations


Applied Optics, Vol. 40, Issue 17, pp. 2886-2894 (2001)
http://dx.doi.org/10.1364/AO.40.002886


View Full Text Article

Acrobat PDF (1296 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A new phase-shifting interferometry analysis technique has been developed to overcome the errors introduced by nonlinear, irregular, or unknown phase-step increments. In the presence of a spatial carrier frequency, by observation of the phase of the first-order maximum in the Fourier domain, the global phase-step positions can be measured, phase-shifting elements can be calibrated, and the accuracy of phase-shifting analysis can be improved. Furthermore, reliance on the calibration accuracy of transducers used in phase-shifting interferometry can be reduced; and phase-retrieval errors (e.g., fringe print-through) introduced by uncalibrated fluctuations in the phase-shifting phase increments can be alleviated. The method operates deterministically and does not rely on iterative global error minimization. Relative to other techniques, the number of recorded interferograms required for analysis can be reduced.

© 2001 Optical Society of America

OCIS Codes
(100.5070) Image processing : Phase retrieval
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

Citation
Kenneth A. Goldberg and Jeffrey Bokor, "Fourier-Transform Method of Phase-Shift Determination," Appl. Opt. 40, 2886-2894 (2001)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-40-17-2886


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. P. Carre, “Installation et utilisation du comparateur photoelectrique et interferential du bureau international des poids et mesures,” Metrologia 2, 13–23 (1966).
  2. R. Crane, “Interference phase measurement,” Appl. Opt. 8, 538–542 (1969).
  3. 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).
  4. J. C. Wyant, “Use of an ac heterodyne lateral shear interferometer with real-time wavefront corrections systems (for telescopes),” Appl. Opt. 14, 2622–2626 (1975).
  5. J. Schwider, R. Burrow, K. E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, “Digital wavefront measuring interferometry: some systematic error sources,” Appl. Opt. 22, 3421–3432 (1983).
  6. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase-calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987).
  7. K. G. Larkin and B. F. Oreb, “Design and assessment of symmetrical phase-shifting algorithms,” J. Opt. Soc. Am. A 9, 1740–1748 (1992).
  8. J. Schwider, O. Falkenstorfer, H. Schreiber, A. Zoller, and N. Streibel, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. 32, 1883–1885 (1995).
  9. Y. Surrel, “Phase stepping: a new self-calibrating algorithm,” Appl. Opt. 32, 3598–3600 (1993).
  10. K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, “Phase shifting for nonsinusoidal waveforms with phase-shift errors,” J. Opt. Soc. Am. A 12, 761–768 (1995).
  11. Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt. 35, 51–60 (1996).
  12. D. W. Phillion, “General methods for generating phase-shifting interferometry algorithms,” Appl. Opt. 36, 8098–8115 (1997).
  13. J. Schmidt and K. Creath, “Spatial and temporal phase-measurement techniques: a comparison of major error sources in one dimension,” in Interferometry: Techniques and Analysis, G. M. Brown, O. Y. Kwon, M. Kujawinska, and G. T. Reid, eds., Proc. SPIE 1755, 202–211 (1992).
  14. P. J. de Groot, “Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window,” Appl. Opt. 34, 4723–4730 (1995).
  15. J. Wingerden, H. J. Frankena, and C. Smorenburg, “Linear approximation for measurement errors in phase-shifting interferometry,” Appl. Opt. 30, 2718–2729 (1991).
  16. K. Hibino, “Susceptibility of systematic error-compensating algorithms to random noise in phase-shifting interferometry,” Appl. Opt. 36, 2084–2093 (1997).
  17. C. P. Brophy, “Effect of intensity error correlation on the computed phase of phase-shifting interferometry,” J. Opt. Soc. Am. A 7, 542–551 (1990).
  18. C. Rathjen, “Statistical properties of phase-shift algorithms,” J. Opt. Soc. Am. A 12, 1997–2008 (1995).
  19. K. Kinnstaetter, A. W. Lohmann, J. Schwider, and N. Streibl, “Accuracy of phase shifting interferometry,” Appl. Opt. 27, 5082–5089 (1988).
  20. G.-S. Han and S.-W. Kim, “Numerical correction of reference phases in phase-shifting interferometry by iterative least-squares fitting,” Appl. Opt. 33, 7321–7325 (1994).
  21. S.-W. Kim, M.-G. Kang, and G.-S. Han, “Accelerated phase-measuring algorithm of least squares for phase-shifting interferometry,” Opt. Eng. 36, 3101–3106 (1997).
  22. A. Dobroiu, P. C. Lagofatu, D. Apostol, and V. Damian, “Statistical self-calibrating algorithm for three-sample phase-shift interferometry,” Meas. Sci. Technol. 8, 738–745 (1997).
  23. A. Dobroiu, D. Apostol, V. Nascov, and V. Damian, “Statistical self-calibrating algorithm for phase-shift interferometry based on a smoothness assessment of the intensity offset map,” Meas. Sci. Technol. 9, 1451–1455 (1998).
  24. M. Chen, H. Guo, and C. Wei, “Algorithm immune to tilt phase-shifting error for phase-shifting interferometers,” Appl. Opt. 39, 3894–3898 (2000).
  25. J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. 23, 350–352 (1984).
  26. J. E. Greivenkamp and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 2nd ed. D. Malacara, ed. (Wiley, New York, 1992), pp. 522–524.
  27. D. J. Bone, H.-A. Bachor, and R. J. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986).
  28. 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).
  29. K. A. Nugent, “Interferogram analysis using an accurate fully automatic algorithm,” Appl. Opt. 24, 3101–3105 (1985).
  30. K. A. Goldberg, “EUV interferometry,” Ph.D. dissertation (University of California, Berkeley, Berkeley, Calif., 1997).
  31. P. P. Naulleau, K. A. Goldberg, S. H. Lee, C. Chang, D. Attwood, and J. Bokor, “Extreme-ultraviolet phase-shifting point-diffraction interferometer: a wave-front metrology tool with subangstrom reference-wave accuracy,” Appl. Opt. 38, 7252–7263 (1999).
  32. D. A. Tichenor, G. D. Kubiak, M. E. Malinowski, R. H. Stulen, S. J. Haney, K. W. Berger, L. A. Brown, W. C. Sweatt, J. E. Bjorkholm, R. R. Freeman, M. D. Himel, A. A. MacDowell, D. M. Tennant, O. R. Wood II, J. Bokor, T. E. Jewell, W. M. Mansfield, W. K. Waskiewicz, D. L. White, and D. L. Windt, “Soft-x-ray projection lithography experiments using Schwarzschild imaging optics,” Appl. Opt. 32, 7068–7071 (1993).
  33. K. A. Goldberg, P. Naulleau, and J. Bokor, “EUV interferometric measurements of diffraction-limited optics,” J. Vac. Sci. Technol. B 17, 2982–2986 (1999).
  34. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2505 (1987).
  35. P. P. Naulleau and K. A. Goldberg, “Dual-domain point diffraction interferometer,” Appl. Opt. 38, 3523–3533 (1999).
  36. N. Ohyama, S. Kinoshita, A. Cornejo-Rodriguez, T. Honda, and J. Tsujiuchi, “Accuracy of phase determination with unequal reference phase shift,” J. Opt. Soc. Am. A 5, 2019–2025 (1988).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited