Abstract

The theory and measurement of angle-resolved scatter are described. Values of rms roughness that were obtained by using this technique to characterize four different materials are compared with values that were obtained by using a total integrated scatter measuring instrument, an optical profiler, and a mechanical profiler. The spatial frequency bandwidths and modulation transfer functions of the four instruments are different, and results are described in light of these differences.

© 1992 Optical Society of America

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References

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  1. G. A. Al-Jumaily, S. R. Wilson, J. J. McNally, J. R. McNeil, J. M. Bennett, H. H. Hurt, “Influence of metal films on the optical scatter and related microstructure of coated surfaces,” Appl. Opt. 25, 3631–3634 (1986); G. A. Al-Jumaily, “Influence of metal films on the optical scatter and related surface microstructure of coated surfaces,” Ph.D. dissertation (University of New Mexico, Albuquerque, N.M., 1986).
    [CrossRef] [PubMed]
  2. E. L. Church, H. A. Jenkinson, J. M. Zavada, “Measurement of the finish of diamond-turned metal surfaces by differential light scattering,” Opt. Eng. 16, 360–374 (1977).
    [CrossRef]
  3. L. D. Brooks, W. L. Wolfe, “Microprocessor-based instrumentation for bidirectional reflectance distribution function (BRDF) measurements from visible to far infrared (FIR),” in Radiation Scattering in Optical Systems I, W. H. Hunt, ed., Proc. Soc. Photo-Opt. Instrum. Eng.257, 177–183 (1980).
  4. P. Roche, E. Pelletier, “Characterizations of optical surfaces by measurement of scattering distribution,” Appl. Opt. 23, 3561–3566 (1984).
    [CrossRef] [PubMed]
  5. J. C. Stover, F. M. Cady, E. Sklar, “Measurement of low angle scatter,” Opt. Eng. 24, 404–407 (1985).
    [CrossRef]
  6. R. M. Silva, F. D. Orazio, J. M. Bennett, “Nondestructive measurement of subsurface structural defects in polished single-crystal silicon,” Opt. News 12(2), 10–17 (1986).
    [CrossRef]
  7. R. M. Silva, F. D. Orazio, J. M. Bennett, “Subsurface structural defects in GaAs wafers,” Semicond. Int. 9(7), 81–87 (1986).
  8. H. E. Bennett, “Scattering characteristics of optical materials,” Opt. Eng. 17, 480–488 (1978).
    [CrossRef]
  9. L. Mattsson, “Total integrated scatter measurement system for quality assessment of coatings on optical surfaces,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.652, 264–271 (1986).
  10. Talystep Surface Profiler sold by Rank Taylor Hobson, 411 East Jarvis Avenue, Des Plaines, Ill. 60018. See also J. M. Bennett, J. H. Dancy, “Stylus profiling instrument for measuring statistical properties of smooth optical surfaces,” Appl. Opt. 20, 1785–1802 (1981).
    [CrossRef] [PubMed]
  11. Alpha-Step 250 High-Sensitivity Profiler manufactured by Tencor Instruments, 2400 Charleston Road, Mountain View, Calif. 94043.
  12. Dektak IIA and Dektak 3030 manufactured by Veeco Instruments, Inc., Sloan Technology Division, 602 East Montecito Street, Santa Barbara, Calif. 93103.
  13. Wyko TOPO-2D and TOPO-3D manufactured by Wyko Corporation, 2650 Elvira Road, Tucson, Ariz. 85706. See also B. Bushan, J. C. Wyant, C. L. Koliopoulos, “Measurement of surface topography of magnetic tapes by Mirau interferometry,” Appl. Opt. 24, 1489–1497 (1985).
    [CrossRef]
  14. Heterodyne Profiler, Model 5500, manufactured by Zygo Corporation, Laurel Brook Road, P.O. Box 448, Middlefield, Conn. 06455. See also G. E. Sommargren, “Optical heterodyne profilometry,” Appl. Opt. 20, 610–618 (1981).
    [CrossRef] [PubMed]
  15. Laser Interferometric Microscope, Maxim 3D, manufactured by Zygo Corporation, address same as in Ref. 14.
  16. MP 2000 Non-Contact Surface Profiler manufactured by Chapman Instruments, Inc., 50 Saginaw Drive, Rochester, N.Y. 14623. See also T. C. Bristow, A. Bouzid, J. Bietry, “Surface measurements and applications for manufactured parts using noncontact profilometer,” in Optical Testing and Metrology II, C. P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.954, 217–225 (1988).
  17. G. A. Al-Jumaily, S. R. Wilson, K. C. Jungling, J. R. McNeil, Jean M. Bennett, “Frequency response characteristics of a mechanical surface profilometer,” Opt. Eng. 26, 953–958 (1987).
    [CrossRef]
  18. E. L. Church, P. Z. Takacs, T. A. Leonard, “The prediction of BRDFs from surface profile measurements,” in Scatter from Optical Components, J. C. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1165, 136–150 (1990).
  19. H. Davies, “The reflection of electromagnetic waves from a rough surface,” Proc. Inst. Electr. Eng. Part 4 101, 209–214 (1954).
  20. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces, (Pergamon, London, 1963), and references contained therein.
  21. See the feature on waves in random media, J. Opt. Soc. Am. A 2(12) (1985).
    [PubMed]
  22. E. L. Church, J. M. Zavada, “Residual roughness of diamond-turned optics,” Appl. Opt. 14, 1788–1795 (1975).
    [CrossRef] [PubMed]
  23. E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
    [CrossRef]
  24. J. M. Elson, J. M. Bennett, “Relation between the angular dependence of scattering and the statistical properties of smooth optical surfaces,” J. Opt. Soc. Am. 69, 31–47 (1979).
    [CrossRef]
  25. J. M. Elson, J. M. Bennett, “Vector scattering theory,” Opt. Eng. 18, 116–124 (1979).
    [CrossRef]
  26. 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]
  27. J. M. Elson, J. P. Rahn, J. M. Bennett, “Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation length, and roughness cross-correlation properties,” Appl. Opt. 22, 3207–3219 (1983).
    [CrossRef] [PubMed]
  28. Small scatter angles strictly refer to small angles measured relative to the specular direction. However, in both the ARS and TIS instruments the angle of incidence was very close to normal so that the incident and reflected angles were essentially 0°.
  29. F. E. Nicodemus, “Directional reflectance and emissivity of an opaque surface,” Appl. Opt. 4, 767–771 (1965); Appl. Opt. 5, 715(E)1966);-“Reflectance nomenclature and directional reflectance and emissivity,” Appl. Opt. 9, 1474–1475 (1970).
    [CrossRef] [PubMed]
  30. J. C. Stover, “Optical scatter,” Lasers Optron. 7(8), 61–69 (August1988).
  31. J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D. C., 1989), pp. 31–37.
  32. N. J. Brown, W. K. Eickelberg, “Some comparisons of noncontact surface profiling instruments,” in Optical Fabrication and Testing, Vol. 12 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 52–55.
  33. J. M. Bennett, “Comparison of techniques for measuring the roughness of optical surfaces,” Opt. Eng. 24, 380–387 (1985).
    [CrossRef]
  34. E. L. Church, T. V. Vorburger, J. C. Wyant, “Direct comparison of mechanical and optical measurements of the finish of precision machined optical surfaces,” Opt. Eng. 24, 388–395 (1985).
    [CrossRef]
  35. J. C. Stover, B. Hourmand, J. A. Kahler, C. H. Gillespie, “Comparison of roughness measurements by differential scatter and total integrated scatter,” in Stray Radiation TV, R. P. Breault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.511, 2–6 (1984).
  36. J. M. Bennett, “Measurement of the rms roughness, autocovariance function, and other statistical properties of optical surfaces using a FECO scanning interferometer,” Appl. Opt. 15, 2705–2721 (1976).
    [CrossRef] [PubMed]
  37. K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 820–3836 (1984).
    [CrossRef]
  38. K. Creath, J. C. Wyant, “Absolute measurement of surface roughness,” Appl. Opt. 29, 823–3827 (1990).
    [CrossRef]
  39. J. M. Bennett, T. C. Bristow, K. Arackellian, J. C. Wyant, “Surface profiling with optical and mechanical instruments,” in Technical Digest on Optical Fabrication and Testing (Optical Society of America, Washington, D.C., 1986), paper ThB4;see also Ref. 31, pp. 14–15.
  40. J. C. Stover, B. Hourmand, “Some deviations associated with vector perturbation diffraction theory,” in Stray Radiation IV, R. P. Breault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.511, 12–17 (1984).
  41. E. L. Church, P. Z. Takacs, “Effects of the optical transfer function in surface profile measurements,” in Surface Characterization and Testing II, J. E. Greivenkamp, M. Young, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1164, 46–59 (1989).
  42. E. L. Church, G. M. Sanger, P. Z. Takacs, “Comparison of Wyko and TIS measurement of surface finish,” in Metrology: Figure and Finish, B. Truax, ed., Proc. Soc. Photo-Opt. Instrum. Eng.749, 5–73 (1987).
  43. C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: Recent advances for a better investigation of experiment,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 82–97 (1988); see also earlier papers listed in the references.
  44. E. Pelletier, R. Roche, C. Grèzes-Besset, in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 98–110 (1988); see also earlier papers listed in the references.
  45. A reviewer has suggested that the rms roughness measurements for the Wyko profiler (and presumably also for the Talystep profiler) should have been calculated from a two-dimensional PSD rather than measured directly on a one-dimensional profile. His back-of-the-envelope calculations for the two-dimensional case assume a constant slope for the PSD when plotted on a log–log scale and yield roughness values that are higher than those measured by using the Wyko instrument. He thus is suggesting that a two-dimensional roughness measured by a profiler on an isotropic surface should be larger than a one-dimensional roughness measured by the profiler on the same surface. Possible differences between one- and two-dimensional roughnesses on isotropic surfaces should be carefully checked before drawing any firm conclusions. However, the intention of this investigation was to present results from different measurement techniques by using accepted analysis methods.

1990 (1)

K. Creath, J. C. Wyant, “Absolute measurement of surface roughness,” Appl. Opt. 29, 823–3827 (1990).
[CrossRef]

1988 (1)

J. C. Stover, “Optical scatter,” Lasers Optron. 7(8), 61–69 (August1988).

1987 (1)

G. A. Al-Jumaily, S. R. Wilson, K. C. Jungling, J. R. McNeil, Jean M. Bennett, “Frequency response characteristics of a mechanical surface profilometer,” Opt. Eng. 26, 953–958 (1987).
[CrossRef]

1986 (3)

R. M. Silva, F. D. Orazio, J. M. Bennett, “Nondestructive measurement of subsurface structural defects in polished single-crystal silicon,” Opt. News 12(2), 10–17 (1986).
[CrossRef]

R. M. Silva, F. D. Orazio, J. M. Bennett, “Subsurface structural defects in GaAs wafers,” Semicond. Int. 9(7), 81–87 (1986).

G. A. Al-Jumaily, S. R. Wilson, J. J. McNally, J. R. McNeil, J. M. Bennett, H. H. Hurt, “Influence of metal films on the optical scatter and related microstructure of coated surfaces,” Appl. Opt. 25, 3631–3634 (1986); G. A. Al-Jumaily, “Influence of metal films on the optical scatter and related surface microstructure of coated surfaces,” Ph.D. dissertation (University of New Mexico, Albuquerque, N.M., 1986).
[CrossRef] [PubMed]

1985 (5)

Wyko TOPO-2D and TOPO-3D manufactured by Wyko Corporation, 2650 Elvira Road, Tucson, Ariz. 85706. See also B. Bushan, J. C. Wyant, C. L. Koliopoulos, “Measurement of surface topography of magnetic tapes by Mirau interferometry,” Appl. Opt. 24, 1489–1497 (1985).
[CrossRef]

See the feature on waves in random media, J. Opt. Soc. Am. A 2(12) (1985).
[PubMed]

J. M. Bennett, “Comparison of techniques for measuring the roughness of optical surfaces,” Opt. Eng. 24, 380–387 (1985).
[CrossRef]

E. L. Church, T. V. Vorburger, J. C. Wyant, “Direct comparison of mechanical and optical measurements of the finish of precision machined optical surfaces,” Opt. Eng. 24, 388–395 (1985).
[CrossRef]

J. C. Stover, F. M. Cady, E. Sklar, “Measurement of low angle scatter,” Opt. Eng. 24, 404–407 (1985).
[CrossRef]

1984 (2)

K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 820–3836 (1984).
[CrossRef]

P. Roche, E. Pelletier, “Characterizations of optical surfaces by measurement of scattering distribution,” Appl. Opt. 23, 3561–3566 (1984).
[CrossRef] [PubMed]

1983 (1)

1981 (2)

1979 (3)

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

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

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

1978 (1)

H. E. Bennett, “Scattering characteristics of optical materials,” Opt. Eng. 17, 480–488 (1978).
[CrossRef]

1977 (1)

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Measurement of the finish of diamond-turned metal surfaces by differential light scattering,” Opt. Eng. 16, 360–374 (1977).
[CrossRef]

1976 (1)

1975 (1)

1965 (1)

1961 (1)

1954 (1)

H. Davies, “The reflection of electromagnetic waves from a rough surface,” Proc. Inst. Electr. Eng. Part 4 101, 209–214 (1954).

Al-Jumaily, G. A.

Amra, C.

C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: Recent advances for a better investigation of experiment,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 82–97 (1988); see also earlier papers listed in the references.

Arackellian, K.

J. M. Bennett, T. C. Bristow, K. Arackellian, J. C. Wyant, “Surface profiling with optical and mechanical instruments,” in Technical Digest on Optical Fabrication and Testing (Optical Society of America, Washington, D.C., 1986), paper ThB4;see also Ref. 31, pp. 14–15.

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces, (Pergamon, London, 1963), and references contained therein.

Bennett, H. E.

Bennett, J. M.

R. M. Silva, F. D. Orazio, J. M. Bennett, “Nondestructive measurement of subsurface structural defects in polished single-crystal silicon,” Opt. News 12(2), 10–17 (1986).
[CrossRef]

R. M. Silva, F. D. Orazio, J. M. Bennett, “Subsurface structural defects in GaAs wafers,” Semicond. Int. 9(7), 81–87 (1986).

G. A. Al-Jumaily, S. R. Wilson, J. J. McNally, J. R. McNeil, J. M. Bennett, H. H. Hurt, “Influence of metal films on the optical scatter and related microstructure of coated surfaces,” Appl. Opt. 25, 3631–3634 (1986); G. A. Al-Jumaily, “Influence of metal films on the optical scatter and related surface microstructure of coated surfaces,” Ph.D. dissertation (University of New Mexico, Albuquerque, N.M., 1986).
[CrossRef] [PubMed]

J. M. Bennett, “Comparison of techniques for measuring the roughness of optical surfaces,” Opt. Eng. 24, 380–387 (1985).
[CrossRef]

K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 820–3836 (1984).
[CrossRef]

J. M. Elson, J. P. Rahn, J. M. Bennett, “Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation length, and roughness cross-correlation properties,” Appl. Opt. 22, 3207–3219 (1983).
[CrossRef] [PubMed]

Talystep Surface Profiler sold by Rank Taylor Hobson, 411 East Jarvis Avenue, Des Plaines, Ill. 60018. See also J. M. Bennett, J. H. Dancy, “Stylus profiling instrument for measuring statistical properties of smooth optical surfaces,” Appl. Opt. 20, 1785–1802 (1981).
[CrossRef] [PubMed]

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

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

J. M. Bennett, “Measurement of the rms roughness, autocovariance function, and other statistical properties of optical surfaces using a FECO scanning interferometer,” Appl. Opt. 15, 2705–2721 (1976).
[CrossRef] [PubMed]

J. M. Bennett, T. C. Bristow, K. Arackellian, J. C. Wyant, “Surface profiling with optical and mechanical instruments,” in Technical Digest on Optical Fabrication and Testing (Optical Society of America, Washington, D.C., 1986), paper ThB4;see also Ref. 31, pp. 14–15.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D. C., 1989), pp. 31–37.

Bennett, Jean M.

G. A. Al-Jumaily, S. R. Wilson, K. C. Jungling, J. R. McNeil, Jean M. Bennett, “Frequency response characteristics of a mechanical surface profilometer,” Opt. Eng. 26, 953–958 (1987).
[CrossRef]

Bietry, J.

MP 2000 Non-Contact Surface Profiler manufactured by Chapman Instruments, Inc., 50 Saginaw Drive, Rochester, N.Y. 14623. See also T. C. Bristow, A. Bouzid, J. Bietry, “Surface measurements and applications for manufactured parts using noncontact profilometer,” in Optical Testing and Metrology II, C. P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.954, 217–225 (1988).

Bousquet, P.

C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: Recent advances for a better investigation of experiment,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 82–97 (1988); see also earlier papers listed in the references.

Bouzid, A.

MP 2000 Non-Contact Surface Profiler manufactured by Chapman Instruments, Inc., 50 Saginaw Drive, Rochester, N.Y. 14623. See also T. C. Bristow, A. Bouzid, J. Bietry, “Surface measurements and applications for manufactured parts using noncontact profilometer,” in Optical Testing and Metrology II, C. P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.954, 217–225 (1988).

Bristow, T. C.

MP 2000 Non-Contact Surface Profiler manufactured by Chapman Instruments, Inc., 50 Saginaw Drive, Rochester, N.Y. 14623. See also T. C. Bristow, A. Bouzid, J. Bietry, “Surface measurements and applications for manufactured parts using noncontact profilometer,” in Optical Testing and Metrology II, C. P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.954, 217–225 (1988).

J. M. Bennett, T. C. Bristow, K. Arackellian, J. C. Wyant, “Surface profiling with optical and mechanical instruments,” in Technical Digest on Optical Fabrication and Testing (Optical Society of America, Washington, D.C., 1986), paper ThB4;see also Ref. 31, pp. 14–15.

Brooks, L. D.

L. D. Brooks, W. L. Wolfe, “Microprocessor-based instrumentation for bidirectional reflectance distribution function (BRDF) measurements from visible to far infrared (FIR),” in Radiation Scattering in Optical Systems I, W. H. Hunt, ed., Proc. Soc. Photo-Opt. Instrum. Eng.257, 177–183 (1980).

Brown, N. J.

N. J. Brown, W. K. Eickelberg, “Some comparisons of noncontact surface profiling instruments,” in Optical Fabrication and Testing, Vol. 12 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 52–55.

Bushan, B.

Cady, F. M.

J. C. Stover, F. M. Cady, E. Sklar, “Measurement of low angle scatter,” Opt. Eng. 24, 404–407 (1985).
[CrossRef]

Church, E. L.

E. L. Church, T. V. Vorburger, J. C. Wyant, “Direct comparison of mechanical and optical measurements of the finish of precision machined optical surfaces,” Opt. Eng. 24, 388–395 (1985).
[CrossRef]

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

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Measurement of the finish of diamond-turned metal surfaces by differential light scattering,” Opt. Eng. 16, 360–374 (1977).
[CrossRef]

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

E. L. Church, P. Z. Takacs, T. A. Leonard, “The prediction of BRDFs from surface profile measurements,” in Scatter from Optical Components, J. C. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1165, 136–150 (1990).

E. L. Church, P. Z. Takacs, “Effects of the optical transfer function in surface profile measurements,” in Surface Characterization and Testing II, J. E. Greivenkamp, M. Young, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1164, 46–59 (1989).

E. L. Church, G. M. Sanger, P. Z. Takacs, “Comparison of Wyko and TIS measurement of surface finish,” in Metrology: Figure and Finish, B. Truax, ed., Proc. Soc. Photo-Opt. Instrum. Eng.749, 5–73 (1987).

Creath, K.

K. Creath, J. C. Wyant, “Absolute measurement of surface roughness,” Appl. Opt. 29, 823–3827 (1990).
[CrossRef]

Dancy, J. H.

Davies, H.

H. Davies, “The reflection of electromagnetic waves from a rough surface,” Proc. Inst. Electr. Eng. Part 4 101, 209–214 (1954).

Eickelberg, W. K.

N. J. Brown, W. K. Eickelberg, “Some comparisons of noncontact surface profiling instruments,” in Optical Fabrication and Testing, Vol. 12 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 52–55.

Elson, J. M.

Gillespie, C. H.

J. C. Stover, B. Hourmand, J. A. Kahler, C. H. Gillespie, “Comparison of roughness measurements by differential scatter and total integrated scatter,” in Stray Radiation TV, R. P. Breault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.511, 2–6 (1984).

Grèzes-Besset, C.

E. Pelletier, R. Roche, C. Grèzes-Besset, in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 98–110 (1988); see also earlier papers listed in the references.

Guenther, K. H.

K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 820–3836 (1984).
[CrossRef]

Hourmand, B.

J. C. Stover, B. Hourmand, J. A. Kahler, C. H. Gillespie, “Comparison of roughness measurements by differential scatter and total integrated scatter,” in Stray Radiation TV, R. P. Breault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.511, 2–6 (1984).

J. C. Stover, B. Hourmand, “Some deviations associated with vector perturbation diffraction theory,” in Stray Radiation IV, R. P. Breault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.511, 12–17 (1984).

Hurt, H. H.

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).
[CrossRef]

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Measurement of the finish of diamond-turned metal surfaces by differential light scattering,” Opt. Eng. 16, 360–374 (1977).
[CrossRef]

Jungling, K. C.

G. A. Al-Jumaily, S. R. Wilson, K. C. Jungling, J. R. McNeil, Jean M. Bennett, “Frequency response characteristics of a mechanical surface profilometer,” Opt. Eng. 26, 953–958 (1987).
[CrossRef]

Kahler, J. A.

J. C. Stover, B. Hourmand, J. A. Kahler, C. H. Gillespie, “Comparison of roughness measurements by differential scatter and total integrated scatter,” in Stray Radiation TV, R. P. Breault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.511, 2–6 (1984).

Koliopoulos, C. L.

Leonard, T. A.

E. L. Church, P. Z. Takacs, T. A. Leonard, “The prediction of BRDFs from surface profile measurements,” in Scatter from Optical Components, J. C. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1165, 136–150 (1990).

Mattsson, L.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D. C., 1989), pp. 31–37.

L. Mattsson, “Total integrated scatter measurement system for quality assessment of coatings on optical surfaces,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.652, 264–271 (1986).

McNally, J. J.

McNeil, J. R.

Nicodemus, F. E.

Orazio, F. D.

R. M. Silva, F. D. Orazio, J. M. Bennett, “Nondestructive measurement of subsurface structural defects in polished single-crystal silicon,” Opt. News 12(2), 10–17 (1986).
[CrossRef]

R. M. Silva, F. D. Orazio, J. M. Bennett, “Subsurface structural defects in GaAs wafers,” Semicond. Int. 9(7), 81–87 (1986).

Pelletier, E.

P. Roche, E. Pelletier, “Characterizations of optical surfaces by measurement of scattering distribution,” Appl. Opt. 23, 3561–3566 (1984).
[CrossRef] [PubMed]

E. Pelletier, R. Roche, C. Grèzes-Besset, in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 98–110 (1988); see also earlier papers listed in the references.

Porteus, J. O.

Rahn, J. P.

Roche, P.

Roche, R.

E. Pelletier, R. Roche, C. Grèzes-Besset, in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 98–110 (1988); see also earlier papers listed in the references.

Sanger, G. M.

E. L. Church, G. M. Sanger, P. Z. Takacs, “Comparison of Wyko and TIS measurement of surface finish,” in Metrology: Figure and Finish, B. Truax, ed., Proc. Soc. Photo-Opt. Instrum. Eng.749, 5–73 (1987).

Silva, R. M.

R. M. Silva, F. D. Orazio, J. M. Bennett, “Nondestructive measurement of subsurface structural defects in polished single-crystal silicon,” Opt. News 12(2), 10–17 (1986).
[CrossRef]

R. M. Silva, F. D. Orazio, J. M. Bennett, “Subsurface structural defects in GaAs wafers,” Semicond. Int. 9(7), 81–87 (1986).

Sklar, E.

J. C. Stover, F. M. Cady, E. Sklar, “Measurement of low angle scatter,” Opt. Eng. 24, 404–407 (1985).
[CrossRef]

Sommargren, G. E.

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces, (Pergamon, London, 1963), and references contained therein.

Stover, J. C.

J. C. Stover, “Optical scatter,” Lasers Optron. 7(8), 61–69 (August1988).

J. C. Stover, F. M. Cady, E. Sklar, “Measurement of low angle scatter,” Opt. Eng. 24, 404–407 (1985).
[CrossRef]

J. C. Stover, B. Hourmand, J. A. Kahler, C. H. Gillespie, “Comparison of roughness measurements by differential scatter and total integrated scatter,” in Stray Radiation TV, R. P. Breault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.511, 2–6 (1984).

J. C. Stover, B. Hourmand, “Some deviations associated with vector perturbation diffraction theory,” in Stray Radiation IV, R. P. Breault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.511, 12–17 (1984).

Takacs, P. Z.

E. L. Church, P. Z. Takacs, “Effects of the optical transfer function in surface profile measurements,” in Surface Characterization and Testing II, J. E. Greivenkamp, M. Young, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1164, 46–59 (1989).

E. L. Church, G. M. Sanger, P. Z. Takacs, “Comparison of Wyko and TIS measurement of surface finish,” in Metrology: Figure and Finish, B. Truax, ed., Proc. Soc. Photo-Opt. Instrum. Eng.749, 5–73 (1987).

E. L. Church, P. Z. Takacs, T. A. Leonard, “The prediction of BRDFs from surface profile measurements,” in Scatter from Optical Components, J. C. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1165, 136–150 (1990).

Vorburger, T. V.

E. L. Church, T. V. Vorburger, J. C. Wyant, “Direct comparison of mechanical and optical measurements of the finish of precision machined optical surfaces,” Opt. Eng. 24, 388–395 (1985).
[CrossRef]

Wierer, P. G.

K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 820–3836 (1984).
[CrossRef]

Wilson, S. R.

Wolfe, W. L.

L. D. Brooks, W. L. Wolfe, “Microprocessor-based instrumentation for bidirectional reflectance distribution function (BRDF) measurements from visible to far infrared (FIR),” in Radiation Scattering in Optical Systems I, W. H. Hunt, ed., Proc. Soc. Photo-Opt. Instrum. Eng.257, 177–183 (1980).

Wyant, J. C.

K. Creath, J. C. Wyant, “Absolute measurement of surface roughness,” Appl. Opt. 29, 823–3827 (1990).
[CrossRef]

Wyko TOPO-2D and TOPO-3D manufactured by Wyko Corporation, 2650 Elvira Road, Tucson, Ariz. 85706. See also B. Bushan, J. C. Wyant, C. L. Koliopoulos, “Measurement of surface topography of magnetic tapes by Mirau interferometry,” Appl. Opt. 24, 1489–1497 (1985).
[CrossRef]

E. L. Church, T. V. Vorburger, J. C. Wyant, “Direct comparison of mechanical and optical measurements of the finish of precision machined optical surfaces,” Opt. Eng. 24, 388–395 (1985).
[CrossRef]

J. M. Bennett, T. C. Bristow, K. Arackellian, J. C. Wyant, “Surface profiling with optical and mechanical instruments,” in Technical Digest on Optical Fabrication and Testing (Optical Society of America, Washington, D.C., 1986), paper ThB4;see also Ref. 31, pp. 14–15.

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).
[CrossRef]

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Measurement of the finish of diamond-turned metal surfaces by differential light scattering,” Opt. Eng. 16, 360–374 (1977).
[CrossRef]

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

Appl. Opt. (11)

P. Roche, E. Pelletier, “Characterizations of optical surfaces by measurement of scattering distribution,” Appl. Opt. 23, 3561–3566 (1984).
[CrossRef] [PubMed]

G. A. Al-Jumaily, S. R. Wilson, J. J. McNally, J. R. McNeil, J. M. Bennett, H. H. Hurt, “Influence of metal films on the optical scatter and related microstructure of coated surfaces,” Appl. Opt. 25, 3631–3634 (1986); G. A. Al-Jumaily, “Influence of metal films on the optical scatter and related surface microstructure of coated surfaces,” Ph.D. dissertation (University of New Mexico, Albuquerque, N.M., 1986).
[CrossRef] [PubMed]

Wyko TOPO-2D and TOPO-3D manufactured by Wyko Corporation, 2650 Elvira Road, Tucson, Ariz. 85706. See also B. Bushan, J. C. Wyant, C. L. Koliopoulos, “Measurement of surface topography of magnetic tapes by Mirau interferometry,” Appl. Opt. 24, 1489–1497 (1985).
[CrossRef]

Heterodyne Profiler, Model 5500, manufactured by Zygo Corporation, Laurel Brook Road, P.O. Box 448, Middlefield, Conn. 06455. See also G. E. Sommargren, “Optical heterodyne profilometry,” Appl. Opt. 20, 610–618 (1981).
[CrossRef] [PubMed]

Talystep Surface Profiler sold by Rank Taylor Hobson, 411 East Jarvis Avenue, Des Plaines, Ill. 60018. See also J. M. Bennett, J. H. Dancy, “Stylus profiling instrument for measuring statistical properties of smooth optical surfaces,” Appl. Opt. 20, 1785–1802 (1981).
[CrossRef] [PubMed]

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

F. E. Nicodemus, “Directional reflectance and emissivity of an opaque surface,” Appl. Opt. 4, 767–771 (1965); Appl. Opt. 5, 715(E)1966);-“Reflectance nomenclature and directional reflectance and emissivity,” Appl. Opt. 9, 1474–1475 (1970).
[CrossRef] [PubMed]

J. M. Elson, J. P. Rahn, J. M. Bennett, “Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation length, and roughness cross-correlation properties,” Appl. Opt. 22, 3207–3219 (1983).
[CrossRef] [PubMed]

J. M. Bennett, “Measurement of the rms roughness, autocovariance function, and other statistical properties of optical surfaces using a FECO scanning interferometer,” Appl. Opt. 15, 2705–2721 (1976).
[CrossRef] [PubMed]

K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 820–3836 (1984).
[CrossRef]

K. Creath, J. C. Wyant, “Absolute measurement of surface roughness,” Appl. Opt. 29, 823–3827 (1990).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

See the feature on waves in random media, J. Opt. Soc. Am. A 2(12) (1985).
[PubMed]

Lasers Optron. (1)

J. C. Stover, “Optical scatter,” Lasers Optron. 7(8), 61–69 (August1988).

Opt. Eng. (8)

J. M. Bennett, “Comparison of techniques for measuring the roughness of optical surfaces,” Opt. Eng. 24, 380–387 (1985).
[CrossRef]

E. L. Church, T. V. Vorburger, J. C. Wyant, “Direct comparison of mechanical and optical measurements of the finish of precision machined optical surfaces,” Opt. Eng. 24, 388–395 (1985).
[CrossRef]

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

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

G. A. Al-Jumaily, S. R. Wilson, K. C. Jungling, J. R. McNeil, Jean M. Bennett, “Frequency response characteristics of a mechanical surface profilometer,” Opt. Eng. 26, 953–958 (1987).
[CrossRef]

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Measurement of the finish of diamond-turned metal surfaces by differential light scattering,” Opt. Eng. 16, 360–374 (1977).
[CrossRef]

H. E. Bennett, “Scattering characteristics of optical materials,” Opt. Eng. 17, 480–488 (1978).
[CrossRef]

J. C. Stover, F. M. Cady, E. Sklar, “Measurement of low angle scatter,” Opt. Eng. 24, 404–407 (1985).
[CrossRef]

Opt. News (1)

R. M. Silva, F. D. Orazio, J. M. Bennett, “Nondestructive measurement of subsurface structural defects in polished single-crystal silicon,” Opt. News 12(2), 10–17 (1986).
[CrossRef]

Proc. Inst. Electr. Eng. Part 4 (1)

H. Davies, “The reflection of electromagnetic waves from a rough surface,” Proc. Inst. Electr. Eng. Part 4 101, 209–214 (1954).

Semicond. Int. (1)

R. M. Silva, F. D. Orazio, J. M. Bennett, “Subsurface structural defects in GaAs wafers,” Semicond. Int. 9(7), 81–87 (1986).

Other (19)

L. Mattsson, “Total integrated scatter measurement system for quality assessment of coatings on optical surfaces,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.652, 264–271 (1986).

L. D. Brooks, W. L. Wolfe, “Microprocessor-based instrumentation for bidirectional reflectance distribution function (BRDF) measurements from visible to far infrared (FIR),” in Radiation Scattering in Optical Systems I, W. H. Hunt, ed., Proc. Soc. Photo-Opt. Instrum. Eng.257, 177–183 (1980).

E. L. Church, P. Z. Takacs, T. A. Leonard, “The prediction of BRDFs from surface profile measurements,” in Scatter from Optical Components, J. C. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1165, 136–150 (1990).

Alpha-Step 250 High-Sensitivity Profiler manufactured by Tencor Instruments, 2400 Charleston Road, Mountain View, Calif. 94043.

Dektak IIA and Dektak 3030 manufactured by Veeco Instruments, Inc., Sloan Technology Division, 602 East Montecito Street, Santa Barbara, Calif. 93103.

Laser Interferometric Microscope, Maxim 3D, manufactured by Zygo Corporation, address same as in Ref. 14.

MP 2000 Non-Contact Surface Profiler manufactured by Chapman Instruments, Inc., 50 Saginaw Drive, Rochester, N.Y. 14623. See also T. C. Bristow, A. Bouzid, J. Bietry, “Surface measurements and applications for manufactured parts using noncontact profilometer,” in Optical Testing and Metrology II, C. P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.954, 217–225 (1988).

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces, (Pergamon, London, 1963), and references contained therein.

J. C. Stover, B. Hourmand, J. A. Kahler, C. H. Gillespie, “Comparison of roughness measurements by differential scatter and total integrated scatter,” in Stray Radiation TV, R. P. Breault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.511, 2–6 (1984).

Small scatter angles strictly refer to small angles measured relative to the specular direction. However, in both the ARS and TIS instruments the angle of incidence was very close to normal so that the incident and reflected angles were essentially 0°.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D. C., 1989), pp. 31–37.

N. J. Brown, W. K. Eickelberg, “Some comparisons of noncontact surface profiling instruments,” in Optical Fabrication and Testing, Vol. 12 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 52–55.

J. M. Bennett, T. C. Bristow, K. Arackellian, J. C. Wyant, “Surface profiling with optical and mechanical instruments,” in Technical Digest on Optical Fabrication and Testing (Optical Society of America, Washington, D.C., 1986), paper ThB4;see also Ref. 31, pp. 14–15.

J. C. Stover, B. Hourmand, “Some deviations associated with vector perturbation diffraction theory,” in Stray Radiation IV, R. P. Breault, ed., Proc. Soc. Photo-Opt. Instrum. Eng.511, 12–17 (1984).

E. L. Church, P. Z. Takacs, “Effects of the optical transfer function in surface profile measurements,” in Surface Characterization and Testing II, J. E. Greivenkamp, M. Young, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1164, 46–59 (1989).

E. L. Church, G. M. Sanger, P. Z. Takacs, “Comparison of Wyko and TIS measurement of surface finish,” in Metrology: Figure and Finish, B. Truax, ed., Proc. Soc. Photo-Opt. Instrum. Eng.749, 5–73 (1987).

C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: Recent advances for a better investigation of experiment,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 82–97 (1988); see also earlier papers listed in the references.

E. Pelletier, R. Roche, C. Grèzes-Besset, in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 98–110 (1988); see also earlier papers listed in the references.

A reviewer has suggested that the rms roughness measurements for the Wyko profiler (and presumably also for the Talystep profiler) should have been calculated from a two-dimensional PSD rather than measured directly on a one-dimensional profile. His back-of-the-envelope calculations for the two-dimensional case assume a constant slope for the PSD when plotted on a log–log scale and yield roughness values that are higher than those measured by using the Wyko instrument. He thus is suggesting that a two-dimensional roughness measured by a profiler on an isotropic surface should be larger than a one-dimensional roughness measured by the profiler on the same surface. Possible differences between one- and two-dimensional roughnesses on isotropic surfaces should be carefully checked before drawing any firm conclusions. However, the intention of this investigation was to present results from different measurement techniques by using accepted analysis methods.

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram showing the notation for the ARS arrangement. Light is incident at a polar angle θ0 with azimuthal angle ϕ0 = 0; the polar and azimuthal scatter angles are θs and ϕs, respectively.

Fig. 2
Fig. 2

Schematic diagram of the ARS instrument.

Fig. 3
Fig. 3

Illustration of the spatial wavelength bandwidths for four instruments.

Fig. 4
Fig. 4

Nomarski micrograph of the surface of a polished copper sample.

Fig. 5
Fig. 5

Talystep surface profile of a polished copper sample.

Fig. 6
Fig. 6

Nomarski micrograph of the surface of a polished molybdenum sample.

Fig. 7
Fig. 7

Talystep surface profile of a polished molybdenum sample.

Fig. 8
Fig. 8

Curves of the PSD for molybdenum and copper obtained from ARS scatterometer measurements.

Tables (1)

Tables Icon

Table I Rms Roughness Values (Å) Measured on the Same Samples with an ARS Scatterometer, a TIS Scatterometer, Contact Profiler (Talystep), and Noncontact Profiler (Wyko)

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

1 I 0 d I s d ω s = C λ 4 Q ( θ 0 , ϕ 0 , θ s , ϕ s , n ˆ , χ 0 , χ s ) W ( p , q ) ,
W ( p , q ) = 1 A { 1 2 π d x d y exp [ i ( p x + q y ) ] Z ( x , y ) } 2 ,
1 I 0 d I s d ω s d ω s = 4 k 4 cos θ 0 cos 2 θ s Q W ( p , q ) d ω s ,
TIS = R d R 0 = R 0 R s R 0 = 1 exp [ ( 4 πσ / λ ) 2 ] ( 4 πσ / λ ) 2 ,
I ~ ( k a cos θ 0 ) 2
sin θ s = sin θ 0 ± λ d .
σ 2 = p min p max d p q min q max d q G ( p , q ) W ( p , q ) ,
G ( p ) ( 1 p p 0 } 2 ,

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