Abstract

I propose a systematic way to derive efficient, error-compensating algorithms for phase-shifting interferometry by integer approximation of well-known data-sampling windows. The theoretical basis of the approach is the observation that many of the common sources of phase-estimation error can be related to the frequency-domain characteristics of the sampling window. Improving these characteristics can therefore improve the overall performance of the algorithm. Analysis of a seven-frame example algorithm demonstrates an exceptionally good resistance to first- and second-order distortions in the phase shift and a much reduced sensitivity to low-frequency mechanical vibration.

© 1995 Optical Society of America

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  1. J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), Chap. 14.
  2. P. Hariharan, Optical Interferometry (Academic, Orlando, Fla., 1985).
  3. K. Creath, “Comparison of phase-measurement algorithms,” in Surface Characterization and Testing, K. Creath, ed., Proc. Soc. Photo-Opt. Instrum. Eng.680, 19–28 (1986).
  4. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital wavefront measuring interferometry: some systematic error sources,” Appl. Opt. 22, 3421–3432 (1983).
    [CrossRef] [PubMed]
  5. P. Hariharan, B. F. Oreb, T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987).
    [CrossRef] [PubMed]
  6. J. Schmit, K. Creath, “Some new error-compensating algorithms for phase-shifting interferometry,” in Optical Fabrication and Testing Workshop, Vol. 13 of OSA 1994 Technical Digest Series (Optical Society of America, Washington, D.C., 1994), Postdeadline paper PD4.
  7. K. Freischlad, C. L. Koliopoulos, “Fourier description of digital phase-measuring interferometry,” J. Opt. Soc. Am. A 7, 542–551 (1990).
    [CrossRef]
  8. K. G. Larkin, B. F. Oreb, “Design and assessment of symmetrical phase-shifting algorithms,” J. Opt. Soc. Am. A 9, 1740–1748 (1992).
    [CrossRef]
  9. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
    [CrossRef] [PubMed]
  10. R. P. Grosso, R. Crane, “Precise optical evaluation using phase measuring interferometric techniques,” in Interferometry, G. W. Hopkins, ed., Proc. Soc. Photo-Opt. Instrum. Eng.192, 65–74 (1979).
  11. P. de Groot, “Phase-shift calibration errors in interferometers with spherical Fizeau cavities,” Appl. Opt. 34, 2856–2863 (1995).
    [CrossRef]
  12. F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66, 51–83 (1978).
    [CrossRef]
  13. C. S. Williams, Designing Digital Filters (Prentice-Hall, Engle-wood Cliffs, N.J., 1986), Chap. 4.
  14. K. Creath, P. Hariharan, “Phase-shifting errors in interferometric tests with high-numerical aperture reference surfaces,” Appl. Opt. 33, 24–25 (1994).
    [CrossRef] [PubMed]
  15. P. de Groot, L. Deck, “Long-wavelength laser diode interferometer for surface flatness measurement,” in Optical Measurements and Sensors for the Process Industries, C. Gorecki, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2248, 136–140 (1994).
  16. J. van Wingerden, H. J. Frankena, C. Smorenburg, “Linear approximation for measurement errors in phase shifting interferometry,” Appl. Opt. 30, 2718–2729 (1991).
    [CrossRef] [PubMed]
  17. P. de Groot, “Predicting the effects of vibration in phase shifting interferometry,” in Optical Fabrication and Testing Workshop, Vol. 13 of OSA 1994 Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 189–192.
  18. P. de Groot, “Vibration in phase-shifting interferometry,” J. Opt. Soc. Am. A 12, 354–365 (1995).
    [CrossRef]

1995

1994

1992

1991

1990

1987

1983

1978

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66, 51–83 (1978).
[CrossRef]

1974

Brangaccio, D. J.

Bruning, J. H.

Burow, R.

Crane, R.

R. P. Grosso, R. Crane, “Precise optical evaluation using phase measuring interferometric techniques,” in Interferometry, G. W. Hopkins, ed., Proc. Soc. Photo-Opt. Instrum. Eng.192, 65–74 (1979).

Creath, K.

K. Creath, P. Hariharan, “Phase-shifting errors in interferometric tests with high-numerical aperture reference surfaces,” Appl. Opt. 33, 24–25 (1994).
[CrossRef] [PubMed]

K. Creath, “Comparison of phase-measurement algorithms,” in Surface Characterization and Testing, K. Creath, ed., Proc. Soc. Photo-Opt. Instrum. Eng.680, 19–28 (1986).

J. Schmit, K. Creath, “Some new error-compensating algorithms for phase-shifting interferometry,” in Optical Fabrication and Testing Workshop, Vol. 13 of OSA 1994 Technical Digest Series (Optical Society of America, Washington, D.C., 1994), Postdeadline paper PD4.

de Groot, P.

P. de Groot, “Vibration in phase-shifting interferometry,” J. Opt. Soc. Am. A 12, 354–365 (1995).
[CrossRef]

P. de Groot, “Phase-shift calibration errors in interferometers with spherical Fizeau cavities,” Appl. Opt. 34, 2856–2863 (1995).
[CrossRef]

P. de Groot, L. Deck, “Long-wavelength laser diode interferometer for surface flatness measurement,” in Optical Measurements and Sensors for the Process Industries, C. Gorecki, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2248, 136–140 (1994).

P. de Groot, “Predicting the effects of vibration in phase shifting interferometry,” in Optical Fabrication and Testing Workshop, Vol. 13 of OSA 1994 Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 189–192.

Deck, L.

P. de Groot, L. Deck, “Long-wavelength laser diode interferometer for surface flatness measurement,” in Optical Measurements and Sensors for the Process Industries, C. Gorecki, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2248, 136–140 (1994).

Eiju, T.

Elssner, K.-E.

Frankena, H. J.

Freischlad, K.

Gallagher, J. E.

Greivenkamp, J. E.

J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), Chap. 14.

Grosso, R. P.

R. P. Grosso, R. Crane, “Precise optical evaluation using phase measuring interferometric techniques,” in Interferometry, G. W. Hopkins, ed., Proc. Soc. Photo-Opt. Instrum. Eng.192, 65–74 (1979).

Grzanna, J.

Hariharan, P.

Harris, F. J.

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66, 51–83 (1978).
[CrossRef]

Herriott, D. R.

Koliopoulos, C. L.

Larkin, K. G.

Merkel, K.

Oreb, B. F.

Rosenfeld, D. P.

Schmit, J.

J. Schmit, K. Creath, “Some new error-compensating algorithms for phase-shifting interferometry,” in Optical Fabrication and Testing Workshop, Vol. 13 of OSA 1994 Technical Digest Series (Optical Society of America, Washington, D.C., 1994), Postdeadline paper PD4.

Schwider, J.

Smorenburg, C.

Spolaczyk, R.

van Wingerden, J.

White, A. D.

Williams, C. S.

C. S. Williams, Designing Digital Filters (Prentice-Hall, Engle-wood Cliffs, N.J., 1986), Chap. 4.

Appl. Opt.

J. Opt. Soc. Am. A

Proc. IEEE

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66, 51–83 (1978).
[CrossRef]

Other

C. S. Williams, Designing Digital Filters (Prentice-Hall, Engle-wood Cliffs, N.J., 1986), Chap. 4.

P. de Groot, L. Deck, “Long-wavelength laser diode interferometer for surface flatness measurement,” in Optical Measurements and Sensors for the Process Industries, C. Gorecki, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2248, 136–140 (1994).

P. de Groot, “Predicting the effects of vibration in phase shifting interferometry,” in Optical Fabrication and Testing Workshop, Vol. 13 of OSA 1994 Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 189–192.

J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), Chap. 14.

P. Hariharan, Optical Interferometry (Academic, Orlando, Fla., 1985).

K. Creath, “Comparison of phase-measurement algorithms,” in Surface Characterization and Testing, K. Creath, ed., Proc. Soc. Photo-Opt. Instrum. Eng.680, 19–28 (1986).

J. Schmit, K. Creath, “Some new error-compensating algorithms for phase-shifting interferometry,” in Optical Fabrication and Testing Workshop, Vol. 13 of OSA 1994 Technical Digest Series (Optical Society of America, Washington, D.C., 1994), Postdeadline paper PD4.

R. P. Grosso, R. Crane, “Precise optical evaluation using phase measuring interferometric techniques,” in Interferometry, G. W. Hopkins, ed., Proc. Soc. Photo-Opt. Instrum. Eng.192, 65–74 (1979).

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