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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 7, Iss. 4 — Apr. 1, 1990
  • pp: 542–551

Fourier description of digital phase-measuring interferometry

Klaus Freischlad and Chris L. Koliopoulos  »View Author Affiliations

JOSA A, Vol. 7, Issue 4, pp. 542-551 (1990)

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A general description of phase measurement by digital heterodyne techniques is presented in which the heterodyning is explained as a filtering process in the frequency domain. Examples of commonly used algorithms are given. Special emphasis is given to the analysis of systematic errors. Gaussian error propagation is used to derive equations for the random phase errors of common algorithms.

© 1990 Optical Society of America

Original Manuscript: May 1, 1989
Manuscript Accepted: November 18, 1989
Published: April 1, 1990

Klaus Freischlad and Chris L. Koliopoulos, "Fourier description of digital phase-measuring interferometry," J. Opt. Soc. Am. A 7, 542-551 (1990)

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  1. 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]
  2. J. H. Bruning, “Fringe scanning interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978).
  3. J. C. Wyant, “Use of an ac heterodyne lateral shear interferometer with real time wavefront correction systems,” Appl. Opt. 14, 2622–2626 (1975). [CrossRef] [PubMed]
  4. C. L. Koliopoulos, “Interferometric optical phase measurement techniques,” Ph.D. dissertation (University of Arizona, Tucson, Arizona, 1981).
  5. K. Creath, “Comparison of phase measuring algorithms,” in Surface Characterization and Testing, K. Creath, ed., Soc. Photo-Opt. Instrum. Eng.680, 19–28 (1986). [CrossRef]
  6. C. W. Helstrom, Statistical Theory of Signal Detection (Pergamon, Oxford, 1968).
  7. E. Hardtwig, Fehler- und Ausgleichsrechnung (Bibliographisches Institut, Mannheim, 1968).
  8. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).
  9. C. J. Morgan, “Least-squares estimation in phase-measurement interferometry,” Opt. Lett. 7, 368–370 (1982). [CrossRef] [PubMed]
  10. J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. 23, 350–351 (1984). [CrossRef]
  11. W. R. C. Rowley, J. Hamon, “Quelques mesures de dyssymétrie de profils spectraux,” R. Opt. Theor. Instrum. 42, 519–523 (1963).
  12. P. Carre, “Installation et utilisation du comparateur photoelectrique et interferentiel du Bureau International des Poids et Mésures,” Metrologia 2, 13–16 (1966). [CrossRef]
  13. J. B. Hayes, “Linear methods of computer controlled optical figuring,” Ph.D. dissertation (University of Arizona, Tucson, Arizona, 1984).
  14. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaszyk, K. Merkel, “Digital wave-front measuring interferometry: some systematic error sources,” Appl. Opt. 22, 3421–3432 (1983). [CrossRef] [PubMed]
  15. P. Hariharan, “Digital phase shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987). [CrossRef] [PubMed]
  16. Y.-Y. Cheng, J. C. Wyant, “Phase shifter calibration in phase-shifting interferometry,” Appl. Opt. 24, 3049–3052 (1985). [CrossRef] [PubMed]
  17. K. Freischlad, “Wavefront sensing by heterodyne shearing interferometry,” Ph.D. dissertation (University of Arizona, Tucson, Arizona, 1986).
  18. C. L. Koliopoulos, “Radial grating lateral shear heterodyne interferometer,” Appl. Opt. 19, 1523–1528 (1980). [CrossRef] [PubMed]
  19. C. Ai, J. C. Wyant, “Effect of piezoelectric transducer nonlinearity on phase-shift interferometry,” Appl. Opt. 26, 1112–1116 (1987). [CrossRef] [PubMed]
  20. B. R. Frieden, Probability, Statistical Optics, and Data Testing (Springer-Verlag, Berlin, 1983). [CrossRef]
  21. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  22. Y. Ichioka, M. Inuiya, “Direct phase detecting system,” Appl. Opt. 11, 1507–1514 (1972). [CrossRef] [PubMed]
  23. L. Mertz, “Real-time fringe-pattern analysis,” Appl. Opt. 22, 1535–1539 (1983). [CrossRef] [PubMed]
  24. K. H. Womack, “Frequency domain description of interferogram analysis,” Opt. Eng. 23, 396–400 (1984). [CrossRef]
  25. P. Hariharan, “Digital phase stepping interferometry: effects of multiply reflected beams,” Appl. Opt. 26, 2506–2507 (1987). [CrossRef] [PubMed]

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