Abstract

As a practical monitoring tool for measurements of surface roughness properties, a new instrument is actually constructed on the basis of using the average contrast of image speckle patterns. With this instrument an experimental investigation on the contrast variation of image speckle patterns is conducted systematically for various surface roughnesses of the objects under different conditions of an optical imaging system. It is found that the roughness and correlation length of the objects can be precisely determined from the experimental curve of the contrast variation versus the point spread of the imaging system. The present method using image speckle patterns is superior to the previous one which uses the contrast variation of speckle patterns in the diffraction field.

© 1976 Optical Society of America

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References

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  1. H. Fujii and T. Askura, Opt. Commun. 11, 35 (1974).
    [Crossref]
  2. H. Fujii and T. Asakura, Opt. Commun. 12, 32 (1975).
    [Crossref]
  3. H. Fujii and T. Asakura, Nouv. Rev. Opt. 6, 5 (1975).
    [Crossref]
  4. J. Ohtsubo, H. Fujii, and T. Asakura, Jpn. J. Appl. Phys. Suppl. 14-1, 293 (1975).
  5. J. Ohtsubo and T. Asakura, Opt. Commun. 14, 30 (1975).
    [Crossref]
  6. J. Ohtsubo and T. Asakura, Nouv. Rev. Opt. 6, 189 (1975).
    [Crossref]
  7. J. Ohtsubo and T. Asakura, Bull. Res. Inst. Elec. Hokkaido Univ. 27, 18 (1975).
  8. J. Ohtsubo and T. Asakura, Optik (Stuttg.) 45, 65 (1976).
  9. H. Fujii, T. Asakura, and Y. Shindo, Opt. Commun. 16, 68 (1976).
    [Crossref]
  10. R. A. Sprague, Appl. Opt. 11, 2811 (1972).
    [Crossref] [PubMed]
  11. H. M. Pedersen, Opt. Commun. 12, 156 (1974).
    [Crossref]
  12. J. W. Goodman, Opt. Commun. 14, 324 (1975).
    [Crossref]
  13. N. George, A. Jain, and R. D. S. Melville, Appl. Phys. 7, 157 (1975).
    [Crossref]
  14. E. Jakeman and P. N. Pusey, J. Phys. A 8, 369 (1975).
    [Crossref]
  15. H. M. Pedersen, Opt. Commun. 16, 63 (1976).
    [Crossref]

1976 (3)

J. Ohtsubo and T. Asakura, Optik (Stuttg.) 45, 65 (1976).

H. Fujii, T. Asakura, and Y. Shindo, Opt. Commun. 16, 68 (1976).
[Crossref]

H. M. Pedersen, Opt. Commun. 16, 63 (1976).
[Crossref]

1975 (9)

J. W. Goodman, Opt. Commun. 14, 324 (1975).
[Crossref]

N. George, A. Jain, and R. D. S. Melville, Appl. Phys. 7, 157 (1975).
[Crossref]

E. Jakeman and P. N. Pusey, J. Phys. A 8, 369 (1975).
[Crossref]

H. Fujii and T. Asakura, Opt. Commun. 12, 32 (1975).
[Crossref]

H. Fujii and T. Asakura, Nouv. Rev. Opt. 6, 5 (1975).
[Crossref]

J. Ohtsubo, H. Fujii, and T. Asakura, Jpn. J. Appl. Phys. Suppl. 14-1, 293 (1975).

J. Ohtsubo and T. Asakura, Opt. Commun. 14, 30 (1975).
[Crossref]

J. Ohtsubo and T. Asakura, Nouv. Rev. Opt. 6, 189 (1975).
[Crossref]

J. Ohtsubo and T. Asakura, Bull. Res. Inst. Elec. Hokkaido Univ. 27, 18 (1975).

1974 (2)

H. M. Pedersen, Opt. Commun. 12, 156 (1974).
[Crossref]

H. Fujii and T. Askura, Opt. Commun. 11, 35 (1974).
[Crossref]

1972 (1)

Asakura, T.

J. Ohtsubo and T. Asakura, Optik (Stuttg.) 45, 65 (1976).

H. Fujii, T. Asakura, and Y. Shindo, Opt. Commun. 16, 68 (1976).
[Crossref]

H. Fujii and T. Asakura, Opt. Commun. 12, 32 (1975).
[Crossref]

H. Fujii and T. Asakura, Nouv. Rev. Opt. 6, 5 (1975).
[Crossref]

J. Ohtsubo, H. Fujii, and T. Asakura, Jpn. J. Appl. Phys. Suppl. 14-1, 293 (1975).

J. Ohtsubo and T. Asakura, Opt. Commun. 14, 30 (1975).
[Crossref]

J. Ohtsubo and T. Asakura, Nouv. Rev. Opt. 6, 189 (1975).
[Crossref]

J. Ohtsubo and T. Asakura, Bull. Res. Inst. Elec. Hokkaido Univ. 27, 18 (1975).

Askura, T.

H. Fujii and T. Askura, Opt. Commun. 11, 35 (1974).
[Crossref]

Fujii, H.

H. Fujii, T. Asakura, and Y. Shindo, Opt. Commun. 16, 68 (1976).
[Crossref]

H. Fujii and T. Asakura, Opt. Commun. 12, 32 (1975).
[Crossref]

H. Fujii and T. Asakura, Nouv. Rev. Opt. 6, 5 (1975).
[Crossref]

J. Ohtsubo, H. Fujii, and T. Asakura, Jpn. J. Appl. Phys. Suppl. 14-1, 293 (1975).

H. Fujii and T. Askura, Opt. Commun. 11, 35 (1974).
[Crossref]

George, N.

N. George, A. Jain, and R. D. S. Melville, Appl. Phys. 7, 157 (1975).
[Crossref]

Goodman, J. W.

J. W. Goodman, Opt. Commun. 14, 324 (1975).
[Crossref]

Jain, A.

N. George, A. Jain, and R. D. S. Melville, Appl. Phys. 7, 157 (1975).
[Crossref]

Jakeman, E.

E. Jakeman and P. N. Pusey, J. Phys. A 8, 369 (1975).
[Crossref]

Melville, R. D. S.

N. George, A. Jain, and R. D. S. Melville, Appl. Phys. 7, 157 (1975).
[Crossref]

Ohtsubo, J.

J. Ohtsubo and T. Asakura, Optik (Stuttg.) 45, 65 (1976).

J. Ohtsubo and T. Asakura, Bull. Res. Inst. Elec. Hokkaido Univ. 27, 18 (1975).

J. Ohtsubo and T. Asakura, Nouv. Rev. Opt. 6, 189 (1975).
[Crossref]

J. Ohtsubo and T. Asakura, Opt. Commun. 14, 30 (1975).
[Crossref]

J. Ohtsubo, H. Fujii, and T. Asakura, Jpn. J. Appl. Phys. Suppl. 14-1, 293 (1975).

Pedersen, H. M.

H. M. Pedersen, Opt. Commun. 16, 63 (1976).
[Crossref]

H. M. Pedersen, Opt. Commun. 12, 156 (1974).
[Crossref]

Pusey, P. N.

E. Jakeman and P. N. Pusey, J. Phys. A 8, 369 (1975).
[Crossref]

Shindo, Y.

H. Fujii, T. Asakura, and Y. Shindo, Opt. Commun. 16, 68 (1976).
[Crossref]

Sprague, R. A.

Appl. Opt. (1)

Appl. Phys. (1)

N. George, A. Jain, and R. D. S. Melville, Appl. Phys. 7, 157 (1975).
[Crossref]

Bull. Res. Inst. Elec. Hokkaido Univ. (1)

J. Ohtsubo and T. Asakura, Bull. Res. Inst. Elec. Hokkaido Univ. 27, 18 (1975).

J. Phys. A (1)

E. Jakeman and P. N. Pusey, J. Phys. A 8, 369 (1975).
[Crossref]

Jpn. J. Appl. Phys. Suppl. (1)

J. Ohtsubo, H. Fujii, and T. Asakura, Jpn. J. Appl. Phys. Suppl. 14-1, 293 (1975).

Nouv. Rev. Opt. (2)

H. Fujii and T. Asakura, Nouv. Rev. Opt. 6, 5 (1975).
[Crossref]

J. Ohtsubo and T. Asakura, Nouv. Rev. Opt. 6, 189 (1975).
[Crossref]

Opt. Commun. (7)

J. Ohtsubo and T. Asakura, Opt. Commun. 14, 30 (1975).
[Crossref]

H. Fujii and T. Askura, Opt. Commun. 11, 35 (1974).
[Crossref]

H. Fujii and T. Asakura, Opt. Commun. 12, 32 (1975).
[Crossref]

H. M. Pedersen, Opt. Commun. 16, 63 (1976).
[Crossref]

H. M. Pedersen, Opt. Commun. 12, 156 (1974).
[Crossref]

J. W. Goodman, Opt. Commun. 14, 324 (1975).
[Crossref]

H. Fujii, T. Asakura, and Y. Shindo, Opt. Commun. 16, 68 (1976).
[Crossref]

Optik (Stuttg.) (1)

J. Ohtsubo and T. Asakura, Optik (Stuttg.) 45, 65 (1976).

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Figures (8)

FIG. 1
FIG. 1

Optical system, in the measuring instrument of the surface roughness properties, used for producing image speckle patterns.

FIG. 2
FIG. 2

Photograph of the optical system shown schematically in Fig. 1.

FIG. 3
FIG. 3

Schematic diagram of the signal-analyzing system for the image speckle intensity variations.

FIG. 4
FIG. 4

Average contrast V of the image speckle intensity variations as a function of the point spread km of the optical imaging system for three objects having different rms roughness 〈ΔL21/2 and the same correlation length α = 12μ.

FIG. 5
FIG. 5

Average contrast V of the image speckle intensity variations as a function of the point spread km of the imaging system for three objects having different rms roughness 〈ΔL21/2 and the same correlation length α = 9μ.

FIG. 6
FIG. 6

Average contrast V of the image speckle intensity variations as a function of the point spread km of the imaging system for three objects having different rms roughness 〈ΔL21/2 and the same correlation length α = 8μ.

FIG. 7
FIG. 7

Maximum average contrast Vmax of the image speckle intensity variations as a function of the rms roughness 〈ΔL21/ of the objects.

FIG. 8
FIG. 8

Average contrast V of image speckle patterns as a function of the defocus distance Ld of the receiving plane, for five different point spreads of the optical imaging system. The focused point for the optical system of km = 3.7μ is set to be an origin Ld = 0 and the defocus plane from this point is taken for both directions indicated by ± symbols.

Tables (2)

Tables Icon

TABLE I Values of the rms roughness 〈ΔL21/2 and the correlation length for the test sample objects used in the experiment.

Tables Icon

TABLE II Ratio of Vα/Vmax for the test sample objects.

Equations (4)

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Δ L 2 1 / 2 = ( n 1 - n 2 ) Δ h 2 1 / 2 ,
V = Δ I 2 1 / 2 I = [ I ( x ) 2 - I ( x ) 2 ] 1 / 2 I ( x ) ,
k m = 0.61 λ / NA ,
( V α V max ) av = 0.80 ± 0.03.