Abstract

We describe a novel feedback interferometer for real-time, unambiguous measurement of surface profiles that consists of a polarization Sagnac interferometer and an optically addressed phase-only spatial light modulator. In this system the output intensity from the Sagnac interferometer is optically fed back to the phase modulator placed in one arm of the interferometer, which produces a sawtooth fringe intensity profile (instead of the conventional cosinusoidal one) that is directly and unambiguously related to the surface profile. Preliminary experimental results demonstrate the feasibility of applying this system to surface-profile measurement.

© 1999 Optical Society of America

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References

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  1. For example, K. Creath, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. XXVI, pp. 349–393.
    [CrossRef]
  2. A. D. Fisher and C. Warde, Opt. Lett. 4, 131 (1979).
    [CrossRef] [PubMed]
  3. A. D. Fisher and C. Warde, Opt. Lett. 8, 353 (1983).
    [CrossRef] [PubMed]
  4. T. H. Barnes, T. Eiju, S. Kokaji, K. Matsuda, and N. Yoshida, Optik 96, 107 (1994).
  5. T. H. Barnes, T. Eiju, and K. Matsuda, Optik 101, 17 (1995).
  6. T. Yoshino, M. Nara, S. Mnatzakanian, B. S. Lee, and T. C. Strand, Appl. Opt. 26, 892 (1987).
    [CrossRef] [PubMed]
  7. T. Suzuki, O. Sasaki, and T. Murayama, Appl. Opt. 28, 4407 (1989).
    [CrossRef] [PubMed]
  8. A. R. D. Somervell, “Feedback interferometry for surface profile measurement,” M.S.??thesis (University of Auckland, Auckland, New Zealand, 1996).

1995 (1)

T. H. Barnes, T. Eiju, and K. Matsuda, Optik 101, 17 (1995).

1994 (1)

T. H. Barnes, T. Eiju, S. Kokaji, K. Matsuda, and N. Yoshida, Optik 96, 107 (1994).

1989 (1)

1987 (1)

1983 (1)

1979 (1)

Barnes, T. H.

T. H. Barnes, T. Eiju, and K. Matsuda, Optik 101, 17 (1995).

T. H. Barnes, T. Eiju, S. Kokaji, K. Matsuda, and N. Yoshida, Optik 96, 107 (1994).

Creath, K.

For example, K. Creath, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. XXVI, pp. 349–393.
[CrossRef]

Eiju, T.

T. H. Barnes, T. Eiju, and K. Matsuda, Optik 101, 17 (1995).

T. H. Barnes, T. Eiju, S. Kokaji, K. Matsuda, and N. Yoshida, Optik 96, 107 (1994).

Fisher, A. D.

Kokaji, S.

T. H. Barnes, T. Eiju, S. Kokaji, K. Matsuda, and N. Yoshida, Optik 96, 107 (1994).

Lee, B. S.

Matsuda, K.

T. H. Barnes, T. Eiju, and K. Matsuda, Optik 101, 17 (1995).

T. H. Barnes, T. Eiju, S. Kokaji, K. Matsuda, and N. Yoshida, Optik 96, 107 (1994).

Mnatzakanian, S.

Murayama, T.

Nara, M.

Sasaki, O.

Somervell, A. R. D.

A. R. D. Somervell, “Feedback interferometry for surface profile measurement,” M.S.??thesis (University of Auckland, Auckland, New Zealand, 1996).

Strand, T. C.

Suzuki, T.

Warde, C.

Yoshida, N.

T. H. Barnes, T. Eiju, S. Kokaji, K. Matsuda, and N. Yoshida, Optik 96, 107 (1994).

Yoshino, T.

Appl. Opt. (2)

Opt. Lett. (2)

Optik (2)

T. H. Barnes, T. Eiju, S. Kokaji, K. Matsuda, and N. Yoshida, Optik 96, 107 (1994).

T. H. Barnes, T. Eiju, and K. Matsuda, Optik 101, 17 (1995).

Other (2)

A. R. D. Somervell, “Feedback interferometry for surface profile measurement,” M.S.??thesis (University of Auckland, Auckland, New Zealand, 1996).

For example, K. Creath, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. XXVI, pp. 349–393.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(a) Cosinusoidal and (b) sawtoothed output intensities from conventional and feedback interferometers.

Fig. 2
Fig. 2

Experimental setup. See text for definitions.

Fig. 3
Fig. 3

Interferometer output without feedback in testing a flat mirror. (a) Fringe pattern and (b) intensity profile for a horizontal scan [(a) and (b) have the same meaning in Figs.  46].

Fig. 4
Fig. 4

Interferometer output with feedback in testing a flat mirror.

Fig. 5
Fig. 5

Interferometer output without feedback in testing a concave mirror.

Fig. 6
Fig. 6

Interferometer output with feedback in testing a concave mirror.

Equations (2)

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Iout=x,y=A1+Vcosϕx,y,
Ioutx,y=A(1+Vcosϕx,y+fBIoutx,y),

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