Abstract

Angle-resolved light scattering (ARLS) is used to estimate the root-mean-square (rms) slopes of rough surfaces having a well-defined lay, and the effect on slope measurements caused by changing the angles of incidence and scattering is investigated. The ARLS patterns are taken with the Detector Array for Laser Light Angular Scattering (Dallas) research instrument, and the rms slopes are obtained from the angular widths of these patterns. In general, it was found that the angular width, and thus the estimated rms slope, is surprisingly insensitive to relatively large changes in both the incident and scattering angles of light. These results are independent of surface material and are valid for both sinusoidal and random rough surfaces with lay. The principles, experiments, analyses, and conclusions involved in using ARLS to estimate rms surface slopes are described.

© 1991 Optical Society of America

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References

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  1. T. V. Vorburger, E. C. Teague, “Optical techniques for online measurement of surface topography,” Precis. Eng. 3, 61–83 (1981).
    [CrossRef]
  2. See, for example, J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989).
  3. J. H. Rakels, “Recognized surface finish parameters obtained from diffraction patterns of rough surfaces,” in Proceedings on Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 119–125 (1988).
  4. P. Z. Takacs, R. C. Hewitt, E. L. Church, “Correlation between the performance and metrology of glancing-incidence synchrotron-radiation mirrors containing millimeter-wavelength shape errors,” in Proceedings on Metrology: Figure and Finish, B. Truax, ed., Proc. Soc. Photo-Opt. Instrum. Eng.749, 119–124 (1987).
  5. R. Brodmann, M. Allgauer, “Comparison of light scattering from rough surfaces with optical and mechanical profilometry,” in Proceedings on Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Photo-Opt. Instrum. Eng.1009, 111–118 (1988).
  6. M. Kamei, T. Inari, “On-line monitoring of surface roughness by using laser,” in Proceedings on Production Aspects of Single Point Machined Optics, D. P. Brehm, ed., Proc. Soc. Photo-Opt. Instrum. Eng.508, 56–63 (1984).
  7. See, for example, P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).
  8. T. V. Vorburger, E. C. Teague, F. E. Scire, M. J. McLay, D. E. Gilsinn, “Surface roughness studies with DALLAS—Detector array for laser light angular scattering,” J. Res. Natl. Bur. Stand. 89, 3–16 (1984).
    [CrossRef]
  9. E. C. Teague, F. E. Scire, T. V. Vorburger, “Sinusoidal profile precision roughness specimens,” Wear 83, 61–73 (1982).
    [CrossRef]
  10. ASME/ANSI B46.1-1985, Surface Texture (American Society of Mechanical Engineers, New York, 1985).
  11. D. G. Chetwynd, “The digitization of surface profiles,” Wear 57, 137–140 (1979).
    [CrossRef]
  12. P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).
  13. These models are valid, strictly speaking, only in the Fraunhofer region, whereas in the present experiments the scattering was in the Fresnel region. However, the difference is expected to be negligible.
  14. R. Brodmann, D. Gerstorfer, G. Thurn, “Optical roughness measuring instrument for fine-machined surfaces,” Opt. Eng. 24, 408–413 (1985).

1985 (1)

R. Brodmann, D. Gerstorfer, G. Thurn, “Optical roughness measuring instrument for fine-machined surfaces,” Opt. Eng. 24, 408–413 (1985).

1984 (1)

T. V. Vorburger, E. C. Teague, F. E. Scire, M. J. McLay, D. E. Gilsinn, “Surface roughness studies with DALLAS—Detector array for laser light angular scattering,” J. Res. Natl. Bur. Stand. 89, 3–16 (1984).
[CrossRef]

1982 (1)

E. C. Teague, F. E. Scire, T. V. Vorburger, “Sinusoidal profile precision roughness specimens,” Wear 83, 61–73 (1982).
[CrossRef]

1981 (1)

T. V. Vorburger, E. C. Teague, “Optical techniques for online measurement of surface topography,” Precis. Eng. 3, 61–83 (1981).
[CrossRef]

1979 (1)

D. G. Chetwynd, “The digitization of surface profiles,” Wear 57, 137–140 (1979).
[CrossRef]

Allgauer, M.

R. Brodmann, M. Allgauer, “Comparison of light scattering from rough surfaces with optical and mechanical profilometry,” in Proceedings on Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Photo-Opt. Instrum. Eng.1009, 111–118 (1988).

Beckmann, P.

See, for example, P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Bennett, J. M.

See, for example, J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989).

Bevington, P. R.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

Brodmann, R.

R. Brodmann, D. Gerstorfer, G. Thurn, “Optical roughness measuring instrument for fine-machined surfaces,” Opt. Eng. 24, 408–413 (1985).

R. Brodmann, M. Allgauer, “Comparison of light scattering from rough surfaces with optical and mechanical profilometry,” in Proceedings on Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Photo-Opt. Instrum. Eng.1009, 111–118 (1988).

Chetwynd, D. G.

D. G. Chetwynd, “The digitization of surface profiles,” Wear 57, 137–140 (1979).
[CrossRef]

Church, E. L.

P. Z. Takacs, R. C. Hewitt, E. L. Church, “Correlation between the performance and metrology of glancing-incidence synchrotron-radiation mirrors containing millimeter-wavelength shape errors,” in Proceedings on Metrology: Figure and Finish, B. Truax, ed., Proc. Soc. Photo-Opt. Instrum. Eng.749, 119–124 (1987).

Gerstorfer, D.

R. Brodmann, D. Gerstorfer, G. Thurn, “Optical roughness measuring instrument for fine-machined surfaces,” Opt. Eng. 24, 408–413 (1985).

Gilsinn, D. E.

T. V. Vorburger, E. C. Teague, F. E. Scire, M. J. McLay, D. E. Gilsinn, “Surface roughness studies with DALLAS—Detector array for laser light angular scattering,” J. Res. Natl. Bur. Stand. 89, 3–16 (1984).
[CrossRef]

Hewitt, R. C.

P. Z. Takacs, R. C. Hewitt, E. L. Church, “Correlation between the performance and metrology of glancing-incidence synchrotron-radiation mirrors containing millimeter-wavelength shape errors,” in Proceedings on Metrology: Figure and Finish, B. Truax, ed., Proc. Soc. Photo-Opt. Instrum. Eng.749, 119–124 (1987).

Inari, T.

M. Kamei, T. Inari, “On-line monitoring of surface roughness by using laser,” in Proceedings on Production Aspects of Single Point Machined Optics, D. P. Brehm, ed., Proc. Soc. Photo-Opt. Instrum. Eng.508, 56–63 (1984).

Kamei, M.

M. Kamei, T. Inari, “On-line monitoring of surface roughness by using laser,” in Proceedings on Production Aspects of Single Point Machined Optics, D. P. Brehm, ed., Proc. Soc. Photo-Opt. Instrum. Eng.508, 56–63 (1984).

Mattsson, L.

See, for example, J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989).

McLay, M. J.

T. V. Vorburger, E. C. Teague, F. E. Scire, M. J. McLay, D. E. Gilsinn, “Surface roughness studies with DALLAS—Detector array for laser light angular scattering,” J. Res. Natl. Bur. Stand. 89, 3–16 (1984).
[CrossRef]

Rakels, J. H.

J. H. Rakels, “Recognized surface finish parameters obtained from diffraction patterns of rough surfaces,” in Proceedings on Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 119–125 (1988).

Scire, F. E.

T. V. Vorburger, E. C. Teague, F. E. Scire, M. J. McLay, D. E. Gilsinn, “Surface roughness studies with DALLAS—Detector array for laser light angular scattering,” J. Res. Natl. Bur. Stand. 89, 3–16 (1984).
[CrossRef]

E. C. Teague, F. E. Scire, T. V. Vorburger, “Sinusoidal profile precision roughness specimens,” Wear 83, 61–73 (1982).
[CrossRef]

Spizzichino, A.

See, for example, P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Takacs, P. Z.

P. Z. Takacs, R. C. Hewitt, E. L. Church, “Correlation between the performance and metrology of glancing-incidence synchrotron-radiation mirrors containing millimeter-wavelength shape errors,” in Proceedings on Metrology: Figure and Finish, B. Truax, ed., Proc. Soc. Photo-Opt. Instrum. Eng.749, 119–124 (1987).

Teague, E. C.

T. V. Vorburger, E. C. Teague, F. E. Scire, M. J. McLay, D. E. Gilsinn, “Surface roughness studies with DALLAS—Detector array for laser light angular scattering,” J. Res. Natl. Bur. Stand. 89, 3–16 (1984).
[CrossRef]

E. C. Teague, F. E. Scire, T. V. Vorburger, “Sinusoidal profile precision roughness specimens,” Wear 83, 61–73 (1982).
[CrossRef]

T. V. Vorburger, E. C. Teague, “Optical techniques for online measurement of surface topography,” Precis. Eng. 3, 61–83 (1981).
[CrossRef]

Thurn, G.

R. Brodmann, D. Gerstorfer, G. Thurn, “Optical roughness measuring instrument for fine-machined surfaces,” Opt. Eng. 24, 408–413 (1985).

Vorburger, T. V.

T. V. Vorburger, E. C. Teague, F. E. Scire, M. J. McLay, D. E. Gilsinn, “Surface roughness studies with DALLAS—Detector array for laser light angular scattering,” J. Res. Natl. Bur. Stand. 89, 3–16 (1984).
[CrossRef]

E. C. Teague, F. E. Scire, T. V. Vorburger, “Sinusoidal profile precision roughness specimens,” Wear 83, 61–73 (1982).
[CrossRef]

T. V. Vorburger, E. C. Teague, “Optical techniques for online measurement of surface topography,” Precis. Eng. 3, 61–83 (1981).
[CrossRef]

J. Res. Natl. Bur. Stand. (1)

T. V. Vorburger, E. C. Teague, F. E. Scire, M. J. McLay, D. E. Gilsinn, “Surface roughness studies with DALLAS—Detector array for laser light angular scattering,” J. Res. Natl. Bur. Stand. 89, 3–16 (1984).
[CrossRef]

Opt. Eng. (1)

R. Brodmann, D. Gerstorfer, G. Thurn, “Optical roughness measuring instrument for fine-machined surfaces,” Opt. Eng. 24, 408–413 (1985).

Precis. Eng. (1)

T. V. Vorburger, E. C. Teague, “Optical techniques for online measurement of surface topography,” Precis. Eng. 3, 61–83 (1981).
[CrossRef]

Wear (2)

E. C. Teague, F. E. Scire, T. V. Vorburger, “Sinusoidal profile precision roughness specimens,” Wear 83, 61–73 (1982).
[CrossRef]

D. G. Chetwynd, “The digitization of surface profiles,” Wear 57, 137–140 (1979).
[CrossRef]

Other (9)

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

These models are valid, strictly speaking, only in the Fraunhofer region, whereas in the present experiments the scattering was in the Fresnel region. However, the difference is expected to be negligible.

ASME/ANSI B46.1-1985, Surface Texture (American Society of Mechanical Engineers, New York, 1985).

See, for example, J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989).

J. H. Rakels, “Recognized surface finish parameters obtained from diffraction patterns of rough surfaces,” in Proceedings on Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 119–125 (1988).

P. Z. Takacs, R. C. Hewitt, E. L. Church, “Correlation between the performance and metrology of glancing-incidence synchrotron-radiation mirrors containing millimeter-wavelength shape errors,” in Proceedings on Metrology: Figure and Finish, B. Truax, ed., Proc. Soc. Photo-Opt. Instrum. Eng.749, 119–124 (1987).

R. Brodmann, M. Allgauer, “Comparison of light scattering from rough surfaces with optical and mechanical profilometry,” in Proceedings on Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Photo-Opt. Instrum. Eng.1009, 111–118 (1988).

M. Kamei, T. Inari, “On-line monitoring of surface roughness by using laser,” in Proceedings on Production Aspects of Single Point Machined Optics, D. P. Brehm, ed., Proc. Soc. Photo-Opt. Instrum. Eng.508, 56–63 (1984).

See, for example, P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the DALLAS system.

Fig. 2
Fig. 2

The DALLAS coordinate system.

Fig. 3
Fig. 3

Schematic diagram of the conical scattering geometry.

Fig. 4
Fig. 4

Angle-resolved light scattering distributions for the sinusoidal brass (1/100) specimen: θi = −30°, 0°, and +30°; in all cases ϕs = −20.

Fig. 5
Fig. 5

Angle-resolved light scattering distributions for the sinusoidal brass (1/100) specimen: ϕi = ϕs = −6° and −12°; in both cases θi = 0°.

Fig. 6
Fig. 6

Plots of Γ vs ϕs sampling increment for different types of rough surface.

Fig. 7
Fig. 7

Linear regression for Γ2 vs Δq for all fifteen data points.

Tables (4)

Tables Icon

Table I Data for Nickel and Brass Sinusoidal Specimensa

Tables Icon

Table II Data for Hand-Lapped Stainless Steel Specimensa,b

Tables Icon

Table III Values of Γ (In Radians) for Different Values of θi

Tables Icon

Table IV Values of Γ (In Radians) for Different Values of ϕs

Equations (12)

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R a = ( 1 / N ) j z j ,
R q = [ ( 1 / N ) j z j 2 ] 1 / 2 ,
Δ q - [ ( 1 / N ) j Δ j 2 ] 1 / 2 ,
R q = A / 2 ,
Δ q = 2 π R q / λ ,
Γ = { j [ ( θ j - θ s ) ] 2 I s j / I tot } 1 / 2 ,
I tot = j I s j ,
θ s = j I s j θ j / I tot .
Δ q = 0.542 Γ 2 - 0.012 ,
Δ q = 0.542 Γ 1 - 0.013 ,
Δ q = 0.528 Γ 2 - 0.005 ,
Δ q = 0.539 Γ 2 - 0.010 ,

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