Abstract

The usual automated interferometric profilometers suffer from phase-unwrapping problems. We discuss a one-dimensional method for the absolute determination of the path difference in interferometers to obtain unique surface profiles with high accuracy.

© 1994 Optical Society of America

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References

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  1. J. Schwider, Prog. Opt. 28, 271 (1990).
    [CrossRef]
  2. U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, Opt. Eng. 32, 781 (1993).
    [CrossRef]
  3. W. Krug, J. Rienitz, G. Schulz, Beiträge zur Interferenzmikroskopie (Akademie-Verlag, Berlin, 1961), Part I, Chap. 2, p. 79;Part II, Chap. 3, p. 175.
  4. Y. Y. Cheng, J. C. Wyant, Appl. Opt. 24, 804 (1985).
    [CrossRef] [PubMed]
  5. J. Schwider, Opt. Lett. 19, 231 (1994).
    [CrossRef] [PubMed]
  6. P. Becker, J. Stümpel, Phys. Unserer Zeit 24, 246 (1993).
    [CrossRef]
  7. O. Lummer, Müller-Pouillets Lehrbuch der Physik, 11th ed. (Vieweg, Braunschweig, 1926), Vol. II, Chap. 15, p. 782.
  8. E. Gehrcke, Handbuch der physikalischen Optik (Barth, Leipzig, 1926), p. 408.
  9. S. Tolansky, Multiple-Beam Interferometry (Clarendon, Oxford, 1948), Chap. 8, p. 96.
  10. R. S. Longhurst, Geometrical and Physical Optics, 3rd ed. (Longman, London, 1984), Chap. 9, p. 203.
  11. J. J. Snyder, Appl. Opt. 19, 1223 (1980).
    [CrossRef] [PubMed]
  12. M. Takeda, H. Ina, S. Kobayashi, J. Opt. Soc. Am. 72, 156 (1982).
    [CrossRef]
  13. P. de Groot, L. Deck, Opt. Lett. 18, 1462 (1993).
    [CrossRef] [PubMed]
  14. J. Schwider, Appl. Opt. 18, 2364 (1979).
    [CrossRef] [PubMed]
  15. C. C. Huang, Proc. Soc. Photo-Opt. Instrum. Eng. 429, 65 (1983).

1994 (1)

1993 (3)

P. Becker, J. Stümpel, Phys. Unserer Zeit 24, 246 (1993).
[CrossRef]

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, Opt. Eng. 32, 781 (1993).
[CrossRef]

P. de Groot, L. Deck, Opt. Lett. 18, 1462 (1993).
[CrossRef] [PubMed]

1990 (1)

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

1985 (1)

1983 (1)

C. C. Huang, Proc. Soc. Photo-Opt. Instrum. Eng. 429, 65 (1983).

1982 (1)

1980 (1)

1979 (1)

Becker, P.

P. Becker, J. Stümpel, Phys. Unserer Zeit 24, 246 (1993).
[CrossRef]

Cheng, Y. Y.

de Groot, P.

Deck, L.

Gehrcke, E.

E. Gehrcke, Handbuch der physikalischen Optik (Barth, Leipzig, 1926), p. 408.

Huang, C. C.

C. C. Huang, Proc. Soc. Photo-Opt. Instrum. Eng. 429, 65 (1983).

Ina, H.

Kobayashi, S.

Krackhardt, U.

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, Opt. Eng. 32, 781 (1993).
[CrossRef]

Krug, W.

W. Krug, J. Rienitz, G. Schulz, Beiträge zur Interferenzmikroskopie (Akademie-Verlag, Berlin, 1961), Part I, Chap. 2, p. 79;Part II, Chap. 3, p. 175.

Longhurst, R. S.

R. S. Longhurst, Geometrical and Physical Optics, 3rd ed. (Longman, London, 1984), Chap. 9, p. 203.

Lummer, O.

O. Lummer, Müller-Pouillets Lehrbuch der Physik, 11th ed. (Vieweg, Braunschweig, 1926), Vol. II, Chap. 15, p. 782.

Rienitz, J.

W. Krug, J. Rienitz, G. Schulz, Beiträge zur Interferenzmikroskopie (Akademie-Verlag, Berlin, 1961), Part I, Chap. 2, p. 79;Part II, Chap. 3, p. 175.

Schrader, M.

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, Opt. Eng. 32, 781 (1993).
[CrossRef]

Schulz, G.

W. Krug, J. Rienitz, G. Schulz, Beiträge zur Interferenzmikroskopie (Akademie-Verlag, Berlin, 1961), Part I, Chap. 2, p. 79;Part II, Chap. 3, p. 175.

Schwider, J.

J. Schwider, Opt. Lett. 19, 231 (1994).
[CrossRef] [PubMed]

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, Opt. Eng. 32, 781 (1993).
[CrossRef]

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

J. Schwider, Appl. Opt. 18, 2364 (1979).
[CrossRef] [PubMed]

Snyder, J. J.

Streibl, N.

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, Opt. Eng. 32, 781 (1993).
[CrossRef]

Stümpel, J.

P. Becker, J. Stümpel, Phys. Unserer Zeit 24, 246 (1993).
[CrossRef]

Takeda, M.

Tolansky, S.

S. Tolansky, Multiple-Beam Interferometry (Clarendon, Oxford, 1948), Chap. 8, p. 96.

Wyant, J. C.

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

U. Krackhardt, J. Schwider, M. Schrader, N. Streibl, Opt. Eng. 32, 781 (1993).
[CrossRef]

Opt. Lett. (2)

Phys. Unserer Zeit (1)

P. Becker, J. Stümpel, Phys. Unserer Zeit 24, 246 (1993).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

C. C. Huang, Proc. Soc. Photo-Opt. Instrum. Eng. 429, 65 (1983).

Prog. Opt. (1)

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

Other (5)

O. Lummer, Müller-Pouillets Lehrbuch der Physik, 11th ed. (Vieweg, Braunschweig, 1926), Vol. II, Chap. 15, p. 782.

E. Gehrcke, Handbuch der physikalischen Optik (Barth, Leipzig, 1926), p. 408.

S. Tolansky, Multiple-Beam Interferometry (Clarendon, Oxford, 1948), Chap. 8, p. 96.

R. S. Longhurst, Geometrical and Physical Optics, 3rd ed. (Longman, London, 1984), Chap. 9, p. 203.

W. Krug, J. Rienitz, G. Schulz, Beiträge zur Interferenzmikroskopie (Akademie-Verlag, Berlin, 1961), Part I, Chap. 2, p. 79;Part II, Chap. 3, p. 175.

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Figures (3)

Fig. 1
Fig. 1

Schematic of the dispersive interferometric profilometer.

Fig. 2
Fig. 2

Evaluation result of the profile of a four-step grating with the convolution method.

Fig. 3
Fig. 3

Evaluation result of the profile of a four-step grating with the fast-Fourier-transform method.

Equations (10)

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2 t = ( m 0 + j ) λ j ,
a + bj = σ j ,
h ( σ ) = { 1 B σ 0 1 0 σ B ,
r = r + | I ( r ) | | I ( r + 1 ) | + | I ( r ) | .
S = j = 1 n [ σ j ( a + b j ) ] 2 .
t = 1 2 b = n ( n 1 ) ( n + 1 ) 12 [ 2 j = 1 n j σ j ( n + 1 ) j = 1 n σ j ] .
I [ t ( x ) , σ ] = O ( x , σ ) + P ( x , σ ) cos { 2 π σ [ 2 t ( x ) ] } ,
ϕ ( σ ) = 2 π σ [ 2 t ( x ) ]
δ t t = ( δ ϕ ϕ ) 1 N ,
t ' = t Fizeau t FPE .

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