Abstract

A technique is described for calculating the roughness and probability density function of a surface based on the decorrelation of imaged speckle with wavelength. The decorrelation provides information about the first-order statistical properties of the imaged surface. Surfaces with rms roughnesses of greater than ~1 μm. can be scanned over the 80-nm range of the dye-laser system.

© 1993 Optical Society of America

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References

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  1. N. George, A. Jain, Appl. Phys. 4, 201 (1974).
    [CrossRef]
  2. N. George, A. Jain, R. D. S. Melville, Appl. Phys. 7, 157 (1975).
    [CrossRef]
  3. T. S. McKechnie, in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, New York, 1982), p. 123.
  4. C. Wykes, Opt. Acta 24, 517 (1977).
    [CrossRef]
  5. J. W. Goodman, in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, New York, 1982), p. 9.
  6. D. Leger, J. C. Perrin, J. Opt. Soc. Am. 66, 1210 (1976).
    [CrossRef]
  7. W. T. Welford, Opt. Quantum Electron. 9, 269 (1977).
    [CrossRef]
  8. H. Fujii, T. Asakura, Opt. Commun. 11, 35 (1974).
    [CrossRef]
  9. N. George, Opt. Eng. 25, 754 (1986).

1986 (1)

N. George, Opt. Eng. 25, 754 (1986).

1977 (2)

W. T. Welford, Opt. Quantum Electron. 9, 269 (1977).
[CrossRef]

C. Wykes, Opt. Acta 24, 517 (1977).
[CrossRef]

1976 (1)

1975 (1)

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

1974 (2)

N. George, A. Jain, Appl. Phys. 4, 201 (1974).
[CrossRef]

H. Fujii, T. Asakura, Opt. Commun. 11, 35 (1974).
[CrossRef]

Asakura, T.

H. Fujii, T. Asakura, Opt. Commun. 11, 35 (1974).
[CrossRef]

Fujii, H.

H. Fujii, T. Asakura, Opt. Commun. 11, 35 (1974).
[CrossRef]

George, N.

N. George, Opt. Eng. 25, 754 (1986).

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

N. George, A. Jain, Appl. Phys. 4, 201 (1974).
[CrossRef]

Goodman, J. W.

J. W. Goodman, in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, New York, 1982), p. 9.

Jain, A.

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

N. George, A. Jain, Appl. Phys. 4, 201 (1974).
[CrossRef]

Leger, D.

McKechnie, T. S.

T. S. McKechnie, in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, New York, 1982), p. 123.

Melville, R. D. S.

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

Perrin, J. C.

Welford, W. T.

W. T. Welford, Opt. Quantum Electron. 9, 269 (1977).
[CrossRef]

Wykes, C.

C. Wykes, Opt. Acta 24, 517 (1977).
[CrossRef]

Appl. Phys. (2)

N. George, A. Jain, Appl. Phys. 4, 201 (1974).
[CrossRef]

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

J. Opt. Soc. Am. (1)

Opt. Acta (1)

C. Wykes, Opt. Acta 24, 517 (1977).
[CrossRef]

Opt. Commun. (1)

H. Fujii, T. Asakura, Opt. Commun. 11, 35 (1974).
[CrossRef]

Opt. Eng. (1)

N. George, Opt. Eng. 25, 754 (1986).

Opt. Quantum Electron. (1)

W. T. Welford, Opt. Quantum Electron. 9, 269 (1977).
[CrossRef]

Other (2)

J. W. Goodman, in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, New York, 1982), p. 9.

T. S. McKechnie, in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, New York, 1982), p. 123.

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Figures (5)

Fig. 1
Fig. 1

Speckle-imaging system for a reflective object.

Fig. 2
Fig. 2

Calculated autocorrelations for a surface with (a) a Gaussian density function and (b) a triangular density function.

Fig. 3
Fig. 3

Autocorrelation for a uniform density function: expected value and computer average of nine members from an ensemble.

Fig. 4
Fig. 4

Frequency scans from two surfaces: surface 2 (solid curve) has a small rms roughness, and surface 5 (dashed curve) has a large roughness.

Fig. 5
Fig. 5

Autocorrelations for five surfaces of varying roughness.

Tables (1)

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Table 1 Surface Roughness Results

Equations (9)

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R I ( x 2 x 1 , y 2 y 1 ; ν 1 , ν 2 ) = I ( x 1 , y 1 ; ν 1 ) I ( x 2 , y 2 ; ν 2 ) = I ( x 1 , y 1 ; ν 1 ) I ( x 2 , y 2 ; ν 2 ) + | d ξ d ζ F 2 [ η 1 , η 2 ; r 12 ( ξ , ζ ) ] P ( x 2 x 1 ξ , y 2 y 1 ζ ; ν 1 , ν 2 ) | 2 ,
p ( ξ , ζ ; ν 1 , ν 2 ) = d x d y p ( x , y ; ν 1 ) p * ( x ξ , y ζ ; ν 2 ) .
I ( 0 , 0 ; ν ) = d x d y d x d y p ( x , y ; ν ) p * ( x , y ; ν ) × exp { i η [ h ( x , y ) h ( x , y ) ] } .
F 2 ( η 1 , η 2 ; r 12 ) = exp { i [ η 1 h ( x , y ) η 2 h ( x , y ) ] } = exp [ ½ ( η 1 η 2 ) 2 σ 2 η 1 η 2 σ 2 ( 1 r 12 ) ] .
I ( 0 , 0 ; ν 1 ) = d ξ d ζ F 2 [ η 1 , η 1 ; r 12 ( ξ , ζ ) ] × p ( ξ , ζ ; ν 1 ) .
I ( 0 , 0 ; ν 1 , ν 2 ) = I ( 0 , 0 ; ν 1 ) I ( 0 , 0 ; ν 2 ) + F 1 2 ( η 1 η 2 ) C ( ν 1 , ν 2 ) .
R I ( 0 , 0 ; ν 1 , ν 2 ) C ( ν 1 , ν 2 ) [ 1 + F 1 2 ( η 1 η 2 ) ]
C ( ν 1 , ν 2 ) { 1 + exp [ ( η 1 η 2 ) 2 σ 2 ] } .
C ( ν 1 , ν 2 ) = ( π D l c 2 σ ) 1 η 1 2 η 2 2 .

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