Abstract

The relationship between the statistical structure parameters of a rough surface and the associated correlation parameters of a scattered field is used to develop a method for rough-surface diagnostics. The treatment is based on the model of a random phase object with an inhomogeneity phase dispersion σ2<1. The proposed diagnostic methods are applicable to surfaces with a roughness period comparable to the radiation wavelength employed and the surfaces of a thin plane-parallel plate. The sensitivity limit of the methods in measuring the standard deviation of surface-roughness element heights is ~0.003 μm.

© 1992 Optical Society of America

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References

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  1. H. P. Baltes, Inverse Source Problems in Optics (Springer-Verlag, Berlin, 1978).
    [CrossRef]
  2. V. N. Moiseyev, V. I. Mandrosov, “Informativeness of speckled coherent images,” Zarubezhnaya Radioelektron. 2, 3–21 (1982).
  3. H. Fujii, F. Asakura, Y. Shindo, “Measurement of surface roughness properties by means of laser speckle techniques,” Opt. Commun. 16, 68–72 (1976).
    [CrossRef]
  4. J. W. Goodman, “Dependence of image speckle contrast of surface roughness,” Opt. Commun. 14, 324–327 (1975).
    [CrossRef]
  5. O. V. Angelsky, V. G. Zhitaryuk, P. P. Maksimyak, “On the possibility of optical correlation measurement of inhomogeneous phase statistical surfaces,” Opt. Spektrosk. 60, 1013–1017 (1986).
  6. O. V. Angelsky, P. P. Maksimyak, T. O. Perun, “Optical correlation systems for studying weak surface roughness,” in Fringe ’89 Automatic Processing of Fringe Patterns, W. Osten, R. J. Pryputniewicz, G. T. Reid, H. Rottenkolber, eds. (Akademie, Berlin, 1989), p. 53.
  7. O. V. Anglesky, I. I. Magun, P. P. Maksimyak, “Optical correlation methods in the studies of inhomogeneous phase samples,” presented at the Third International Symposium on Modern Optics, Budapest, Hungary, 1988.
  8. S. M. Rytov, Yu. A. Kravtsov, B. I. Tatarsky, Introduction to Statistical Radiophysics. Part II. Random Fields (Nauka, Moscow, 1978), p. 464.

1986 (1)

O. V. Angelsky, V. G. Zhitaryuk, P. P. Maksimyak, “On the possibility of optical correlation measurement of inhomogeneous phase statistical surfaces,” Opt. Spektrosk. 60, 1013–1017 (1986).

1982 (1)

V. N. Moiseyev, V. I. Mandrosov, “Informativeness of speckled coherent images,” Zarubezhnaya Radioelektron. 2, 3–21 (1982).

1976 (1)

H. Fujii, F. Asakura, Y. Shindo, “Measurement of surface roughness properties by means of laser speckle techniques,” Opt. Commun. 16, 68–72 (1976).
[CrossRef]

1975 (1)

J. W. Goodman, “Dependence of image speckle contrast of surface roughness,” Opt. Commun. 14, 324–327 (1975).
[CrossRef]

Angelsky, O. V.

O. V. Angelsky, V. G. Zhitaryuk, P. P. Maksimyak, “On the possibility of optical correlation measurement of inhomogeneous phase statistical surfaces,” Opt. Spektrosk. 60, 1013–1017 (1986).

O. V. Angelsky, P. P. Maksimyak, T. O. Perun, “Optical correlation systems for studying weak surface roughness,” in Fringe ’89 Automatic Processing of Fringe Patterns, W. Osten, R. J. Pryputniewicz, G. T. Reid, H. Rottenkolber, eds. (Akademie, Berlin, 1989), p. 53.

Anglesky, O. V.

O. V. Anglesky, I. I. Magun, P. P. Maksimyak, “Optical correlation methods in the studies of inhomogeneous phase samples,” presented at the Third International Symposium on Modern Optics, Budapest, Hungary, 1988.

Asakura, F.

H. Fujii, F. Asakura, Y. Shindo, “Measurement of surface roughness properties by means of laser speckle techniques,” Opt. Commun. 16, 68–72 (1976).
[CrossRef]

Baltes, H. P.

H. P. Baltes, Inverse Source Problems in Optics (Springer-Verlag, Berlin, 1978).
[CrossRef]

Fujii, H.

H. Fujii, F. Asakura, Y. Shindo, “Measurement of surface roughness properties by means of laser speckle techniques,” Opt. Commun. 16, 68–72 (1976).
[CrossRef]

Goodman, J. W.

J. W. Goodman, “Dependence of image speckle contrast of surface roughness,” Opt. Commun. 14, 324–327 (1975).
[CrossRef]

Kravtsov, Yu. A.

S. M. Rytov, Yu. A. Kravtsov, B. I. Tatarsky, Introduction to Statistical Radiophysics. Part II. Random Fields (Nauka, Moscow, 1978), p. 464.

Magun, I. I.

O. V. Anglesky, I. I. Magun, P. P. Maksimyak, “Optical correlation methods in the studies of inhomogeneous phase samples,” presented at the Third International Symposium on Modern Optics, Budapest, Hungary, 1988.

Maksimyak, P. P.

O. V. Angelsky, V. G. Zhitaryuk, P. P. Maksimyak, “On the possibility of optical correlation measurement of inhomogeneous phase statistical surfaces,” Opt. Spektrosk. 60, 1013–1017 (1986).

O. V. Anglesky, I. I. Magun, P. P. Maksimyak, “Optical correlation methods in the studies of inhomogeneous phase samples,” presented at the Third International Symposium on Modern Optics, Budapest, Hungary, 1988.

O. V. Angelsky, P. P. Maksimyak, T. O. Perun, “Optical correlation systems for studying weak surface roughness,” in Fringe ’89 Automatic Processing of Fringe Patterns, W. Osten, R. J. Pryputniewicz, G. T. Reid, H. Rottenkolber, eds. (Akademie, Berlin, 1989), p. 53.

Mandrosov, V. I.

V. N. Moiseyev, V. I. Mandrosov, “Informativeness of speckled coherent images,” Zarubezhnaya Radioelektron. 2, 3–21 (1982).

Moiseyev, V. N.

V. N. Moiseyev, V. I. Mandrosov, “Informativeness of speckled coherent images,” Zarubezhnaya Radioelektron. 2, 3–21 (1982).

Perun, T. O.

O. V. Angelsky, P. P. Maksimyak, T. O. Perun, “Optical correlation systems for studying weak surface roughness,” in Fringe ’89 Automatic Processing of Fringe Patterns, W. Osten, R. J. Pryputniewicz, G. T. Reid, H. Rottenkolber, eds. (Akademie, Berlin, 1989), p. 53.

Rytov, S. M.

S. M. Rytov, Yu. A. Kravtsov, B. I. Tatarsky, Introduction to Statistical Radiophysics. Part II. Random Fields (Nauka, Moscow, 1978), p. 464.

Shindo, Y.

H. Fujii, F. Asakura, Y. Shindo, “Measurement of surface roughness properties by means of laser speckle techniques,” Opt. Commun. 16, 68–72 (1976).
[CrossRef]

Tatarsky, B. I.

S. M. Rytov, Yu. A. Kravtsov, B. I. Tatarsky, Introduction to Statistical Radiophysics. Part II. Random Fields (Nauka, Moscow, 1978), p. 464.

Zhitaryuk, V. G.

O. V. Angelsky, V. G. Zhitaryuk, P. P. Maksimyak, “On the possibility of optical correlation measurement of inhomogeneous phase statistical surfaces,” Opt. Spektrosk. 60, 1013–1017 (1986).

Opt. Commun. (2)

H. Fujii, F. Asakura, Y. Shindo, “Measurement of surface roughness properties by means of laser speckle techniques,” Opt. Commun. 16, 68–72 (1976).
[CrossRef]

J. W. Goodman, “Dependence of image speckle contrast of surface roughness,” Opt. Commun. 14, 324–327 (1975).
[CrossRef]

Opt. Spektrosk. (1)

O. V. Angelsky, V. G. Zhitaryuk, P. P. Maksimyak, “On the possibility of optical correlation measurement of inhomogeneous phase statistical surfaces,” Opt. Spektrosk. 60, 1013–1017 (1986).

Zarubezhnaya Radioelektron. (1)

V. N. Moiseyev, V. I. Mandrosov, “Informativeness of speckled coherent images,” Zarubezhnaya Radioelektron. 2, 3–21 (1982).

Other (4)

H. P. Baltes, Inverse Source Problems in Optics (Springer-Verlag, Berlin, 1978).
[CrossRef]

O. V. Angelsky, P. P. Maksimyak, T. O. Perun, “Optical correlation systems for studying weak surface roughness,” in Fringe ’89 Automatic Processing of Fringe Patterns, W. Osten, R. J. Pryputniewicz, G. T. Reid, H. Rottenkolber, eds. (Akademie, Berlin, 1989), p. 53.

O. V. Anglesky, I. I. Magun, P. P. Maksimyak, “Optical correlation methods in the studies of inhomogeneous phase samples,” presented at the Third International Symposium on Modern Optics, Budapest, Hungary, 1988.

S. M. Rytov, Yu. A. Kravtsov, B. I. Tatarsky, Introduction to Statistical Radiophysics. Part II. Random Fields (Nauka, Moscow, 1978), p. 464.

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Figures (3)

Fig. 1
Fig. 1

Optical arrangement for surface roughness measurements: 1, laser; 2, telescopic systems; 3, diaphragm; 4, polarizer cube; 5, quarter-wave plate; 6, integrating sphere; 7, sample; 8, calcite wedges; 9, electromechanical modulator; 10, polarizer; 11, objective lens; 12, field diaphragm; and 13, and 14, photodetectors.

Fig. 2
Fig. 2

Interference pattern formation.

Fig. 3
Fig. 3

Optical arrangement for measuring the surface roughness of plane-parallel plates: 1, laser; 2, telescopic system; 3, goniometer; 4, plane-parallel plate; 5, objective lens; 6, field diaphragm; 7, photodetector.

Tables (2)

Tables Icon

Table I Standard Height Deviation Rq as Measured by Profilometric (Rqp), Standard Interference (Rqi) and the Present (Rqs) Methods

Tables Icon

Table II Standard Height Deviation Rq as Measured by Profilometric (Rqp) and the Present (Rqs) Methods on Samples with Different l φ 0

Equations (15)

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Γ ( ρ ) = exp { σ φ 0 2 [ k φ 0 ( ρ ) 1 ] } ,
Γ ( ρ > l φ 0 ) = exp ( σ φ 0 2 ) .
Γ ( ρ > l φ 0 ) = I c I c + I s + I d .
Γ ( ρ > l φ 0 ) = I max I min I max + I min = I c I c + I s ,
Γ ( ρ > l φ 0 ) = I max I min I max + I min ( I p I d ) I p I d + I d .
σ φ 0 2 = ln ( I max I min I max + I min ) ln ( I p I d I p ) .
R q = λ 4 π σ φ 0 .
σ A 2 = σ φ 2 = 1 2 σ φ 0 2 ,
I s ( x , y ) = a 2 ( x , y ) + b 2 ( x , y ) + 2 a ( x , y ) b ( x , y ) cos φ ( x , y ) ,
φ ( x , y ) = π + φ ˜ ( x , y ) ,
I s min ( x , y ) = a 2 ( x , y ) + b 2 ( x , y ) 2 a ( x , y ) b ( x , y ) + 4 a ( x , y ) b ( x , y ) sin 2 φ ˜ ( x , y ) 2 ·
I s min = σ a 2 I A + [ ( I A I B ) 2 ] + σ b 2 I B + ( I A I B ) 1 / 2 ( σ a 2 + σ b 2 ) ,
I s max = σ a 2 I A + σ b 2 I B [ ( I A I B ) 2 ] 1 / 2 ( I A I B ) 1 / 2 ( σ a 2 + σ b 2 ) .
I A = I 0 ρ 1 , I B = I 0 τ 1 ρ 2 τ 2 ,
σ a 2 = 1 2 ( 2 k R q 1 cos φ 1 ) 2 , σ b 2 = 1 2 ( 4 π λ n R q 2 cos Ψ ) 2 + [ 4 π λ ( n 1 ) R q 1 cos φ 1 ] 2 ,

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