Abstract

We report a novel algorithm for the analysis of interferometric images for surface profiling. The algorithm can be used with any interferometric system in which the two interfering beams are orthogonally polarized. The algorithm is based on a measurement of the polarization state and gives a unique value for the path difference that is not subject to the ambiguities associated with fringe counting or phase unwrapping. A detector array allows the polarization state and hence the height of every pixel in the image to be determined simultaneously. The concept is easily extended to enable one to obtain the profiles of moving surfaces from a single pulse of illumination.

© 1998 Optical Society of America

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References

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  1. M. Francon, Optical Interferometry (Academic, New York, 1966).
  2. K. Creath, Prog. Opt. 28, 350 (1988).
  3. J. Schwider, Prog. Opt. 28, 271 (1990).
    [CrossRef]
  4. L. Dick and P. D. Groot, Appl. Opt. 33, 7334 (1994).
    [CrossRef]
  5. H. Huang, H. Swanson, E. A. Charles, P. L. Schuman, and J. Stinson, Science 254, 1178 (1991).
    [CrossRef] [PubMed]
  6. P. Sandoz, R. Devillers, and A. Plata, J. Mod. Opt. 44, 519 (1997).
    [CrossRef]
  7. R. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).
  8. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).
  9. D. Clarke and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, Oxford, 1971).
  10. J. Golby, M. J. Padgett, and S. P. Woodall, “Inspection interferometer with scanning autofocus and phase angle control features,” U.S. patent5,469,259 (November21, 1995).
  11. H. P. Ho, M. G. Somekh, M. Liu, and C. W. See, Meas. Sci. Technol. 5, 1480 (1994).
    [CrossRef]
  12. P. Gleyzes, A. Boccara, and H. Saint-Jalmes, Opt. Lett. 22, 1529 (1997).
    [CrossRef]
  13. D. L. Lessor, J. S. Hartmann, and R. L. Gordon, J. Opt. Soc. Am. 69, (1979).
    [CrossRef]
  14. M. Francon and S. Mallick, Polarization Interferometers (Wiley-Interscience, New York, 1971).

1997 (2)

P. Sandoz, R. Devillers, and A. Plata, J. Mod. Opt. 44, 519 (1997).
[CrossRef]

P. Gleyzes, A. Boccara, and H. Saint-Jalmes, Opt. Lett. 22, 1529 (1997).
[CrossRef]

1994 (2)

H. P. Ho, M. G. Somekh, M. Liu, and C. W. See, Meas. Sci. Technol. 5, 1480 (1994).
[CrossRef]

L. Dick and P. D. Groot, Appl. Opt. 33, 7334 (1994).
[CrossRef]

1991 (1)

H. Huang, H. Swanson, E. A. Charles, P. L. Schuman, and J. Stinson, Science 254, 1178 (1991).
[CrossRef] [PubMed]

1990 (1)

J. Schwider, Prog. Opt. 28, 271 (1990).
[CrossRef]

1988 (1)

K. Creath, Prog. Opt. 28, 350 (1988).

1979 (1)

D. L. Lessor, J. S. Hartmann, and R. L. Gordon, J. Opt. Soc. Am. 69, (1979).
[CrossRef]

Azzam, R.

R. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).

Bashara, N. M.

R. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).

Boccara, A.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

Charles, E. A.

H. Huang, H. Swanson, E. A. Charles, P. L. Schuman, and J. Stinson, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Clarke, D.

D. Clarke and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, Oxford, 1971).

Creath, K.

K. Creath, Prog. Opt. 28, 350 (1988).

Devillers, R.

P. Sandoz, R. Devillers, and A. Plata, J. Mod. Opt. 44, 519 (1997).
[CrossRef]

Dick, L.

Francon, M.

M. Francon, Optical Interferometry (Academic, New York, 1966).

M. Francon and S. Mallick, Polarization Interferometers (Wiley-Interscience, New York, 1971).

Gleyzes, P.

Golby, J.

J. Golby, M. J. Padgett, and S. P. Woodall, “Inspection interferometer with scanning autofocus and phase angle control features,” U.S. patent5,469,259 (November21, 1995).

Gordon, R. L.

D. L. Lessor, J. S. Hartmann, and R. L. Gordon, J. Opt. Soc. Am. 69, (1979).
[CrossRef]

Grainger, J. F.

D. Clarke and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, Oxford, 1971).

Groot, P. D.

Hartmann, J. S.

D. L. Lessor, J. S. Hartmann, and R. L. Gordon, J. Opt. Soc. Am. 69, (1979).
[CrossRef]

Ho, H. P.

H. P. Ho, M. G. Somekh, M. Liu, and C. W. See, Meas. Sci. Technol. 5, 1480 (1994).
[CrossRef]

Huang, H.

H. Huang, H. Swanson, E. A. Charles, P. L. Schuman, and J. Stinson, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Lessor, D. L.

D. L. Lessor, J. S. Hartmann, and R. L. Gordon, J. Opt. Soc. Am. 69, (1979).
[CrossRef]

Liu, M.

H. P. Ho, M. G. Somekh, M. Liu, and C. W. See, Meas. Sci. Technol. 5, 1480 (1994).
[CrossRef]

Mallick, S.

M. Francon and S. Mallick, Polarization Interferometers (Wiley-Interscience, New York, 1971).

Padgett, M. J.

J. Golby, M. J. Padgett, and S. P. Woodall, “Inspection interferometer with scanning autofocus and phase angle control features,” U.S. patent5,469,259 (November21, 1995).

Plata, A.

P. Sandoz, R. Devillers, and A. Plata, J. Mod. Opt. 44, 519 (1997).
[CrossRef]

Saint-Jalmes, H.

Sandoz, P.

P. Sandoz, R. Devillers, and A. Plata, J. Mod. Opt. 44, 519 (1997).
[CrossRef]

Schuman, P. L.

H. Huang, H. Swanson, E. A. Charles, P. L. Schuman, and J. Stinson, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Schwider, J.

J. Schwider, Prog. Opt. 28, 271 (1990).
[CrossRef]

See, C. W.

H. P. Ho, M. G. Somekh, M. Liu, and C. W. See, Meas. Sci. Technol. 5, 1480 (1994).
[CrossRef]

Somekh, M. G.

H. P. Ho, M. G. Somekh, M. Liu, and C. W. See, Meas. Sci. Technol. 5, 1480 (1994).
[CrossRef]

Stinson, J.

H. Huang, H. Swanson, E. A. Charles, P. L. Schuman, and J. Stinson, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Swanson, H.

H. Huang, H. Swanson, E. A. Charles, P. L. Schuman, and J. Stinson, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

Woodall, S. P.

J. Golby, M. J. Padgett, and S. P. Woodall, “Inspection interferometer with scanning autofocus and phase angle control features,” U.S. patent5,469,259 (November21, 1995).

Appl. Opt. (1)

J. Mod. Opt. (1)

P. Sandoz, R. Devillers, and A. Plata, J. Mod. Opt. 44, 519 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

D. L. Lessor, J. S. Hartmann, and R. L. Gordon, J. Opt. Soc. Am. 69, (1979).
[CrossRef]

Meas. Sci. Technol. (1)

H. P. Ho, M. G. Somekh, M. Liu, and C. W. See, Meas. Sci. Technol. 5, 1480 (1994).
[CrossRef]

Opt. Lett. (1)

Prog. Opt. (2)

K. Creath, Prog. Opt. 28, 350 (1988).

J. Schwider, Prog. Opt. 28, 271 (1990).
[CrossRef]

Science (1)

H. Huang, H. Swanson, E. A. Charles, P. L. Schuman, and J. Stinson, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Other (6)

R. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

D. Clarke and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, Oxford, 1971).

J. Golby, M. J. Padgett, and S. P. Woodall, “Inspection interferometer with scanning autofocus and phase angle control features,” U.S. patent5,469,259 (November21, 1995).

M. Francon and S. Mallick, Polarization Interferometers (Wiley-Interscience, New York, 1971).

M. Francon, Optical Interferometry (Academic, New York, 1966).

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Figures (3)

Fig. 1
Fig. 1

Delay d between two orthogonally polarized components from a light source with a finite coherence length can be related through the Stokes polarization parameters to the modulus of the complex degree of coherence μxy. The dependence of μxy on d is shown for a 10-nm bandwidth source centered at 633 nm.

Fig. 2
Fig. 2

Schematic layout of the shearing interferometer based on a Wollaston prism. Two laterally displaced images of the surface interfere at the detector. Appropriate orientation of polarizer 2 and the wave plate allows μxy to be calculated for each pixel element in the image.

Fig. 3
Fig. 3

Surface profiles of a fabricated silicon wafer obtained by use of the technique presented in this Letter. Relating the surface height to the modulus of the complex degree of coherence eliminates any problems associated with fringe-counting techniques.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

μxy=p22+p321-p121/2,
p1=I0-I90I0+I90,
p2=I45-I-45I45+I-45,
p3=IRight-ILeftIRight+ILeft,

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