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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 8 — Aug. 1, 2001
  • pp: 1972–1979

Phase-map measurements by interferometry with sinusoidal phase modulation and four integrating buckets

Arnaud Dubois  »View Author Affiliations

JOSA A, Vol. 18, Issue 8, pp. 1972-1979 (2001)

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Phase-shifting interferometry based on the integrating-bucket technique with sinusoidal phase modulation is studied theoretically and demonstrated experimentally to obtain phase maps from double-beam interferometers. The method uses four frames obtained by integration of the time-varying intensity in an interference pattern during the four quarters of the modulation period. An optimum sinusoidal phase modulation is found to minimize the effect of the additive noise. The absolute accuracy of the phase measurements is discussed. Possible applications of the method are demonstrated with two interference microscopes with which the phase modulation is achieved by sinusoidal oscillation of a mirror attached to a piezoelectric transducer and by sinusoidal birefringence modulation with a photoelastic modulator. In both experimental arrangements, phase images can be produced in real time at a rate of several hertz. Noise measurements are reported and compared with theory.

© 2001 Optical Society of America

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(120.5060) Instrumentation, measurement, and metrology : Phase modulation
(180.3170) Microscopy : Interference microscopy

Original Manuscript: September 18, 2000
Revised Manuscript: January 5, 2001
Manuscript Accepted: January 5, 2001
Published: August 1, 2001

Arnaud Dubois, "Phase-map measurements by interferometry with sinusoidal phase modulation and four integrating buckets," J. Opt. Soc. Am. A 18, 1972-1979 (2001)

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  1. K. Creath, “Phase-measurements interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, New York, 1988), Vol. 26, pp. 349–393.
  2. J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, New York, 1990), Vol. 28, pp. 271–359.
  3. J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1991), Chap. 14, pp. 501–598.
  4. R. S. Sirohi, M. P. Kothiyal, “Heterodyne and phase shifting interferometry,” in Optical Components, Systems, and Measurement Techniques, R. S. Sirohi, M. P. Kothiyal, eds. (Marcel Dekker, New York, 1991), pp. 219–246.
  5. D. W. Phillion, “General methods for generating phase-shifting interferometry algorithms,” Appl. Opt. 36, 8098–8115 (1997). [CrossRef]
  6. P. Carré, “Installation et utilisation du comparateur photoélectrique et interférentiel du bureau international des poids et mesures,” Metrologia 2, 13–23 (1966). [CrossRef]
  7. P. Hariharan, B. F. Oreb, T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculating algorithm,” Appl. Opt. 26, 2504–2506 (1987). [CrossRef] [PubMed]
  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. Y. Surrel, “Phase stepping: a new self-calibrating algorithm,” Appl. Opt. 39, 3598–3600 (1993). [CrossRef]
  10. J. Schwider, O. Falkenstorfer, H. Schreiber, A. Zoller, N. Streibl, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. 32, 1883–1885 (1993). [CrossRef]
  11. B. Zhao, Y. Surrel, “Phase shifting: six-sample self-calibrating algorithm insensitive to the second harmonic in the fringe signal,” Opt. Eng. 34, 2821–2822 (1995). [CrossRef]
  12. P. de Groot, “Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window,” Appl. Opt. 34, 4723–4730 (1995). [CrossRef]
  13. J. Schmit, K. Creath, “Extended averaging technique for derivation of error compensating algorithms in phase-shifting interferometry,” Appl. Opt. 34, 3610–3619 (1995). [CrossRef] [PubMed]
  14. Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt. 35, 51–60 (1996). [CrossRef] [PubMed]
  15. K. G. Larkin, “Efficient nonlinear algorithm for envelope detection in white light interferometry,” J. Opt. Soc. Am. A 13, 832–843 (1996). [CrossRef]
  16. K. D. Stumpf, “Real-time interferometer,” Opt. Eng. 18, 648–653 (1979). [CrossRef]
  17. B. Bhushan, J. C. Wyant, C. L. Koliopoulos, “Measurements of surfaces topography of magnetic tapes by Mirau interferometry,” Appl. Opt. 24, 1489–1497 (1985). [CrossRef]
  18. 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]
  19. O. Sasaki, H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25, 3137–3140 (1986). [CrossRef] [PubMed]
  20. O. Sasaki, H. Okazaki, “Analysis of measurement accuracy in sinusoidal phase modulating interferometry,” Appl. Opt. 25, 3152–3158 (1986). [CrossRef] [PubMed]
  21. O. Sasaki, H. Okazaki, M. Sakai, “Sinusoidal phase modulating interferometer using the integrating-bucket method,” Appl. Opt. 26, 1089–1093 (1987). [CrossRef] [PubMed]
  22. C. P. Brophy, “Effect of intensity error correlation on the computed phase of phase-shifting interferometry,” J. Opt. Soc. Am. A 7, 537–541 (1990). [CrossRef]
  23. M. Davidson, K. Kaufman, I. Mazor, F. Cohen, “An application of interference microscopy to integrated circuit inspection and metrology,” in Integrated Circuit Metrology, Inspection, and Process Control, K. M. Monahan, ed., Proc. SPIE775, 233–247 (1987). [CrossRef]
  24. G. S. Kino, S. C. Chim, “Mirau correlation microscope,” Appl. Opt. 29, 3775–3783 (1990). [CrossRef] [PubMed]
  25. A. Dubois, J. Selb, L. Vabre, A. C. Boccara, “Phase measurements with wide-aperture interferometers,” Appl. Opt. 39, 2326–2331 (1999). [CrossRef]
  26. D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping, Theory, Algorithms, and Software (Wiley, New York, 1998).
  27. A. Dubois, A. C. Boccara, M. Lebec, “Real-time reflectivity and topography imagery of depth-resolved microscopic surfaces,” Opt. Lett. 24, 309–311 (1999). [CrossRef]
  28. P. Gleyzes, A. C. Boccara, H. Saint-Jalmes, “Multichannel Nomarski microscope with polarization modulation: performance and applications,” Opt. Lett. 22, 1529–1531 (1997). [CrossRef]
  29. G. de Villèle, V. Loriette, “Birefringence imaging with imperfect benches: application to large-scale birefringence measurements,” Appl. Opt. 39, 3864–3874 (2000). [CrossRef]
  30. D. Malacara, “Common-path interferometers,” in Optical Shop Testing, 2nd ed., J. W. Goodman, ed. (Wiley, New York, 1992), pp. 106–108.
  31. P. A. Flourney, R. W. McClure, G. Wyntjes, “White-light interferometric thickness gauge,” Appl. Opt. 11, 1907–1915 (1972). [CrossRef]
  32. P. J. Caber, “Interferometric profiler for rough surfaces,” Appl. Opt. 32, 3438–3441 (1993). [CrossRef] [PubMed]

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