Abstract

In this paper we summarize a number of previous experiments on the measurement of the roughness of metallic surfaces by light scattering. We identify several regimes that permit measurement of different surface parameters and functions, and we establish approximate limits for each regime. Using a straightforward criterion, we calculate that the smooth-surface regime, in which the angular distribution of scattered light is closely related to the power spectral density of the roughness, ranges over 0 < σ/ λ ≲ 0.05, where σ is the rms roughness and λ is the opitcal wavelength. Above that the surface autocorrelation function may be calculated from a Fourier transform of the angular distribution over 0 < σ/λ ≲ 0.14. Then comes the specular regime where the specular beam can still be identified and measured over 0 < σ/λ ≲ 0.3. For all these regimes and for rougher surfaces too, the rms width of the scatter distribution is proportional to the rms slope of the surface.

© 1993 Optical Society of America

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  1. H. E. Bennett, J. O. Porteus, “Relation between surface roughness and specular reflectance at normal incidence,” J. Opt. Soc. Am. 51, 123–129 (1961).
    [Crossref]
  2. E. L. Church, J. M. Zavada, “Residual surface roughness of diamond-turned optics,” Appl. Opt. 14, 1788–1795 (1975).
    [Crossref] [PubMed]
  3. J. M. Elson, J. M. Bennett, “Relation between the angular dependence of scattering and the statistical properties of optical surfaces,” J. Opt. Soc. Am. 69, 31–47 (1979).
    [Crossref]
  4. 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]
  5. J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989).
  6. J. C. Stover, Optical Scattering, Measurement, and Analysis (McGraw-Hill, New York, 1990).
  7. J. C. Dainty, N. C. Bruce, A. J. Sant, “Measurements of light scattering by a characterized random rough surface,” Waves Random Media 3, S29–S39 (1991).
    [Crossref]
  8. P. C. Archibald, H. E. Bennett, “Scattering from infrared missile domes,” Opt. Eng. 17, 647–651 (1978).
  9. T. A. Leonard, M. Pantoliano, “BRDF round robin,” in High Bandwidth Analog Applications of Photonics II, B. T. Neyer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.987, 226–235 (1988).
  10. ASTM Standard E1392-90, Standard Practice for Angle Resolved Optical Scatter Measurements on Specular or Diffuse Surfaces (American Society for Testing and Materials, Philadelphia, Pa., 1991).
  11. C. S. Gardner, W. E. Streight, “Surface roughness gauge and method,” U.S. patent4,364,663 (21December1982).
  12. P. Cielo, Optical Techniques for Industrial Inspection (Academic, San Diego, Calif., 1988), p. 221.
  13. J. G. Valliant, “A new QC tool for quantitative surface analysis,” Quality 31, 35–39 (1992).
  14. F. E. Nicodemus, J. C. Richmond, J. C. Hsia, J. J. Ginsberg, I. W. Limperis, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160 (October1977).
  15. C. Asmail, “Bidirectional scattering distribution function (BSDF): a systematized bibliography,” J. Res. Natl. Inst. Stand. Technol. 96, 215–223 (1991).
    [Crossref]
  16. N. A. B. Rao, J. Raja, “A knowledge-based system for selection of surface texture parameters: a preliminary investigation,” Surf. Topogr. 1, 445–454 (1988).
  17. J. F. Song, T. V. Vorburger, “Surface texture,” in ASM Handbook, Friction, Lubrication, and Wear Technology (ASM International, Materials Park, Ohio, 1992), Vol. 18, pp. 334–345.
  18. A. A. Maradudin, “Enhanced backscattering of light from weakly rough random metal surfaces,” Appl. Opt. 32, 000–000 (1993) LN-Insert.
    [Crossref]
  19. J. C. Dainty, ed., Laser Speckle and Related Pheomena, Vol. 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975).
  20. R. K. Erf, ed., Speckle Metrology (Academic, New York, 1978).
  21. R. M. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with application to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
    [Crossref]
  22. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech, Norwood, Mass., 1987), Chaps. 3–5.
  23. F. G. Bass, I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, London, 1979).
  24. T. V. Vorburger, L. X. Cao, C. H. W. Giauque, J. Raja, D. E. Gilsinn, L. Fullana, “Optical scattering from rough surfaces: experiment and theory,” in Proceedings of the Seventh International Colloquium on Surfaces, H. Trumpold, ed. (Technische Universität, Karl-Marx-Stadt, Germany, 1988), pp. 308–316.
  25. E. Marx, T. V. Vorburger, “Direct and inverse problems for light scattered by a rough surface,” Appl. Opt. 29, 3613–3626 (1990).
    [Crossref] [PubMed]
  26. J. C. Stover, “Roughness characterization of smooth machined surfaces by light scattering,” Appl. Opt. 14, 1796–1802 (1975).
    [Crossref] [PubMed]
  27. T. V. Vorburger, D. E. Gilsinn, F. E. Scire, M. J. McLay, C. H. W. Giauque, E. C. Teague, “Optical measurement of the roughness of sinusoidal surfaces,” Wear 109, 15–27 (1986).
    [Crossref]
  28. J. M. Elson, J. M. Bennett, “Vector scattering theory,” Opt. Eng. 18, 116–124 (1979).
  29. E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
  30. E. Marx, T. R. Lettieri, T. V. Vorburger, M. Mcintosh, “Sinusoidal surfaces as standards for BRDF instruments,” in Optical Scatter: Applications, Measurement, and Theory, J. C. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1530, 15–21 (1991).
  31. P. J. Chandley, “Determination of the autocorrelation function of height on a rough surface from coherent light scattering,” Opt. Quantum Electron. 8, 329–333 (1976).
    [Crossref]
  32. D. J. Whitehouse, J. F. Archard, “The properties of random surfaces of significance in their contact,” Proc. R. Soc. London Ser. A 316, 97–121 (1970).
    [Crossref]
  33. E. Marx, B. Leridon, T. R. Lettieri, J. F. Song, T. V. Vorburger, “Autocorrelation functions from optical scattering for one-dimensionally rough surfaces,” Appl. Opt. 32, 67–76 (1993).
    [Crossref] [PubMed]
  34. Reference 22, Section 5.3.
  35. ASTM Standard F1084-87, Standard Test Method for Measuring the Effect of Surface Roughness of Optical Components by Total Integrated Scattering (American Society for Testing and Materials, Philadelphia, Pa., 1987).
  36. E. L. Church, G. M. Sanger, P. Z. Takacs, “Comparison of Wyko and TIS measurements of surface finish,” in Metrology: Figure and Finish, B. E. Truax, ed., Proc. Soc. Photo-Opt. Instrum. Eng.749, 65–73 (1987).
  37. T. V. Vorburger, M. J. McLay, F. E. Scire, D. E. Gilsinn, C. H. W. Giauque, E. C. Teague, “Surface roughness studies for wind tunnel models used in high Reynolds number testing,” J. Aircr. 23, 56–60 (1986).
    [Crossref]
  38. J. H. Rakels, “Recognized surface finish parameters obtained from diffraction patterns of rough surfaces,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 119–125 (1989).
  39. R. Brodmann, M. Allgaüer, “Comparison of light scattering from rough surfaces with optical and mechanical profilometry,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 111–118 (1989).
  40. L. X. Cao, T. V. Vorburger, A. G. Lieberman, T. R. Lettieri, “Light-scattering measurement of the rms slopes of rough surfaces,” Appl. Opt. 30, 3221–3227 (1991).
    [Crossref] [PubMed]
  41. A thorough account of conditions for validity of this approach is given in A. Wirgin, “Scattering from sinusoidal gratings: an evaluation of the Kirchhoff approximation,” J. Opt. Soc. Am. 73, 1028–1041 (1983).
    [Crossref]
  42. E. L. Church, “The measurement of surface texture and topography by differential light scattering,” Wear 57, 93–105 (1979).
    [Crossref]
  43. M. Stedman, “Basis for comparing the performance of surface-measuring machines,” Precis. Eng. 9, 149–152 (1987).
    [Crossref]
  44. T. V. Vorburger, “Optical scattering for roughness inspection,” in Progress Report of the Quality in Automation Project for FY89, NISTIR 4322, T.V. Vorburger, B. R. Scace, eds. (National Institute of Standards and Technology, Gaithersburg, Md, 1990), pp. 127–145.
  45. G. V. Blessing, D. G. Eitzen, “Surface roughness sensed by ultrasound,” in Metrology and Properties of Engineering Surfaces 1988, K. J. Stout, T. V. Vorburger, eds. (Page, London, 1988), pp. 143–157.

1993 (2)

1992 (1)

J. G. Valliant, “A new QC tool for quantitative surface analysis,” Quality 31, 35–39 (1992).

1991 (3)

J. C. Dainty, N. C. Bruce, A. J. Sant, “Measurements of light scattering by a characterized random rough surface,” Waves Random Media 3, S29–S39 (1991).
[Crossref]

C. Asmail, “Bidirectional scattering distribution function (BSDF): a systematized bibliography,” J. Res. Natl. Inst. Stand. Technol. 96, 215–223 (1991).
[Crossref]

L. X. Cao, T. V. Vorburger, A. G. Lieberman, T. R. Lettieri, “Light-scattering measurement of the rms slopes of rough surfaces,” Appl. Opt. 30, 3221–3227 (1991).
[Crossref] [PubMed]

1990 (1)

1988 (1)

N. A. B. Rao, J. Raja, “A knowledge-based system for selection of surface texture parameters: a preliminary investigation,” Surf. Topogr. 1, 445–454 (1988).

1987 (1)

M. Stedman, “Basis for comparing the performance of surface-measuring machines,” Precis. Eng. 9, 149–152 (1987).
[Crossref]

1986 (2)

T. V. Vorburger, M. J. McLay, F. E. Scire, D. E. Gilsinn, C. H. W. Giauque, E. C. Teague, “Surface roughness studies for wind tunnel models used in high Reynolds number testing,” J. Aircr. 23, 56–60 (1986).
[Crossref]

T. V. Vorburger, D. E. Gilsinn, F. E. Scire, M. J. McLay, C. H. W. Giauque, E. C. Teague, “Optical measurement of the roughness of sinusoidal surfaces,” Wear 109, 15–27 (1986).
[Crossref]

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]

1983 (1)

1979 (4)

J. M. Elson, J. M. Bennett, “Relation between the angular dependence of scattering and the statistical properties of optical surfaces,” J. Opt. Soc. Am. 69, 31–47 (1979).
[Crossref]

J. M. Elson, J. M. Bennett, “Vector scattering theory,” Opt. Eng. 18, 116–124 (1979).

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).

E. L. Church, “The measurement of surface texture and topography by differential light scattering,” Wear 57, 93–105 (1979).
[Crossref]

1978 (1)

P. C. Archibald, H. E. Bennett, “Scattering from infrared missile domes,” Opt. Eng. 17, 647–651 (1978).

1977 (1)

F. E. Nicodemus, J. C. Richmond, J. C. Hsia, J. J. Ginsberg, I. W. Limperis, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160 (October1977).

1976 (1)

P. J. Chandley, “Determination of the autocorrelation function of height on a rough surface from coherent light scattering,” Opt. Quantum Electron. 8, 329–333 (1976).
[Crossref]

1975 (2)

1972 (1)

R. M. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with application to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[Crossref]

1970 (1)

D. J. Whitehouse, J. F. Archard, “The properties of random surfaces of significance in their contact,” Proc. R. Soc. London Ser. A 316, 97–121 (1970).
[Crossref]

1961 (1)

Allgaüer, M.

R. Brodmann, M. Allgaüer, “Comparison of light scattering from rough surfaces with optical and mechanical profilometry,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 111–118 (1989).

Archard, J. F.

D. J. Whitehouse, J. F. Archard, “The properties of random surfaces of significance in their contact,” Proc. R. Soc. London Ser. A 316, 97–121 (1970).
[Crossref]

Archibald, P. C.

P. C. Archibald, H. E. Bennett, “Scattering from infrared missile domes,” Opt. Eng. 17, 647–651 (1978).

Asmail, C.

C. Asmail, “Bidirectional scattering distribution function (BSDF): a systematized bibliography,” J. Res. Natl. Inst. Stand. Technol. 96, 215–223 (1991).
[Crossref]

Azzam, R. M.

R. M. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with application to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[Crossref]

Bashara, N. M.

R. M. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with application to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[Crossref]

Bass, F. G.

F. G. Bass, I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, London, 1979).

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech, Norwood, Mass., 1987), Chaps. 3–5.

Bennett, H. E.

P. C. Archibald, H. E. Bennett, “Scattering from infrared missile domes,” Opt. Eng. 17, 647–651 (1978).

H. E. Bennett, J. O. Porteus, “Relation between surface roughness and specular reflectance at normal incidence,” J. Opt. Soc. Am. 51, 123–129 (1961).
[Crossref]

Bennett, J. M.

J. M. Elson, J. M. Bennett, “Relation between the angular dependence of scattering and the statistical properties of optical surfaces,” J. Opt. Soc. Am. 69, 31–47 (1979).
[Crossref]

J. M. Elson, J. M. Bennett, “Vector scattering theory,” Opt. Eng. 18, 116–124 (1979).

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

Blessing, G. V.

G. V. Blessing, D. G. Eitzen, “Surface roughness sensed by ultrasound,” in Metrology and Properties of Engineering Surfaces 1988, K. J. Stout, T. V. Vorburger, eds. (Page, London, 1988), pp. 143–157.

Brodmann, R.

R. Brodmann, M. Allgaüer, “Comparison of light scattering from rough surfaces with optical and mechanical profilometry,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 111–118 (1989).

Bruce, N. C.

J. C. Dainty, N. C. Bruce, A. J. Sant, “Measurements of light scattering by a characterized random rough surface,” Waves Random Media 3, S29–S39 (1991).
[Crossref]

Cao, L. X.

L. X. Cao, T. V. Vorburger, A. G. Lieberman, T. R. Lettieri, “Light-scattering measurement of the rms slopes of rough surfaces,” Appl. Opt. 30, 3221–3227 (1991).
[Crossref] [PubMed]

T. V. Vorburger, L. X. Cao, C. H. W. Giauque, J. Raja, D. E. Gilsinn, L. Fullana, “Optical scattering from rough surfaces: experiment and theory,” in Proceedings of the Seventh International Colloquium on Surfaces, H. Trumpold, ed. (Technische Universität, Karl-Marx-Stadt, Germany, 1988), pp. 308–316.

Chandley, P. J.

P. J. Chandley, “Determination of the autocorrelation function of height on a rough surface from coherent light scattering,” Opt. Quantum Electron. 8, 329–333 (1976).
[Crossref]

Church, E. L.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).

E. L. Church, “The measurement of surface texture and topography by differential light scattering,” Wear 57, 93–105 (1979).
[Crossref]

E. L. Church, J. M. Zavada, “Residual surface roughness of diamond-turned optics,” Appl. Opt. 14, 1788–1795 (1975).
[Crossref] [PubMed]

E. L. Church, G. M. Sanger, P. Z. Takacs, “Comparison of Wyko and TIS measurements of surface finish,” in Metrology: Figure and Finish, B. E. Truax, ed., Proc. Soc. Photo-Opt. Instrum. Eng.749, 65–73 (1987).

Cielo, P.

P. Cielo, Optical Techniques for Industrial Inspection (Academic, San Diego, Calif., 1988), p. 221.

Dainty, J. C.

J. C. Dainty, N. C. Bruce, A. J. Sant, “Measurements of light scattering by a characterized random rough surface,” Waves Random Media 3, S29–S39 (1991).
[Crossref]

Eitzen, D. G.

G. V. Blessing, D. G. Eitzen, “Surface roughness sensed by ultrasound,” in Metrology and Properties of Engineering Surfaces 1988, K. J. Stout, T. V. Vorburger, eds. (Page, London, 1988), pp. 143–157.

Elson, J. M.

Fuks, I. M.

F. G. Bass, I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, London, 1979).

Fullana, L.

T. V. Vorburger, L. X. Cao, C. H. W. Giauque, J. Raja, D. E. Gilsinn, L. Fullana, “Optical scattering from rough surfaces: experiment and theory,” in Proceedings of the Seventh International Colloquium on Surfaces, H. Trumpold, ed. (Technische Universität, Karl-Marx-Stadt, Germany, 1988), pp. 308–316.

Gardner, C. S.

C. S. Gardner, W. E. Streight, “Surface roughness gauge and method,” U.S. patent4,364,663 (21December1982).

Giauque, C. H. W.

T. V. Vorburger, D. E. Gilsinn, F. E. Scire, M. J. McLay, C. H. W. Giauque, E. C. Teague, “Optical measurement of the roughness of sinusoidal surfaces,” Wear 109, 15–27 (1986).
[Crossref]

T. V. Vorburger, M. J. McLay, F. E. Scire, D. E. Gilsinn, C. H. W. Giauque, E. C. Teague, “Surface roughness studies for wind tunnel models used in high Reynolds number testing,” J. Aircr. 23, 56–60 (1986).
[Crossref]

T. V. Vorburger, L. X. Cao, C. H. W. Giauque, J. Raja, D. E. Gilsinn, L. Fullana, “Optical scattering from rough surfaces: experiment and theory,” in Proceedings of the Seventh International Colloquium on Surfaces, H. Trumpold, ed. (Technische Universität, Karl-Marx-Stadt, Germany, 1988), pp. 308–316.

Gilsinn, D. E.

T. V. Vorburger, D. E. Gilsinn, F. E. Scire, M. J. McLay, C. H. W. Giauque, E. C. Teague, “Optical measurement of the roughness of sinusoidal surfaces,” Wear 109, 15–27 (1986).
[Crossref]

T. V. Vorburger, M. J. McLay, F. E. Scire, D. E. Gilsinn, C. H. W. Giauque, E. C. Teague, “Surface roughness studies for wind tunnel models used in high Reynolds number testing,” J. Aircr. 23, 56–60 (1986).
[Crossref]

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]

T. V. Vorburger, L. X. Cao, C. H. W. Giauque, J. Raja, D. E. Gilsinn, L. Fullana, “Optical scattering from rough surfaces: experiment and theory,” in Proceedings of the Seventh International Colloquium on Surfaces, H. Trumpold, ed. (Technische Universität, Karl-Marx-Stadt, Germany, 1988), pp. 308–316.

Ginsberg, J. J.

F. E. Nicodemus, J. C. Richmond, J. C. Hsia, J. J. Ginsberg, I. W. Limperis, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160 (October1977).

Hsia, J. C.

F. E. Nicodemus, J. C. Richmond, J. C. Hsia, J. J. Ginsberg, I. W. Limperis, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160 (October1977).

Jenkinson, H. A.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).

Leonard, T. A.

T. A. Leonard, M. Pantoliano, “BRDF round robin,” in High Bandwidth Analog Applications of Photonics II, B. T. Neyer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.987, 226–235 (1988).

Leridon, B.

Lettieri, T. R.

Lieberman, A. G.

Limperis, I. W.

F. E. Nicodemus, J. C. Richmond, J. C. Hsia, J. J. Ginsberg, I. W. Limperis, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160 (October1977).

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. C. Hsia, J. J. Ginsberg, I. W. Limperis, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160 (October1977).

Maradudin, A. A.

A. A. Maradudin, “Enhanced backscattering of light from weakly rough random metal surfaces,” Appl. Opt. 32, 000–000 (1993) LN-Insert.
[Crossref]

Marx, E.

E. Marx, B. Leridon, T. R. Lettieri, J. F. Song, T. V. Vorburger, “Autocorrelation functions from optical scattering for one-dimensionally rough surfaces,” Appl. Opt. 32, 67–76 (1993).
[Crossref] [PubMed]

E. Marx, T. V. Vorburger, “Direct and inverse problems for light scattered by a rough surface,” Appl. Opt. 29, 3613–3626 (1990).
[Crossref] [PubMed]

E. Marx, T. R. Lettieri, T. V. Vorburger, M. Mcintosh, “Sinusoidal surfaces as standards for BRDF instruments,” in Optical Scatter: Applications, Measurement, and Theory, J. C. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1530, 15–21 (1991).

Mattsson, L.

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

Mcintosh, M.

E. Marx, T. R. Lettieri, T. V. Vorburger, M. Mcintosh, “Sinusoidal surfaces as standards for BRDF instruments,” in Optical Scatter: Applications, Measurement, and Theory, J. C. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1530, 15–21 (1991).

McLay, M. J.

T. V. Vorburger, M. J. McLay, F. E. Scire, D. E. Gilsinn, C. H. W. Giauque, E. C. Teague, “Surface roughness studies for wind tunnel models used in high Reynolds number testing,” J. Aircr. 23, 56–60 (1986).
[Crossref]

T. V. Vorburger, D. E. Gilsinn, F. E. Scire, M. J. McLay, C. H. W. Giauque, E. C. Teague, “Optical measurement of the roughness of sinusoidal surfaces,” Wear 109, 15–27 (1986).
[Crossref]

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]

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. C. Hsia, J. J. Ginsberg, I. W. Limperis, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160 (October1977).

Pantoliano, M.

T. A. Leonard, M. Pantoliano, “BRDF round robin,” in High Bandwidth Analog Applications of Photonics II, B. T. Neyer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.987, 226–235 (1988).

Porteus, J. O.

Raja, J.

N. A. B. Rao, J. Raja, “A knowledge-based system for selection of surface texture parameters: a preliminary investigation,” Surf. Topogr. 1, 445–454 (1988).

T. V. Vorburger, L. X. Cao, C. H. W. Giauque, J. Raja, D. E. Gilsinn, L. Fullana, “Optical scattering from rough surfaces: experiment and theory,” in Proceedings of the Seventh International Colloquium on Surfaces, H. Trumpold, ed. (Technische Universität, Karl-Marx-Stadt, Germany, 1988), pp. 308–316.

Rakels, J. H.

J. H. Rakels, “Recognized surface finish parameters obtained from diffraction patterns of rough surfaces,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 119–125 (1989).

Rao, N. A. B.

N. A. B. Rao, J. Raja, “A knowledge-based system for selection of surface texture parameters: a preliminary investigation,” Surf. Topogr. 1, 445–454 (1988).

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. C. Hsia, J. J. Ginsberg, I. W. Limperis, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160 (October1977).

Sanger, G. M.

E. L. Church, G. M. Sanger, P. Z. Takacs, “Comparison of Wyko and TIS measurements of surface finish,” in Metrology: Figure and Finish, B. E. Truax, ed., Proc. Soc. Photo-Opt. Instrum. Eng.749, 65–73 (1987).

Sant, A. J.

J. C. Dainty, N. C. Bruce, A. J. Sant, “Measurements of light scattering by a characterized random rough surface,” Waves Random Media 3, S29–S39 (1991).
[Crossref]

Scire, F. E.

T. V. Vorburger, M. J. McLay, F. E. Scire, D. E. Gilsinn, C. H. W. Giauque, E. C. Teague, “Surface roughness studies for wind tunnel models used in high Reynolds number testing,” J. Aircr. 23, 56–60 (1986).
[Crossref]

T. V. Vorburger, D. E. Gilsinn, F. E. Scire, M. J. McLay, C. H. W. Giauque, E. C. Teague, “Optical measurement of the roughness of sinusoidal surfaces,” Wear 109, 15–27 (1986).
[Crossref]

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]

Song, J. F.

E. Marx, B. Leridon, T. R. Lettieri, J. F. Song, T. V. Vorburger, “Autocorrelation functions from optical scattering for one-dimensionally rough surfaces,” Appl. Opt. 32, 67–76 (1993).
[Crossref] [PubMed]

J. F. Song, T. V. Vorburger, “Surface texture,” in ASM Handbook, Friction, Lubrication, and Wear Technology (ASM International, Materials Park, Ohio, 1992), Vol. 18, pp. 334–345.

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech, Norwood, Mass., 1987), Chaps. 3–5.

Stedman, M.

M. Stedman, “Basis for comparing the performance of surface-measuring machines,” Precis. Eng. 9, 149–152 (1987).
[Crossref]

Stover, J. C.

Streight, W. E.

C. S. Gardner, W. E. Streight, “Surface roughness gauge and method,” U.S. patent4,364,663 (21December1982).

Takacs, P. Z.

E. L. Church, G. M. Sanger, P. Z. Takacs, “Comparison of Wyko and TIS measurements of surface finish,” in Metrology: Figure and Finish, B. E. Truax, ed., Proc. Soc. Photo-Opt. Instrum. Eng.749, 65–73 (1987).

Teague, E. C.

T. V. Vorburger, M. J. McLay, F. E. Scire, D. E. Gilsinn, C. H. W. Giauque, E. C. Teague, “Surface roughness studies for wind tunnel models used in high Reynolds number testing,” J. Aircr. 23, 56–60 (1986).
[Crossref]

T. V. Vorburger, D. E. Gilsinn, F. E. Scire, M. J. McLay, C. H. W. Giauque, E. C. Teague, “Optical measurement of the roughness of sinusoidal surfaces,” Wear 109, 15–27 (1986).
[Crossref]

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]

Valliant, J. G.

J. G. Valliant, “A new QC tool for quantitative surface analysis,” Quality 31, 35–39 (1992).

Vorburger, T. V.

E. Marx, B. Leridon, T. R. Lettieri, J. F. Song, T. V. Vorburger, “Autocorrelation functions from optical scattering for one-dimensionally rough surfaces,” Appl. Opt. 32, 67–76 (1993).
[Crossref] [PubMed]

L. X. Cao, T. V. Vorburger, A. G. Lieberman, T. R. Lettieri, “Light-scattering measurement of the rms slopes of rough surfaces,” Appl. Opt. 30, 3221–3227 (1991).
[Crossref] [PubMed]

E. Marx, T. V. Vorburger, “Direct and inverse problems for light scattered by a rough surface,” Appl. Opt. 29, 3613–3626 (1990).
[Crossref] [PubMed]

T. V. Vorburger, D. E. Gilsinn, F. E. Scire, M. J. McLay, C. H. W. Giauque, E. C. Teague, “Optical measurement of the roughness of sinusoidal surfaces,” Wear 109, 15–27 (1986).
[Crossref]

T. V. Vorburger, M. J. McLay, F. E. Scire, D. E. Gilsinn, C. H. W. Giauque, E. C. Teague, “Surface roughness studies for wind tunnel models used in high Reynolds number testing,” J. Aircr. 23, 56–60 (1986).
[Crossref]

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]

J. F. Song, T. V. Vorburger, “Surface texture,” in ASM Handbook, Friction, Lubrication, and Wear Technology (ASM International, Materials Park, Ohio, 1992), Vol. 18, pp. 334–345.

E. Marx, T. R. Lettieri, T. V. Vorburger, M. Mcintosh, “Sinusoidal surfaces as standards for BRDF instruments,” in Optical Scatter: Applications, Measurement, and Theory, J. C. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1530, 15–21 (1991).

T. V. Vorburger, L. X. Cao, C. H. W. Giauque, J. Raja, D. E. Gilsinn, L. Fullana, “Optical scattering from rough surfaces: experiment and theory,” in Proceedings of the Seventh International Colloquium on Surfaces, H. Trumpold, ed. (Technische Universität, Karl-Marx-Stadt, Germany, 1988), pp. 308–316.

T. V. Vorburger, “Optical scattering for roughness inspection,” in Progress Report of the Quality in Automation Project for FY89, NISTIR 4322, T.V. Vorburger, B. R. Scace, eds. (National Institute of Standards and Technology, Gaithersburg, Md, 1990), pp. 127–145.

Whitehouse, D. J.

D. J. Whitehouse, J. F. Archard, “The properties of random surfaces of significance in their contact,” Proc. R. Soc. London Ser. A 316, 97–121 (1970).
[Crossref]

Wirgin, A.

Zavada, J. M.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).

E. L. Church, J. M. Zavada, “Residual surface roughness of diamond-turned optics,” Appl. Opt. 14, 1788–1795 (1975).
[Crossref] [PubMed]

Appl. Opt. (6)

J. Aircr. (1)

T. V. Vorburger, M. J. McLay, F. E. Scire, D. E. Gilsinn, C. H. W. Giauque, E. C. Teague, “Surface roughness studies for wind tunnel models used in high Reynolds number testing,” J. Aircr. 23, 56–60 (1986).
[Crossref]

J. Opt. Soc. Am. (3)

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]

J. Res. Natl. Inst. Stand. Technol. (1)

C. Asmail, “Bidirectional scattering distribution function (BSDF): a systematized bibliography,” J. Res. Natl. Inst. Stand. Technol. 96, 215–223 (1991).
[Crossref]

Natl. Bur. Stand. (U.S.) Monogr. 160 (1)

F. E. Nicodemus, J. C. Richmond, J. C. Hsia, J. J. Ginsberg, I. W. Limperis, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160 (October1977).

Opt. Eng. (3)

P. C. Archibald, H. E. Bennett, “Scattering from infrared missile domes,” Opt. Eng. 17, 647–651 (1978).

J. M. Elson, J. M. Bennett, “Vector scattering theory,” Opt. Eng. 18, 116–124 (1979).

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).

Opt. Quantum Electron. (1)

P. J. Chandley, “Determination of the autocorrelation function of height on a rough surface from coherent light scattering,” Opt. Quantum Electron. 8, 329–333 (1976).
[Crossref]

Phys. Rev. B (1)

R. M. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with application to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[Crossref]

Precis. Eng. (1)

M. Stedman, “Basis for comparing the performance of surface-measuring machines,” Precis. Eng. 9, 149–152 (1987).
[Crossref]

Proc. R. Soc. London Ser. A (1)

D. J. Whitehouse, J. F. Archard, “The properties of random surfaces of significance in their contact,” Proc. R. Soc. London Ser. A 316, 97–121 (1970).
[Crossref]

Quality (1)

J. G. Valliant, “A new QC tool for quantitative surface analysis,” Quality 31, 35–39 (1992).

Surf. Topogr. (1)

N. A. B. Rao, J. Raja, “A knowledge-based system for selection of surface texture parameters: a preliminary investigation,” Surf. Topogr. 1, 445–454 (1988).

Waves Random Media (1)

J. C. Dainty, N. C. Bruce, A. J. Sant, “Measurements of light scattering by a characterized random rough surface,” Waves Random Media 3, S29–S39 (1991).
[Crossref]

Wear (2)

T. V. Vorburger, D. E. Gilsinn, F. E. Scire, M. J. McLay, C. H. W. Giauque, E. C. Teague, “Optical measurement of the roughness of sinusoidal surfaces,” Wear 109, 15–27 (1986).
[Crossref]

E. L. Church, “The measurement of surface texture and topography by differential light scattering,” Wear 57, 93–105 (1979).
[Crossref]

Other (20)

T. V. Vorburger, “Optical scattering for roughness inspection,” in Progress Report of the Quality in Automation Project for FY89, NISTIR 4322, T.V. Vorburger, B. R. Scace, eds. (National Institute of Standards and Technology, Gaithersburg, Md, 1990), pp. 127–145.

G. V. Blessing, D. G. Eitzen, “Surface roughness sensed by ultrasound,” in Metrology and Properties of Engineering Surfaces 1988, K. J. Stout, T. V. Vorburger, eds. (Page, London, 1988), pp. 143–157.

E. Marx, T. R. Lettieri, T. V. Vorburger, M. Mcintosh, “Sinusoidal surfaces as standards for BRDF instruments,” in Optical Scatter: Applications, Measurement, and Theory, J. C. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1530, 15–21 (1991).

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech, Norwood, Mass., 1987), Chaps. 3–5.

F. G. Bass, I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, London, 1979).

T. V. Vorburger, L. X. Cao, C. H. W. Giauque, J. Raja, D. E. Gilsinn, L. Fullana, “Optical scattering from rough surfaces: experiment and theory,” in Proceedings of the Seventh International Colloquium on Surfaces, H. Trumpold, ed. (Technische Universität, Karl-Marx-Stadt, Germany, 1988), pp. 308–316.

J. H. Rakels, “Recognized surface finish parameters obtained from diffraction patterns of rough surfaces,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 119–125 (1989).

R. Brodmann, M. Allgaüer, “Comparison of light scattering from rough surfaces with optical and mechanical profilometry,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 111–118 (1989).

Reference 22, Section 5.3.

ASTM Standard F1084-87, Standard Test Method for Measuring the Effect of Surface Roughness of Optical Components by Total Integrated Scattering (American Society for Testing and Materials, Philadelphia, Pa., 1987).

E. L. Church, G. M. Sanger, P. Z. Takacs, “Comparison of Wyko and TIS measurements of surface finish,” in Metrology: Figure and Finish, B. E. Truax, ed., Proc. Soc. Photo-Opt. Instrum. Eng.749, 65–73 (1987).

J. F. Song, T. V. Vorburger, “Surface texture,” in ASM Handbook, Friction, Lubrication, and Wear Technology (ASM International, Materials Park, Ohio, 1992), Vol. 18, pp. 334–345.

J. C. Dainty, ed., Laser Speckle and Related Pheomena, Vol. 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975).

R. K. Erf, ed., Speckle Metrology (Academic, New York, 1978).

T. A. Leonard, M. Pantoliano, “BRDF round robin,” in High Bandwidth Analog Applications of Photonics II, B. T. Neyer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.987, 226–235 (1988).

ASTM Standard E1392-90, Standard Practice for Angle Resolved Optical Scatter Measurements on Specular or Diffuse Surfaces (American Society for Testing and Materials, Philadelphia, Pa., 1991).

C. S. Gardner, W. E. Streight, “Surface roughness gauge and method,” U.S. patent4,364,663 (21December1982).

P. Cielo, Optical Techniques for Industrial Inspection (Academic, San Diego, Calif., 1988), p. 221.

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

J. C. Stover, Optical Scattering, Measurement, and Analysis (McGraw-Hill, New York, 1990).

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram showing regimes of light scattering wherein various types of scattered light measurement are paired with surface parameters and statistical functions that may be derived from them.

Fig. 2
Fig. 2

Schematic diagram of the light-scattering geometry showing the incoming plane with wave vector Ki and angle of incidence θi with respect to the normal vector n of the mean plane of the surface. Also shown are the outgoing wave vector Ks with scattering angle θS; r is the vector from the origin to the surface point under consideration.

Fig. 3
Fig. 3

Schematic diagram of a portion of the light-scattering distribution from a sinusoidal surface with amplitude A < λ showing the specular peak (n = 0) and the first two diffraction peaks (n = 1, 2), which increase in size as A increases.

Fig. 4
Fig. 4

Autocorrelation functions for two uniaxial surface-roughness specimens calculated by both stylus and optical techniques: (a) a hand-lapped stainless-steel specimen, (b) a machine-lapped steel specimen. The wavelength of light was 633 nm.

Fig. 5
Fig. 5

Surface roughness σ measured by optical scattering verus σ measured by a stylus instrument for five hand-lapped stainless-steel specimens measured for angles of incidence of +54° and −54°. The optical wavelength λ was 633 nm.

Fig. 6
Fig. 6

Measured angular-scattering distributions for three hand-lapped surfaces with σ = 0.078, 0.20, and 0.32 μm, respectively. λ was 633 nm. The vertical scale spans 5 orders of magnitude.

Fig. 7
Fig. 7

Root-mean-square slope Δq for 15 surfaces plotted versus the rms width Γ of the scattered light distributions for λ = 633 nm. The solid line is a best-fit straight line to the data.

Equations (27)

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E ( θ s ) = C 0 [ 1 + cos ( θ i θ s ) ] cos θ i + cos θ s 0 L exp ( j V · r ) d x ,
V = k i k s ,
r = x ê x + z ( x ) ê z ,
V · r = V x x + V z z ( x ) = k [ ( sin θ i + sin θ s ) x + ( cos θ i + cos θ s ) z ( x ) ] ,
exp ( j V · r ) = exp ( j V x x ) exp [ j V z z ( x ) ] exp ( j V x x ) [ 1 + j V z z ( x ) ] .
I ( θ s ) = F ( θ s ) λ 4 | 0 L exp ( j V x x ) z ( x ) d x | 2 ,
PSD ( u ) = 1 L | 0 L exp ( j 2 π ux ) z ( x ) d x | 2 .
I ( θ s ) = F 1 ( θ s ) λ 4 PSD [ V x ( θ s ) / 2 π ] ,
z ( x ) = A sin ( 2 π x / D ) ,
sin θ i + sin θ s = ± n λ / D ,
P n P 0 [ J n ( 2 k A ) / J 0 ( 2 k A ) ] 2 P 0 [ ( k A ) n / n ! ] 2
P 2 / P 1 = ( π A / λ ) 2 0.05 .
σ = A / 2 ,
B ( τ ) = 1 L 0 L z ( x ) z ( x + τ ) d x .
B ( τ ) = PSD ( u ) exp ( j 2 π u τ ) d u .
B ( 0 ) = 1 L 0 L z 2 ( x ) d x = σ 2 .
C ( τ ) = B ( τ ) / σ 2 .
C ( τ ) = 1 + ln [ C υ ( τ ) + exp ( 4 k 2 σ 2 ) ] 4 k 2 σ 2 ,
C υ ( τ ) = [ 1 exp ( 4 k 2 σ 2 ) ] I ( ξ ) exp ( j k ξ τ / R 0 ) d ξ I ( ξ ) d ξ .
ξ = R 0 tan θ s .
C υ ( τ ) 0.1 C υ ( 0 ) for C ( τ ) = 1 / e .
σ / λ 0.14 .
P spec / P tot = exp [ ( 4 π σ cos θ i / λ ) 2 ] ,
P tot = P spec + P scat .
P scat / P tot ( 4 π σ cos θ i / λ ) 2 .
P spec = 0.007 P tot
w / f = 2 Δ rms ,

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