OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 34, Iss. 22 — Aug. 1, 1995
  • pp: 4723–4730

Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window

Peter de Groot  »View Author Affiliations


Applied Optics, Vol. 34, Issue 22, pp. 4723-4730 (1995)
http://dx.doi.org/10.1364/AO.34.004723


View Full Text Article

Enhanced HTML    Acrobat PDF (160 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

History
Original Manuscript: May 20, 1994
Revised Manuscript: September 29, 1994
Published: August 1, 1995

Citation
Peter de Groot, "Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window," Appl. Opt. 34, 4723-4730 (1995)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-34-22-4723


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  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]

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