Abstract

The surface roughness of low-scatter mirrors and roughness standards can be measured in various ways: mechanically, optically, and electronoptically. In this paper several useful methods and instruments—total integrated scattering, stylus profilometer, optical heterodyne profilometer, variable angle scatterometer, and electron mirror interference microscope—are presented. Qualitative surface roughness assessment is provided by Nomarski microscopy and transmission electron microscopy of surface replicas. Samples were prepared at Balzers, and their surface roughness was measured at several laboratories using the methods given above. The results of these measurements are compared, and reasons for the differences are discussed.

© 1984 Optical Society of America

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  1. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves From Rough Surfaces (Pergamon, New York, 1963).
  2. J. M. Elson, H. E. Bennett, J. M. Bennett, “Scattering from Optical Surfaces,” in Applied Optics and Optical Engineering, Vol. 7, R. R. Shannon, J. Wyant, Eds. (Academic, New York, 1979), pp. 191–244.
    [CrossRef]
  3. R. P. Edwin, “Light Scattering as a Technique for Measuring the Roughness of Optical Surfaces,” J. Phys. E. 6, 55 (1973).
    [CrossRef]
  4. D. Heitmann, V. Permien, “Determination of Surface Roughness from Light Scattering Measurements,” Opt. Commun. 23, 131 (1977).
    [CrossRef]
  5. B. P. Hildebrand, R. L. Gordon, E. V. Allan, “Instrument for Measuring the Roughness of Supersmooth Surfaces,” Appl. Opt. 13, 177 (1974).
    [CrossRef] [PubMed]
  6. 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 (1979).
    [CrossRef]
  7. P. Bousquet, F. Flory, P. Roche, “Scattering from Multilayer Thin Films: Theory and Experiment,” J. Opt. Soc. Am. 71, 1115 (1981).
    [CrossRef]
  8. F. Aronowitz, “The Laser Gyro,” in Laser Applications, Vol. 1, M. Ross, Ed. (Academic, New York, 1971), p. 131.
  9. M. L. Scott, J. M. Elson, “Multilayer Light Scattering and the Laser Gyro,” Appl. Phys. Lett. 32, 158 (1978).
    [CrossRef]
  10. N. L. Thomas, “Low-Scatter, Low-Loss Mirrors for Laser Gyros,” Proc. Soc. Photo-Opt. Instrum. Eng. 157, 41 (1978).
  11. M. V. Zombeck, C. C. Wyman, M. C. Weisskopf, “High Resolution X-Ray Astrophysics Facility (AXAF),” Opt. Eng. 21, 63 (1982).
    [CrossRef]
  12. H. E. Bennett, J. M. Bennett, “Precision Measurements in Thin Film Optics,” in Physics of Thin Films, Vol. 4, G. Hass, R. E. Thun, Eds. (Academic, New York, 1967), pp. 1–96.
  13. T. V. Vorburger, E. C. Teague, “Optical Techniques for On-Line Measurement of Surface Topography,” Precision Eng. 3, 61 (1981).
    [CrossRef]
  14. J. Peklenik, “New Developments in Surface Characterization and Measurements by Means of Random Process Analysis,” Proc. IME 182, 108 (1967–1968).
  15. R. E. Thomas, “Characterization of Surface Roughness,” Precision Eng. 3, 97 (1981).
    [CrossRef]
  16. T. G. King, T. A. Spedding, “Towards a Rational Surface Profile Characterization System,” Precision Eng. 5, 153 (1983).
    [CrossRef]
  17. E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship Between Surface Scattering and Microtopographic Features,” Opt. Eng. 18, 125 (1979).
    [CrossRef]
  18. K. H. Günther, “Morphologie und Lichtstreuung dielektrischer Wechselschichtsysteme,” Dissertation, U. Innsbruck (1974).
  19. K. H. Guenther, H. L. Gruber, H. K. Pulker, “Morphology and Light Scattering of Dielectric Multilayer Systems,” Thin Solid Films 34, 363 (1976).
    [CrossRef]
  20. J. C. Stover, “Roughness Characterization of Smooth Machined Surfaces by Light Scattering,” Appl. Opt. 14, 1796 (1975).
    [CrossRef] [PubMed]
  21. P. J. Chandley, “Surface Roughness Measurements From Coherent Light Scattering,” Opt. Quantum Electron. 8, 323 (1976).
    [CrossRef]
  22. P. J. Chandley, “Determination of the Autocorrelation Function of Height on a Rough Surface From Coherent Light Scattering,” Opt. Quantum Electron. 8, 329 (1976).
    [CrossRef]
  23. 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 (1977).
    [CrossRef]
  24. H. E. Bennett, J. O. Porteus, “Relation Between Surface Roughness and Specular Reflectance at Normal Incidence,” J. Opt. Soc. Am. 51, 123 (1961).
    [CrossRef]
  25. 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 (1983).
    [CrossRef] [PubMed]
  26. J. M. Elson, “Angle-Resolved Light Scattering from Composite Optical Surfaces,” Proc. Soc. Photo-Opt. Instrum. Eng. 240, 296 (1980).
  27. J. M. Elson, private communication, 1984.
  28. D. J. Whitehouse, “Stylus Techniques,” in Characterization of Solid Surfaces, P. E. Kane, G. P. Larrabee, Eds. (Plenum, New York, 1974), p. 49.
    [CrossRef]
  29. B. Smith, M. J. Edmonds, S. D. Probert, “Use of a Profilometer for Surface Mapping,” Precision Eng. 3, 87 (1981).
    [CrossRef]
  30. A. L. Gauler, “Comparison of Two Common Methods of Surface Topography Evaluation,” Opt. Eng. 21, 991 (1982).
    [CrossRef]
  31. J. M. Bennett, J. H. Dancy, “Stylus Profiling Instrument for Measuring Statistical Properties of Smooth Optical Surfaces,” Appl. Opt. 20, 1785 (1981).
    [CrossRef] [PubMed]
  32. G. E. Sommargren, “Optical Heterodyne Profilometry,” Appl. Opt. 20, 610 (1981).
    [CrossRef] [PubMed]
  33. H. E. Bennett, “Scattering Characteristics of Optical Materials,” Opt. Eng. 17, 480 (1978).
    [CrossRef]
  34. J. A. Detrio, “Light Scattering Surface Roughness Characterization,” Proc. Soc. Photo-Opt. Instrum. Eng. 276, 136 (1981).
  35. P. C. Archibald, H. E. Bennett, “Scattering From Infrared Missile Domes,” Opt. Eng. 17, 647 (1978).
    [CrossRef]
  36. H. Lichte, G. Möllenstedt, “Measurement of the Roughness of Supersmooth Surfaces Using an Electron Mirror Interference Microscope,” J. Phys. E 12, 941 (1979).
    [CrossRef]
  37. F. D. Orazio, R. M. Silva, W. K. Stowell, “Instrumentation of a Variable Angle Scatterometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 384, 123 (1983).
  38. R. M. Silva, F. D. Orazio, W. K. Stowell, “Scatter Evaluation of Supersmooth Surfaces,” Proc. Soc. Photo-Opt. Instrum. Eng. 384, 2 (1983).
  39. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Natl. Bur. Stand. U.S. Monogr. 160, 5 (1977).
  40. V. L. Williams, R. T. Lockie, “Optical Contamination Assessment by Bidirectional Reflectance Distribution Function (BRDF) Measurement,” Opt. Eng. 18, 152 (1979).
    [CrossRef]
  41. W. K. Stowell, R. M. Silva, F. D. Orazio, “Damage Susceptibility of Ring Laser Gyro Class Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 384, 73 (1983).
  42. M. Rasigni, G. Rasigni, J. P. Palmari, A. Llebaria, “Study of Surface Roughness Using a Microdensitometer Analysis of Electron Micrographs of Surface Replicas: I. Surface Profiles, II. Autocovariance Functions,” J. Opt. Soc. Am. 71, 1124, 1230 (1981).
    [CrossRef]
  43. G. M. Nomarski, “Differential Microinterferometer With Polarized Waves,” J. Phys. Radium 16, 9 (1955).
  44. G. M. Nomarski, A. R. Weill, “Application a la Metallographie des Methodes Interferentielles a Deux Ondes Polarisees,” Rev. Metall. 52, 121 (1955).
  45. D. L. Lessor, J. S. Hartmann, R. L. Gordon, “Quantitative Surface Topography Determination by Nomarski Reflection Microscopy, I. Theory,” J. Opt. Soc. Am. 69, 357 (1979).
    [CrossRef]
  46. J. M. Eastman, J. M. Zavislan, “A New Optical Surface Microprofiling Instrument,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 56 (1983).
  47. K. H. Guenther, H. Bangert, A. Kaminitschek, A. Wagen dristel, “Ultra-Microhardness Testing of Optical Coatings,” in Technical Digest, Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1984), paper WA-A5.
  48. E. L. Church, “Direct Comparison of Mechanical and Optical Measurements of the Finish of Precision-Machined Surfaces,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 105 (1983).

1983 (7)

T. G. King, T. A. Spedding, “Towards a Rational Surface Profile Characterization System,” Precision Eng. 5, 153 (1983).
[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 (1983).
[CrossRef] [PubMed]

F. D. Orazio, R. M. Silva, W. K. Stowell, “Instrumentation of a Variable Angle Scatterometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 384, 123 (1983).

R. M. Silva, F. D. Orazio, W. K. Stowell, “Scatter Evaluation of Supersmooth Surfaces,” Proc. Soc. Photo-Opt. Instrum. Eng. 384, 2 (1983).

W. K. Stowell, R. M. Silva, F. D. Orazio, “Damage Susceptibility of Ring Laser Gyro Class Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 384, 73 (1983).

J. M. Eastman, J. M. Zavislan, “A New Optical Surface Microprofiling Instrument,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 56 (1983).

E. L. Church, “Direct Comparison of Mechanical and Optical Measurements of the Finish of Precision-Machined Surfaces,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 105 (1983).

1982 (2)

A. L. Gauler, “Comparison of Two Common Methods of Surface Topography Evaluation,” Opt. Eng. 21, 991 (1982).
[CrossRef]

M. V. Zombeck, C. C. Wyman, M. C. Weisskopf, “High Resolution X-Ray Astrophysics Facility (AXAF),” Opt. Eng. 21, 63 (1982).
[CrossRef]

1981 (8)

T. V. Vorburger, E. C. Teague, “Optical Techniques for On-Line Measurement of Surface Topography,” Precision Eng. 3, 61 (1981).
[CrossRef]

R. E. Thomas, “Characterization of Surface Roughness,” Precision Eng. 3, 97 (1981).
[CrossRef]

P. Bousquet, F. Flory, P. Roche, “Scattering from Multilayer Thin Films: Theory and Experiment,” J. Opt. Soc. Am. 71, 1115 (1981).
[CrossRef]

J. M. Bennett, J. H. Dancy, “Stylus Profiling Instrument for Measuring Statistical Properties of Smooth Optical Surfaces,” Appl. Opt. 20, 1785 (1981).
[CrossRef] [PubMed]

G. E. Sommargren, “Optical Heterodyne Profilometry,” Appl. Opt. 20, 610 (1981).
[CrossRef] [PubMed]

J. A. Detrio, “Light Scattering Surface Roughness Characterization,” Proc. Soc. Photo-Opt. Instrum. Eng. 276, 136 (1981).

M. Rasigni, G. Rasigni, J. P. Palmari, A. Llebaria, “Study of Surface Roughness Using a Microdensitometer Analysis of Electron Micrographs of Surface Replicas: I. Surface Profiles, II. Autocovariance Functions,” J. Opt. Soc. Am. 71, 1124, 1230 (1981).
[CrossRef]

B. Smith, M. J. Edmonds, S. D. Probert, “Use of a Profilometer for Surface Mapping,” Precision Eng. 3, 87 (1981).
[CrossRef]

1980 (1)

J. M. Elson, “Angle-Resolved Light Scattering from Composite Optical Surfaces,” Proc. Soc. Photo-Opt. Instrum. Eng. 240, 296 (1980).

1979 (5)

H. Lichte, G. Möllenstedt, “Measurement of the Roughness of Supersmooth Surfaces Using an Electron Mirror Interference Microscope,” J. Phys. E 12, 941 (1979).
[CrossRef]

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 (1979).
[CrossRef]

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship Between Surface Scattering and Microtopographic Features,” Opt. Eng. 18, 125 (1979).
[CrossRef]

V. L. Williams, R. T. Lockie, “Optical Contamination Assessment by Bidirectional Reflectance Distribution Function (BRDF) Measurement,” Opt. Eng. 18, 152 (1979).
[CrossRef]

D. L. Lessor, J. S. Hartmann, R. L. Gordon, “Quantitative Surface Topography Determination by Nomarski Reflection Microscopy, I. Theory,” J. Opt. Soc. Am. 69, 357 (1979).
[CrossRef]

1978 (4)

M. L. Scott, J. M. Elson, “Multilayer Light Scattering and the Laser Gyro,” Appl. Phys. Lett. 32, 158 (1978).
[CrossRef]

N. L. Thomas, “Low-Scatter, Low-Loss Mirrors for Laser Gyros,” Proc. Soc. Photo-Opt. Instrum. Eng. 157, 41 (1978).

P. C. Archibald, H. E. Bennett, “Scattering From Infrared Missile Domes,” Opt. Eng. 17, 647 (1978).
[CrossRef]

H. E. Bennett, “Scattering Characteristics of Optical Materials,” Opt. Eng. 17, 480 (1978).
[CrossRef]

1977 (3)

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Natl. Bur. Stand. U.S. Monogr. 160, 5 (1977).

D. Heitmann, V. Permien, “Determination of Surface Roughness from Light Scattering Measurements,” Opt. Commun. 23, 131 (1977).
[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 (1977).
[CrossRef]

1976 (3)

P. J. Chandley, “Surface Roughness Measurements From Coherent Light Scattering,” Opt. Quantum Electron. 8, 323 (1976).
[CrossRef]

P. J. Chandley, “Determination of the Autocorrelation Function of Height on a Rough Surface From Coherent Light Scattering,” Opt. Quantum Electron. 8, 329 (1976).
[CrossRef]

K. H. Guenther, H. L. Gruber, H. K. Pulker, “Morphology and Light Scattering of Dielectric Multilayer Systems,” Thin Solid Films 34, 363 (1976).
[CrossRef]

1975 (1)

1974 (1)

1973 (1)

R. P. Edwin, “Light Scattering as a Technique for Measuring the Roughness of Optical Surfaces,” J. Phys. E. 6, 55 (1973).
[CrossRef]

1961 (1)

1955 (2)

G. M. Nomarski, “Differential Microinterferometer With Polarized Waves,” J. Phys. Radium 16, 9 (1955).

G. M. Nomarski, A. R. Weill, “Application a la Metallographie des Methodes Interferentielles a Deux Ondes Polarisees,” Rev. Metall. 52, 121 (1955).

Allan, E. V.

Archibald, P. C.

P. C. Archibald, H. E. Bennett, “Scattering From Infrared Missile Domes,” Opt. Eng. 17, 647 (1978).
[CrossRef]

Aronowitz, F.

F. Aronowitz, “The Laser Gyro,” in Laser Applications, Vol. 1, M. Ross, Ed. (Academic, New York, 1971), p. 131.

Bangert, H.

K. H. Guenther, H. Bangert, A. Kaminitschek, A. Wagen dristel, “Ultra-Microhardness Testing of Optical Coatings,” in Technical Digest, Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1984), paper WA-A5.

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves From Rough Surfaces (Pergamon, New York, 1963).

Bennett, H. E.

H. E. Bennett, “Scattering Characteristics of Optical Materials,” Opt. Eng. 17, 480 (1978).
[CrossRef]

P. C. Archibald, H. E. Bennett, “Scattering From Infrared Missile Domes,” Opt. Eng. 17, 647 (1978).
[CrossRef]

H. E. Bennett, J. O. Porteus, “Relation Between Surface Roughness and Specular Reflectance at Normal Incidence,” J. Opt. Soc. Am. 51, 123 (1961).
[CrossRef]

J. M. Elson, H. E. Bennett, J. M. Bennett, “Scattering from Optical Surfaces,” in Applied Optics and Optical Engineering, Vol. 7, R. R. Shannon, J. Wyant, Eds. (Academic, New York, 1979), pp. 191–244.
[CrossRef]

H. E. Bennett, J. M. Bennett, “Precision Measurements in Thin Film Optics,” in Physics of Thin Films, Vol. 4, G. Hass, R. E. Thun, Eds. (Academic, New York, 1967), pp. 1–96.

Bennett, J. M.

Bousquet, P.

Chandley, P. J.

P. J. Chandley, “Surface Roughness Measurements From Coherent Light Scattering,” Opt. Quantum Electron. 8, 323 (1976).
[CrossRef]

P. J. Chandley, “Determination of the Autocorrelation Function of Height on a Rough Surface From Coherent Light Scattering,” Opt. Quantum Electron. 8, 329 (1976).
[CrossRef]

Church, E. L.

E. L. Church, “Direct Comparison of Mechanical and Optical Measurements of the Finish of Precision-Machined Surfaces,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 105 (1983).

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship Between Surface Scattering and Microtopographic Features,” Opt. Eng. 18, 125 (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 (1977).
[CrossRef]

Dancy, J. H.

Detrio, J. A.

J. A. Detrio, “Light Scattering Surface Roughness Characterization,” Proc. Soc. Photo-Opt. Instrum. Eng. 276, 136 (1981).

Eastman, J. M.

J. M. Eastman, J. M. Zavislan, “A New Optical Surface Microprofiling Instrument,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 56 (1983).

Edmonds, M. J.

B. Smith, M. J. Edmonds, S. D. Probert, “Use of a Profilometer for Surface Mapping,” Precision Eng. 3, 87 (1981).
[CrossRef]

Edwin, R. P.

R. P. Edwin, “Light Scattering as a Technique for Measuring the Roughness of Optical Surfaces,” J. Phys. E. 6, 55 (1973).
[CrossRef]

Elson, J. M.

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 (1983).
[CrossRef] [PubMed]

J. M. Elson, “Angle-Resolved Light Scattering from Composite Optical Surfaces,” Proc. Soc. Photo-Opt. Instrum. Eng. 240, 296 (1980).

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 (1979).
[CrossRef]

M. L. Scott, J. M. Elson, “Multilayer Light Scattering and the Laser Gyro,” Appl. Phys. Lett. 32, 158 (1978).
[CrossRef]

J. M. Elson, H. E. Bennett, J. M. Bennett, “Scattering from Optical Surfaces,” in Applied Optics and Optical Engineering, Vol. 7, R. R. Shannon, J. Wyant, Eds. (Academic, New York, 1979), pp. 191–244.
[CrossRef]

J. M. Elson, private communication, 1984.

Flory, F.

Gauler, A. L.

A. L. Gauler, “Comparison of Two Common Methods of Surface Topography Evaluation,” Opt. Eng. 21, 991 (1982).
[CrossRef]

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Natl. Bur. Stand. U.S. Monogr. 160, 5 (1977).

Gordon, R. L.

Gruber, H. L.

K. H. Guenther, H. L. Gruber, H. K. Pulker, “Morphology and Light Scattering of Dielectric Multilayer Systems,” Thin Solid Films 34, 363 (1976).
[CrossRef]

Guenther, K. H.

K. H. Guenther, H. L. Gruber, H. K. Pulker, “Morphology and Light Scattering of Dielectric Multilayer Systems,” Thin Solid Films 34, 363 (1976).
[CrossRef]

K. H. Guenther, H. Bangert, A. Kaminitschek, A. Wagen dristel, “Ultra-Microhardness Testing of Optical Coatings,” in Technical Digest, Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1984), paper WA-A5.

Günther, K. H.

K. H. Günther, “Morphologie und Lichtstreuung dielektrischer Wechselschichtsysteme,” Dissertation, U. Innsbruck (1974).

Hartmann, J. S.

Heitmann, D.

D. Heitmann, V. Permien, “Determination of Surface Roughness from Light Scattering Measurements,” Opt. Commun. 23, 131 (1977).
[CrossRef]

Hildebrand, B. P.

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Natl. Bur. Stand. U.S. Monogr. 160, 5 (1977).

Jenkinson, H. A.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship Between Surface Scattering and Microtopographic Features,” Opt. Eng. 18, 125 (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 (1977).
[CrossRef]

Kaminitschek, A.

K. H. Guenther, H. Bangert, A. Kaminitschek, A. Wagen dristel, “Ultra-Microhardness Testing of Optical Coatings,” in Technical Digest, Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1984), paper WA-A5.

King, T. G.

T. G. King, T. A. Spedding, “Towards a Rational Surface Profile Characterization System,” Precision Eng. 5, 153 (1983).
[CrossRef]

Lessor, D. L.

Lichte, H.

H. Lichte, G. Möllenstedt, “Measurement of the Roughness of Supersmooth Surfaces Using an Electron Mirror Interference Microscope,” J. Phys. E 12, 941 (1979).
[CrossRef]

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Natl. Bur. Stand. U.S. Monogr. 160, 5 (1977).

Llebaria, A.

M. Rasigni, G. Rasigni, J. P. Palmari, A. Llebaria, “Study of Surface Roughness Using a Microdensitometer Analysis of Electron Micrographs of Surface Replicas: I. Surface Profiles, II. Autocovariance Functions,” J. Opt. Soc. Am. 71, 1124, 1230 (1981).
[CrossRef]

Lockie, R. T.

V. L. Williams, R. T. Lockie, “Optical Contamination Assessment by Bidirectional Reflectance Distribution Function (BRDF) Measurement,” Opt. Eng. 18, 152 (1979).
[CrossRef]

Möllenstedt, G.

H. Lichte, G. Möllenstedt, “Measurement of the Roughness of Supersmooth Surfaces Using an Electron Mirror Interference Microscope,” J. Phys. E 12, 941 (1979).
[CrossRef]

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Natl. Bur. Stand. U.S. Monogr. 160, 5 (1977).

Nomarski, G. M.

G. M. Nomarski, “Differential Microinterferometer With Polarized Waves,” J. Phys. Radium 16, 9 (1955).

G. M. Nomarski, A. R. Weill, “Application a la Metallographie des Methodes Interferentielles a Deux Ondes Polarisees,” Rev. Metall. 52, 121 (1955).

Orazio, F. D.

R. M. Silva, F. D. Orazio, W. K. Stowell, “Scatter Evaluation of Supersmooth Surfaces,” Proc. Soc. Photo-Opt. Instrum. Eng. 384, 2 (1983).

F. D. Orazio, R. M. Silva, W. K. Stowell, “Instrumentation of a Variable Angle Scatterometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 384, 123 (1983).

W. K. Stowell, R. M. Silva, F. D. Orazio, “Damage Susceptibility of Ring Laser Gyro Class Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 384, 73 (1983).

Palmari, J. P.

M. Rasigni, G. Rasigni, J. P. Palmari, A. Llebaria, “Study of Surface Roughness Using a Microdensitometer Analysis of Electron Micrographs of Surface Replicas: I. Surface Profiles, II. Autocovariance Functions,” J. Opt. Soc. Am. 71, 1124, 1230 (1981).
[CrossRef]

Peklenik, J.

J. Peklenik, “New Developments in Surface Characterization and Measurements by Means of Random Process Analysis,” Proc. IME 182, 108 (1967–1968).

Permien, V.

D. Heitmann, V. Permien, “Determination of Surface Roughness from Light Scattering Measurements,” Opt. Commun. 23, 131 (1977).
[CrossRef]

Porteus, J. O.

Probert, S. D.

B. Smith, M. J. Edmonds, S. D. Probert, “Use of a Profilometer for Surface Mapping,” Precision Eng. 3, 87 (1981).
[CrossRef]

Pulker, H. K.

K. H. Guenther, H. L. Gruber, H. K. Pulker, “Morphology and Light Scattering of Dielectric Multilayer Systems,” Thin Solid Films 34, 363 (1976).
[CrossRef]

Rahn, J. P.

Rasigni, G.

M. Rasigni, G. Rasigni, J. P. Palmari, A. Llebaria, “Study of Surface Roughness Using a Microdensitometer Analysis of Electron Micrographs of Surface Replicas: I. Surface Profiles, II. Autocovariance Functions,” J. Opt. Soc. Am. 71, 1124, 1230 (1981).
[CrossRef]

Rasigni, M.

M. Rasigni, G. Rasigni, J. P. Palmari, A. Llebaria, “Study of Surface Roughness Using a Microdensitometer Analysis of Electron Micrographs of Surface Replicas: I. Surface Profiles, II. Autocovariance Functions,” J. Opt. Soc. Am. 71, 1124, 1230 (1981).
[CrossRef]

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Natl. Bur. Stand. U.S. Monogr. 160, 5 (1977).

Roche, P.

Scott, M. L.

M. L. Scott, J. M. Elson, “Multilayer Light Scattering and the Laser Gyro,” Appl. Phys. Lett. 32, 158 (1978).
[CrossRef]

Silva, R. M.

F. D. Orazio, R. M. Silva, W. K. Stowell, “Instrumentation of a Variable Angle Scatterometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 384, 123 (1983).

R. M. Silva, F. D. Orazio, W. K. Stowell, “Scatter Evaluation of Supersmooth Surfaces,” Proc. Soc. Photo-Opt. Instrum. Eng. 384, 2 (1983).

W. K. Stowell, R. M. Silva, F. D. Orazio, “Damage Susceptibility of Ring Laser Gyro Class Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 384, 73 (1983).

Smith, B.

B. Smith, M. J. Edmonds, S. D. Probert, “Use of a Profilometer for Surface Mapping,” Precision Eng. 3, 87 (1981).
[CrossRef]

Sommargren, G. E.

Spedding, T. A.

T. G. King, T. A. Spedding, “Towards a Rational Surface Profile Characterization System,” Precision Eng. 5, 153 (1983).
[CrossRef]

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves From Rough Surfaces (Pergamon, New York, 1963).

Stover, J. C.

Stowell, W. K.

W. K. Stowell, R. M. Silva, F. D. Orazio, “Damage Susceptibility of Ring Laser Gyro Class Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 384, 73 (1983).

F. D. Orazio, R. M. Silva, W. K. Stowell, “Instrumentation of a Variable Angle Scatterometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 384, 123 (1983).

R. M. Silva, F. D. Orazio, W. K. Stowell, “Scatter Evaluation of Supersmooth Surfaces,” Proc. Soc. Photo-Opt. Instrum. Eng. 384, 2 (1983).

Teague, E. C.

T. V. Vorburger, E. C. Teague, “Optical Techniques for On-Line Measurement of Surface Topography,” Precision Eng. 3, 61 (1981).
[CrossRef]

Thomas, N. L.

N. L. Thomas, “Low-Scatter, Low-Loss Mirrors for Laser Gyros,” Proc. Soc. Photo-Opt. Instrum. Eng. 157, 41 (1978).

Thomas, R. E.

R. E. Thomas, “Characterization of Surface Roughness,” Precision Eng. 3, 97 (1981).
[CrossRef]

Vorburger, T. V.

T. V. Vorburger, E. C. Teague, “Optical Techniques for On-Line Measurement of Surface Topography,” Precision Eng. 3, 61 (1981).
[CrossRef]

Wagen dristel, A.

K. H. Guenther, H. Bangert, A. Kaminitschek, A. Wagen dristel, “Ultra-Microhardness Testing of Optical Coatings,” in Technical Digest, Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1984), paper WA-A5.

Weill, A. R.

G. M. Nomarski, A. R. Weill, “Application a la Metallographie des Methodes Interferentielles a Deux Ondes Polarisees,” Rev. Metall. 52, 121 (1955).

Weisskopf, M. C.

M. V. Zombeck, C. C. Wyman, M. C. Weisskopf, “High Resolution X-Ray Astrophysics Facility (AXAF),” Opt. Eng. 21, 63 (1982).
[CrossRef]

Whitehouse, D. J.

D. J. Whitehouse, “Stylus Techniques,” in Characterization of Solid Surfaces, P. E. Kane, G. P. Larrabee, Eds. (Plenum, New York, 1974), p. 49.
[CrossRef]

Williams, V. L.

V. L. Williams, R. T. Lockie, “Optical Contamination Assessment by Bidirectional Reflectance Distribution Function (BRDF) Measurement,” Opt. Eng. 18, 152 (1979).
[CrossRef]

Wyman, C. C.

M. V. Zombeck, C. C. Wyman, M. C. Weisskopf, “High Resolution X-Ray Astrophysics Facility (AXAF),” Opt. Eng. 21, 63 (1982).
[CrossRef]

Zavada, J. M.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship Between Surface Scattering and Microtopographic Features,” Opt. Eng. 18, 125 (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 (1977).
[CrossRef]

Zavislan, J. M.

J. M. Eastman, J. M. Zavislan, “A New Optical Surface Microprofiling Instrument,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 56 (1983).

Zombeck, M. V.

M. V. Zombeck, C. C. Wyman, M. C. Weisskopf, “High Resolution X-Ray Astrophysics Facility (AXAF),” Opt. Eng. 21, 63 (1982).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. Lett. (1)

M. L. Scott, J. M. Elson, “Multilayer Light Scattering and the Laser Gyro,” Appl. Phys. Lett. 32, 158 (1978).
[CrossRef]

J. Opt. Soc. Am. (5)

J. Phys. E (1)

H. Lichte, G. Möllenstedt, “Measurement of the Roughness of Supersmooth Surfaces Using an Electron Mirror Interference Microscope,” J. Phys. E 12, 941 (1979).
[CrossRef]

J. Phys. E. (1)

R. P. Edwin, “Light Scattering as a Technique for Measuring the Roughness of Optical Surfaces,” J. Phys. E. 6, 55 (1973).
[CrossRef]

J. Phys. Radium (1)

G. M. Nomarski, “Differential Microinterferometer With Polarized Waves,” J. Phys. Radium 16, 9 (1955).

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

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Natl. Bur. Stand. U.S. Monogr. 160, 5 (1977).

Opt. Commun. (1)

D. Heitmann, V. Permien, “Determination of Surface Roughness from Light Scattering Measurements,” Opt. Commun. 23, 131 (1977).
[CrossRef]

Opt. Eng. (7)

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship Between Surface Scattering and Microtopographic Features,” Opt. Eng. 18, 125 (1979).
[CrossRef]

M. V. Zombeck, C. C. Wyman, M. C. Weisskopf, “High Resolution X-Ray Astrophysics Facility (AXAF),” Opt. Eng. 21, 63 (1982).
[CrossRef]

V. L. Williams, R. T. Lockie, “Optical Contamination Assessment by Bidirectional Reflectance Distribution Function (BRDF) Measurement,” Opt. Eng. 18, 152 (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 (1977).
[CrossRef]

H. E. Bennett, “Scattering Characteristics of Optical Materials,” Opt. Eng. 17, 480 (1978).
[CrossRef]

P. C. Archibald, H. E. Bennett, “Scattering From Infrared Missile Domes,” Opt. Eng. 17, 647 (1978).
[CrossRef]

A. L. Gauler, “Comparison of Two Common Methods of Surface Topography Evaluation,” Opt. Eng. 21, 991 (1982).
[CrossRef]

Opt. Quantum Electron. (2)

P. J. Chandley, “Surface Roughness Measurements From Coherent Light Scattering,” Opt. Quantum Electron. 8, 323 (1976).
[CrossRef]

P. J. Chandley, “Determination of the Autocorrelation Function of Height on a Rough Surface From Coherent Light Scattering,” Opt. Quantum Electron. 8, 329 (1976).
[CrossRef]

Precision Eng. (4)

T. V. Vorburger, E. C. Teague, “Optical Techniques for On-Line Measurement of Surface Topography,” Precision Eng. 3, 61 (1981).
[CrossRef]

R. E. Thomas, “Characterization of Surface Roughness,” Precision Eng. 3, 97 (1981).
[CrossRef]

T. G. King, T. A. Spedding, “Towards a Rational Surface Profile Characterization System,” Precision Eng. 5, 153 (1983).
[CrossRef]

B. Smith, M. J. Edmonds, S. D. Probert, “Use of a Profilometer for Surface Mapping,” Precision Eng. 3, 87 (1981).
[CrossRef]

Proc. IME (1)

J. Peklenik, “New Developments in Surface Characterization and Measurements by Means of Random Process Analysis,” Proc. IME 182, 108 (1967–1968).

Proc. Soc. Photo-Opt. Instrum. Eng. (8)

N. L. Thomas, “Low-Scatter, Low-Loss Mirrors for Laser Gyros,” Proc. Soc. Photo-Opt. Instrum. Eng. 157, 41 (1978).

E. L. Church, “Direct Comparison of Mechanical and Optical Measurements of the Finish of Precision-Machined Surfaces,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 105 (1983).

J. M. Eastman, J. M. Zavislan, “A New Optical Surface Microprofiling Instrument,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 56 (1983).

J. M. Elson, “Angle-Resolved Light Scattering from Composite Optical Surfaces,” Proc. Soc. Photo-Opt. Instrum. Eng. 240, 296 (1980).

J. A. Detrio, “Light Scattering Surface Roughness Characterization,” Proc. Soc. Photo-Opt. Instrum. Eng. 276, 136 (1981).

W. K. Stowell, R. M. Silva, F. D. Orazio, “Damage Susceptibility of Ring Laser Gyro Class Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 384, 73 (1983).

F. D. Orazio, R. M. Silva, W. K. Stowell, “Instrumentation of a Variable Angle Scatterometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 384, 123 (1983).

R. M. Silva, F. D. Orazio, W. K. Stowell, “Scatter Evaluation of Supersmooth Surfaces,” Proc. Soc. Photo-Opt. Instrum. Eng. 384, 2 (1983).

Rev. Metall. (1)

G. M. Nomarski, A. R. Weill, “Application a la Metallographie des Methodes Interferentielles a Deux Ondes Polarisees,” Rev. Metall. 52, 121 (1955).

Thin Solid Films (1)

K. H. Guenther, H. L. Gruber, H. K. Pulker, “Morphology and Light Scattering of Dielectric Multilayer Systems,” Thin Solid Films 34, 363 (1976).
[CrossRef]

Other (8)

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves From Rough Surfaces (Pergamon, New York, 1963).

J. M. Elson, H. E. Bennett, J. M. Bennett, “Scattering from Optical Surfaces,” in Applied Optics and Optical Engineering, Vol. 7, R. R. Shannon, J. Wyant, Eds. (Academic, New York, 1979), pp. 191–244.
[CrossRef]

K. H. Günther, “Morphologie und Lichtstreuung dielektrischer Wechselschichtsysteme,” Dissertation, U. Innsbruck (1974).

H. E. Bennett, J. M. Bennett, “Precision Measurements in Thin Film Optics,” in Physics of Thin Films, Vol. 4, G. Hass, R. E. Thun, Eds. (Academic, New York, 1967), pp. 1–96.

J. M. Elson, private communication, 1984.

D. J. Whitehouse, “Stylus Techniques,” in Characterization of Solid Surfaces, P. E. Kane, G. P. Larrabee, Eds. (Plenum, New York, 1974), p. 49.
[CrossRef]

K. H. Guenther, H. Bangert, A. Kaminitschek, A. Wagen dristel, “Ultra-Microhardness Testing of Optical Coatings,” in Technical Digest, Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1984), paper WA-A5.

F. Aronowitz, “The Laser Gyro,” in Laser Applications, Vol. 1, M. Ross, Ed. (Academic, New York, 1971), p. 131.

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Figures (13)

Fig. 1
Fig. 1

(a) One-dimensional profile and (b) Gaussian height distribution function for a randomly rough surface.

Fig. 2
Fig. 2

Calculated exponential and Gaussian autocovariance functions.

Fig. 3
Fig. 3

Nomarski micrographs of the roughness standards R1 to R5.

Fig. 4
Fig. 4

Talystep surface profiles of (a) the uncoated surface and (b) the MLD-coated surface of roughness standard R5 polished to laser gyro quality.

Fig. 5
Fig. 5

(a) Slope and height distribution functions and (b) initial portion of the autocovariance function for roughness standard R5. The data are obtained from a profile length of 1 mm, 16,000 data points. The Gaussian curves have the same areas under the curves as the measured histograms, and the same values for the rms slope and rms roughness.

Fig. 6
Fig. 6

(a) OHP profile of the uncoated surface of BK-7 sample 10; (b)–(e), statistical functions derived from the profile data in (a).

Fig. 7
Fig. 7

Schematic diagram of the Balzers TIS instrument.

Fig. 8
Fig. 8

Maps obtained with the variable angle scatterometer for the MLD-coated surface of Zerodur sample 4. Courtesy of W. K. Stowell, Air Force Wright Aeronautical Laboratories, and R. M. Silva and F. D. Orazio, Jr., VTI, Inc., Dayton, Ohio.

Fig. 9
Fig. 9

Transmission electron micrographs of platinum/carbon replicas made from uncoated polished surfaces of (a) Zerodur and (b) BK-7 glass, not fully polished. Arrows indicate the direction of the platinum/carbon shadowing.

Fig. 10
Fig. 10

Transmission electron micrographs of platinum/carbon replicas made from (a) a MLD-coated Zerodur surface and (b) a bare Zerodur surface.

Fig. 11
Fig. 11

Talystep surface profiles of (a) the uncoated surface and (b) the MLD-coated surface of roughness standard R1.

Fig. 12
Fig. 12

Comparison of Balzers and NWC TIS measurements taken on the same roughness standards R1 to R5 for MLD-coated surfaces and aluminum on MLD coatings (data from Table III). The line is for equal roughnesses from each laboratory.

Fig. 13
Fig. 13

Summary of all measurements on roughness standards R1 to R5 plotted vs averages of Balzers and NWC TIS measurements for each sample (data from Table III).

Tables (3)

Tables Icon

Table I Surface Characterization Methods used for Roughness Assessment of Smooth Optical Surfaces and Coatings

Tables Icon

Table II Comparison of rms Roughnesses as Measured by Total Integrated Scattering, Optical Heterodyne Profilometer, and Electron Mirror Interference Microscope; All Values are in Nanometers

Tables Icon

Table III Summary of rms Roughness Measurements. All Values are in Nanometers

Equations (8)

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

δ = [ ( 1 / n ) i = 1 n z 2 ( i ) ] 1 / 2 .
w ( z ) = ( 1 / δ 2 π ) exp [ - ( z / δ 2 ) 2 ] .
G ( τ ) = [ 1 / ( n - 1 ) ] i = 1 n - τ z ( i ) z ( i + τ ) ,
G ( 0 ) = δ 2 .
δ λ .
TIS = 1 - exp [ - ( 4 π δ cos θ 0 / λ ) 2 ] ,
δ = ( λ / 4 π cos θ 0 ) TIS .
TIS = I s / I 0 R 0 .

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