Abstract

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

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [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]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [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]
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    [CrossRef] [PubMed]

2000 (1)

1999 (2)

1997 (2)

1996 (2)

1995 (3)

1993 (3)

P. J. Caber, “Interferometric profiler for rough surfaces,” Appl. Opt. 32, 3438–3441 (1993).
[CrossRef] [PubMed]

Y. Surrel, “Phase stepping: a new self-calibrating algorithm,” Appl. Opt. 39, 3598–3600 (1993).
[CrossRef]

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]

1992 (1)

1990 (2)

1987 (2)

1986 (2)

1985 (1)

1979 (1)

K. D. Stumpf, “Real-time interferometer,” Opt. Eng. 18, 648–653 (1979).
[CrossRef]

1975 (1)

1972 (1)

1966 (1)

P. Carré, “Installation et utilisation du comparateur photoélectrique et interférentiel du bureau international des poids et mesures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Bhushan, B.

Boccara, A. C.

Brophy, C. P.

Bruning, J. H.

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.

Caber, P. J.

Carré, P.

P. Carré, “Installation et utilisation du comparateur photoélectrique et interférentiel du bureau international des poids et mesures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Chim, S. C.

Cohen, F.

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).

Creath, K.

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]

K. Creath, “Phase-measurements interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, New York, 1988), Vol. 26, pp. 349–393.

Davidson, M.

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).

de Groot, P.

de Villèle, G.

Dubois, A.

Eiju, T.

Falkenstorfer, O.

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]

Flourney, P. A.

Ghiglia, D. C.

D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping, Theory, Algorithms, and Software (Wiley, New York, 1998).

Gleyzes, P.

Greivenkamp, J. E.

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.

Hariharan, P.

Kaufman, K.

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).

Kino, G. S.

Koliopoulos, C. L.

Kothiyal, M. P.

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.

Larkin, K. G.

Lebec, M.

Loriette, V.

Malacara, D.

D. Malacara, “Common-path interferometers,” in Optical Shop Testing, 2nd ed., J. W. Goodman, ed. (Wiley, New York, 1992), pp. 106–108.

Mazor, I.

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).

McClure, R. W.

Okazaki, H.

Oreb, B. F.

Phillion, D. W.

Pritt, M. D.

D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping, Theory, Algorithms, and Software (Wiley, New York, 1998).

Saint-Jalmes, H.

Sakai, M.

Sasaki, O.

Schmit, J.

Schreiber, H.

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]

Schwider, J.

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]

J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, New York, 1990), Vol. 28, pp. 271–359.

Selb, J.

Sirohi, R. S.

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.

Streibl, N.

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]

Stumpf, K. D.

K. D. Stumpf, “Real-time interferometer,” Opt. Eng. 18, 648–653 (1979).
[CrossRef]

Surrel, Y.

Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt. 35, 51–60 (1996).
[CrossRef] [PubMed]

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]

Y. Surrel, “Phase stepping: a new self-calibrating algorithm,” Appl. Opt. 39, 3598–3600 (1993).
[CrossRef]

Vabre, L.

Wyant, J. C.

Wyntjes, G.

Zhao, B.

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]

Zoller, A.

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]

Appl. Opt. (16)

Y. Surrel, “Phase stepping: a new self-calibrating algorithm,” Appl. Opt. 39, 3598–3600 (1993).
[CrossRef]

P. A. Flourney, R. W. McClure, G. Wyntjes, “White-light interferometric thickness gauge,” Appl. Opt. 11, 1907–1915 (1972).
[CrossRef]

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]

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]

O. Sasaki, H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25, 3137–3140 (1986).
[CrossRef] [PubMed]

O. Sasaki, H. Okazaki, “Analysis of measurement accuracy in sinusoidal phase modulating interferometry,” Appl. Opt. 25, 3152–3158 (1986).
[CrossRef] [PubMed]

O. Sasaki, H. Okazaki, M. Sakai, “Sinusoidal phase modulating interferometer using the integrating-bucket method,” Appl. Opt. 26, 1089–1093 (1987).
[CrossRef] [PubMed]

G. S. Kino, S. C. Chim, “Mirau correlation microscope,” Appl. Opt. 29, 3775–3783 (1990).
[CrossRef] [PubMed]

P. J. Caber, “Interferometric profiler for rough surfaces,” Appl. Opt. 32, 3438–3441 (1993).
[CrossRef] [PubMed]

D. W. Phillion, “General methods for generating phase-shifting interferometry algorithms,” Appl. Opt. 36, 8098–8115 (1997).
[CrossRef]

A. Dubois, J. Selb, L. Vabre, A. C. Boccara, “Phase measurements with wide-aperture interferometers,” Appl. Opt. 39, 2326–2331 (1999).
[CrossRef]

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]

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]

Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt. 35, 51–60 (1996).
[CrossRef] [PubMed]

G. de Villèle, V. Loriette, “Birefringence imaging with imperfect benches: application to large-scale birefringence measurements,” Appl. Opt. 39, 3864–3874 (2000).
[CrossRef]

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]

J. Opt. Soc. Am. A (3)

Metrologia (1)

P. Carré, “Installation et utilisation du comparateur photoélectrique et interférentiel du bureau international des poids et mesures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Opt. Eng. (3)

K. D. Stumpf, “Real-time interferometer,” Opt. Eng. 18, 648–653 (1979).
[CrossRef]

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]

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]

Opt. Lett. (2)

Other (7)

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).

D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping, Theory, Algorithms, and Software (Wiley, New York, 1998).

D. Malacara, “Common-path interferometers,” in Optical Shop Testing, 2nd ed., J. W. Goodman, ed. (Wiley, New York, 1992), pp. 106–108.

K. Creath, “Phase-measurements interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, New York, 1988), Vol. 26, pp. 349–393.

J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, New York, 1990), Vol. 28, pp. 271–359.

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.

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.

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