Abstract

A brief review of techniques for measuring surface roughness and optical figure is given. One of the most promising of these techniques for measuring the roughness of optical surfaces is interferometry employing fringes of equal chromatic order (feco). A feco scanning interferometer is described, which has been used to determine statistics of polished surfaces having roughnesses under 100 Å rms. The scanning interferometer resolves square surface elements 2 μm on a side and statistically characterizes the surface in terms of these elements. Height- and slope-distribution functions, rms roughness, rms slope, and modified autocovariance length distributions have been measured for selected optical surfaces. Nearly all surfaces had Gaussian distributions of heights and slopes, but none had Gaussian distributions of autocovariance lengths. Surfaces such as electropolished copper, electroless nickel, and single-point diamond-machined copper were found to have smaller rms slopes than other surfaces of comparable roughness and scattered less than predicted by simple scalar scattering theory.1,2 On the other hand, heavily scratched surfaces such as polished potassium chloride had larger slopes and produced more scattering than expected from simple theory.

© 1976 Optical Society of America

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References

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  1. H. E. Bennett, J. O. Porteus, J. Opt. Soc. Am. 51, 123 (1961); H. E. Bennett, J. Opt. Soc. Am. 53, 1389 (1963); J. O. Porteus, J. Opt. Soc. Am. 53, 1394 (1963).
    [CrossRef]
  2. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves From Rough Surfaces (Macmillan, New York, 1963).
  3. H. E. Bennett, J. M. Bennett in Physics of Thin Films, G. Hass, R. E. Thun, Eds. (Academic, New York, 1967), Vol. 4, pp. 1–96.
  4. H. E. Bennett, J. L. Stanford, “Structure-Related Optical Characteristics of Thin Metallic Films in the Visible and Ultraviolet,” presented at Workshop Seminar on Standardization in Spectrophotometry and Luminescence Measurements, Gaithersburg, Md., 19–20 Nov. 1975;Proceedings to be published in J. Res. Natl. Bur. Stand.
  5. H. E. Bennett, J. M. Bennett, E. J. Ashley, R. J. Motyka, Phys. Rev. 165, 755 (1968).
    [CrossRef]
  6. R. M. Anderson, G. W. Neudeck, J. Vac. Sci. Technol. 8, 454 (1971).
    [CrossRef]
  7. J. A. Greenwood, Brit. J. Appl. Phys. 17, 1621 (1966).
    [CrossRef]
  8. J. A. Greenwood, J. B. P. Williamson, Proc. R. Soc. (London) A295, 300 (1966).
  9. D. J. Whitehouse, J. F. Archard, Proc. R. Soc. (London) A316, 97 (1970).
  10. T. R. Thomas, S. D. Probert, J. Phys. D 3, 277 (1970).
    [CrossRef]
  11. R. D. Young, E. C. Teague, in Properties of Electrodeposits: Their Measurement and Significance, R. Sard, H. Leidheiser, F. Ogburn, Eds., Proceedings of Symposium of Corrosion, Electrodeposition, and Electronics Division at 146th (Oct. 1974) Mtg. of Electrochemical Society (Electrochemical Society, Princeton, N.J., 1975), pp. 22–49.
  12. D. W. Freyberg, Res. Dev. 25, 41 (May1974).
  13. V. Radhakrishnan, Wear 23, 339 (1973).
    [CrossRef]
  14. A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957).
  15. T. T. Saito, Appl. Opt. 14, 1773 (1975); T. T. Saito, D. Milam, P. Baker, G. Murphy, in Laser Induced Damage in Optical Materials: 1975, A. J. Glass, A. H. Guenther, Eds. (NBS Special Publication 435, U.S. Department of Commerce, Washington, D.C., April1976), pp. 29–40.
    [CrossRef] [PubMed]
  16. M. J. Soileau, V. Wang, Appl. Opt. 13, 1286 (1974); H. E. Bennett, M. J. Soileau, P. C. Archibald, in Laser Induced Damage in Optical Materials: 1975, A. J. Glass, A. H. Guenther, Eds. (NBS Special Publication 435, U.S. Department of Commerce, Washington, D.C., April1976), pp. 49–56.
    [CrossRef] [PubMed]
  17. J. M. Bennett, J. M. Elson in High Energy Laser Mirrors and Windows (Semi-Annual Report Nos. 7 and 8, ARPA Order 2175, Naval Weapons Center, China Lake, Calif., July1976), pp. 149–165 1976).
  18. J. C. Stover, Appl. Opt. 14, 1796 (1975).
    [CrossRef] [PubMed]
  19. Symposium on Techniques in Surface Interferometry, J. Opt. Soc. Am. 64, 1361 (1974).
  20. S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Clarendon Press, Oxford, 1948).
  21. S. Tolansky, Surface Microtopography (John Wiley, Interscience Division, New York, 1960).
  22. I. J. Hodgkinson, J. Phys. E. 3, 300 (1970).
    [CrossRef]
  23. J. M. Eastman, P. W. Baumeister, J. Opt. Soc. Am. 64, 1369A (1974).
  24. C. J. Pellerin, J. Christensen, R. C. Jerner, J. H. Peavey, J. Vac. Sci. Technol. 12, 496 (1975).
    [CrossRef]
  25. C. F. Bruce, F. P. Sharples, Appl. Opt. 14, 3082 (1975).
    [CrossRef] [PubMed]
  26. The lateral resolution of 2 μm sets a short wavelength limit for scattering calculated from the surface statistics.
  27. W. F. Koehler, J. Opt. Soc. Am. 47, 862 (1957).
    [CrossRef]
  28. See, for example, the window function D1(ρ) given in Ref. 29 and also in M. S. Bartlett, Biometrika 37, 1 (1950), Eq. (18).
  29. R. B. Blackman, J. W. Tukey, Bell Syst. Tech. J. 37, 185, 485 (1958).
  30. J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley-Interscience, New York, 1971), p. 311.
  31. J. M. Elson, R. H. Ritchie, Phys. Status Solidi B 62, 461 (1974).
    [CrossRef]
  32. W. F. Koehler, A. Eberstein, J. Opt. Soc. Am. 43, 747 (1953).
    [CrossRef]
  33. J. M. Bennett in High Energy Laser Mirrors and Windows (Semi-Annual Report No. 4, ARPA Order 2175, Naval Weapons Center, China Lake, Calif., Mar.1974), pp. 9–19.
  34. J. M. Bennett, J. M. Elson in High Energy Laser Mirrors and Windows (Semi-Annual Report No. 5, ARPA Order 2175, Naval Weapons Center, China Lake, Calif., Sept.1974), pp. 4–14.
  35. See, for example, V. Celli, A. Marvin, F. Toigo, Phys. Rev. B 11, 1779 (1975); A. A. Maradudin, D. L. Mills, Phys. Rev. B 11, 1392 (1975); J. M. Elson, Phys. Rev. B. 12, 2541 (1975); J. M. Elson in High Energy Laser Mirrors and Windows (Semi-Annual Report No. 6, ARPA Order 2175, Naval Weapons Center, China Lake, Calif., May1975), pp. 125–138.
    [CrossRef]
  36. E. C. Teague, “Evaluation, Revision and Application of the NBS Stylus/Computer System for the Measurement of Surface Roughness,” NBS Technical Note 902 (U.S. Department of Commerce, Washington, D.C., April1976).

1975 (5)

T. T. Saito, Appl. Opt. 14, 1773 (1975); T. T. Saito, D. Milam, P. Baker, G. Murphy, in Laser Induced Damage in Optical Materials: 1975, A. J. Glass, A. H. Guenther, Eds. (NBS Special Publication 435, U.S. Department of Commerce, Washington, D.C., April1976), pp. 29–40.
[CrossRef] [PubMed]

J. C. Stover, Appl. Opt. 14, 1796 (1975).
[CrossRef] [PubMed]

C. J. Pellerin, J. Christensen, R. C. Jerner, J. H. Peavey, J. Vac. Sci. Technol. 12, 496 (1975).
[CrossRef]

C. F. Bruce, F. P. Sharples, Appl. Opt. 14, 3082 (1975).
[CrossRef] [PubMed]

See, for example, V. Celli, A. Marvin, F. Toigo, Phys. Rev. B 11, 1779 (1975); A. A. Maradudin, D. L. Mills, Phys. Rev. B 11, 1392 (1975); J. M. Elson, Phys. Rev. B. 12, 2541 (1975); J. M. Elson in High Energy Laser Mirrors and Windows (Semi-Annual Report No. 6, ARPA Order 2175, Naval Weapons Center, China Lake, Calif., May1975), pp. 125–138.
[CrossRef]

1974 (5)

J. M. Eastman, P. W. Baumeister, J. Opt. Soc. Am. 64, 1369A (1974).

J. M. Elson, R. H. Ritchie, Phys. Status Solidi B 62, 461 (1974).
[CrossRef]

Symposium on Techniques in Surface Interferometry, J. Opt. Soc. Am. 64, 1361 (1974).

M. J. Soileau, V. Wang, Appl. Opt. 13, 1286 (1974); H. E. Bennett, M. J. Soileau, P. C. Archibald, in Laser Induced Damage in Optical Materials: 1975, A. J. Glass, A. H. Guenther, Eds. (NBS Special Publication 435, U.S. Department of Commerce, Washington, D.C., April1976), pp. 49–56.
[CrossRef] [PubMed]

D. W. Freyberg, Res. Dev. 25, 41 (May1974).

1973 (1)

V. Radhakrishnan, Wear 23, 339 (1973).
[CrossRef]

1971 (1)

R. M. Anderson, G. W. Neudeck, J. Vac. Sci. Technol. 8, 454 (1971).
[CrossRef]

1970 (3)

D. J. Whitehouse, J. F. Archard, Proc. R. Soc. (London) A316, 97 (1970).

T. R. Thomas, S. D. Probert, J. Phys. D 3, 277 (1970).
[CrossRef]

I. J. Hodgkinson, J. Phys. E. 3, 300 (1970).
[CrossRef]

1968 (1)

H. E. Bennett, J. M. Bennett, E. J. Ashley, R. J. Motyka, Phys. Rev. 165, 755 (1968).
[CrossRef]

1966 (2)

J. A. Greenwood, Brit. J. Appl. Phys. 17, 1621 (1966).
[CrossRef]

J. A. Greenwood, J. B. P. Williamson, Proc. R. Soc. (London) A295, 300 (1966).

1961 (1)

1958 (1)

R. B. Blackman, J. W. Tukey, Bell Syst. Tech. J. 37, 185, 485 (1958).

1957 (1)

1953 (1)

1950 (1)

See, for example, the window function D1(ρ) given in Ref. 29 and also in M. S. Bartlett, Biometrika 37, 1 (1950), Eq. (18).

Anderson, R. M.

R. M. Anderson, G. W. Neudeck, J. Vac. Sci. Technol. 8, 454 (1971).
[CrossRef]

Archard, J. F.

D. J. Whitehouse, J. F. Archard, Proc. R. Soc. (London) A316, 97 (1970).

Ashley, E. J.

H. E. Bennett, J. M. Bennett, E. J. Ashley, R. J. Motyka, Phys. Rev. 165, 755 (1968).
[CrossRef]

Bartlett, M. S.

See, for example, the window function D1(ρ) given in Ref. 29 and also in M. S. Bartlett, Biometrika 37, 1 (1950), Eq. (18).

Baumeister, P. W.

J. M. Eastman, P. W. Baumeister, J. Opt. Soc. Am. 64, 1369A (1974).

Beckmann, P.

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

Bendat, J. S.

J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley-Interscience, New York, 1971), p. 311.

Bennett, H. E.

H. E. Bennett, J. M. Bennett, E. J. Ashley, R. J. Motyka, Phys. Rev. 165, 755 (1968).
[CrossRef]

H. E. Bennett, J. O. Porteus, J. Opt. Soc. Am. 51, 123 (1961); H. E. Bennett, J. Opt. Soc. Am. 53, 1389 (1963); J. O. Porteus, J. Opt. Soc. Am. 53, 1394 (1963).
[CrossRef]

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

H. E. Bennett, J. L. Stanford, “Structure-Related Optical Characteristics of Thin Metallic Films in the Visible and Ultraviolet,” presented at Workshop Seminar on Standardization in Spectrophotometry and Luminescence Measurements, Gaithersburg, Md., 19–20 Nov. 1975;Proceedings to be published in J. Res. Natl. Bur. Stand.

Bennett, J. M.

H. E. Bennett, J. M. Bennett, E. J. Ashley, R. J. Motyka, Phys. Rev. 165, 755 (1968).
[CrossRef]

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

J. M. Bennett, J. M. Elson in High Energy Laser Mirrors and Windows (Semi-Annual Report Nos. 7 and 8, ARPA Order 2175, Naval Weapons Center, China Lake, Calif., July1976), pp. 149–165 1976).

J. M. Bennett in High Energy Laser Mirrors and Windows (Semi-Annual Report No. 4, ARPA Order 2175, Naval Weapons Center, China Lake, Calif., Mar.1974), pp. 9–19.

J. M. Bennett, J. M. Elson in High Energy Laser Mirrors and Windows (Semi-Annual Report No. 5, ARPA Order 2175, Naval Weapons Center, China Lake, Calif., Sept.1974), pp. 4–14.

Blackman, R. B.

R. B. Blackman, J. W. Tukey, Bell Syst. Tech. J. 37, 185, 485 (1958).

Bruce, C. F.

Celli, V.

See, for example, V. Celli, A. Marvin, F. Toigo, Phys. Rev. B 11, 1779 (1975); A. A. Maradudin, D. L. Mills, Phys. Rev. B 11, 1392 (1975); J. M. Elson, Phys. Rev. B. 12, 2541 (1975); J. M. Elson in High Energy Laser Mirrors and Windows (Semi-Annual Report No. 6, ARPA Order 2175, Naval Weapons Center, China Lake, Calif., May1975), pp. 125–138.
[CrossRef]

Christensen, J.

C. J. Pellerin, J. Christensen, R. C. Jerner, J. H. Peavey, J. Vac. Sci. Technol. 12, 496 (1975).
[CrossRef]

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957).

Eastman, J. M.

J. M. Eastman, P. W. Baumeister, J. Opt. Soc. Am. 64, 1369A (1974).

Eberstein, A.

Elson, J. M.

J. M. Elson, R. H. Ritchie, Phys. Status Solidi B 62, 461 (1974).
[CrossRef]

J. M. Bennett, J. M. Elson in High Energy Laser Mirrors and Windows (Semi-Annual Report No. 5, ARPA Order 2175, Naval Weapons Center, China Lake, Calif., Sept.1974), pp. 4–14.

J. M. Bennett, J. M. Elson in High Energy Laser Mirrors and Windows (Semi-Annual Report Nos. 7 and 8, ARPA Order 2175, Naval Weapons Center, China Lake, Calif., July1976), pp. 149–165 1976).

Freyberg, D. W.

D. W. Freyberg, Res. Dev. 25, 41 (May1974).

Greenwood, J. A.

J. A. Greenwood, Brit. J. Appl. Phys. 17, 1621 (1966).
[CrossRef]

J. A. Greenwood, J. B. P. Williamson, Proc. R. Soc. (London) A295, 300 (1966).

Hodgkinson, I. J.

I. J. Hodgkinson, J. Phys. E. 3, 300 (1970).
[CrossRef]

Jerner, R. C.

C. J. Pellerin, J. Christensen, R. C. Jerner, J. H. Peavey, J. Vac. Sci. Technol. 12, 496 (1975).
[CrossRef]

Koehler, W. F.

Marvin, A.

See, for example, V. Celli, A. Marvin, F. Toigo, Phys. Rev. B 11, 1779 (1975); A. A. Maradudin, D. L. Mills, Phys. Rev. B 11, 1392 (1975); J. M. Elson, Phys. Rev. B. 12, 2541 (1975); J. M. Elson in High Energy Laser Mirrors and Windows (Semi-Annual Report No. 6, ARPA Order 2175, Naval Weapons Center, China Lake, Calif., May1975), pp. 125–138.
[CrossRef]

Motyka, R. J.

H. E. Bennett, J. M. Bennett, E. J. Ashley, R. J. Motyka, Phys. Rev. 165, 755 (1968).
[CrossRef]

Neudeck, G. W.

R. M. Anderson, G. W. Neudeck, J. Vac. Sci. Technol. 8, 454 (1971).
[CrossRef]

Peavey, J. H.

C. J. Pellerin, J. Christensen, R. C. Jerner, J. H. Peavey, J. Vac. Sci. Technol. 12, 496 (1975).
[CrossRef]

Pellerin, C. J.

C. J. Pellerin, J. Christensen, R. C. Jerner, J. H. Peavey, J. Vac. Sci. Technol. 12, 496 (1975).
[CrossRef]

Piersol, A. G.

J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley-Interscience, New York, 1971), p. 311.

Porteus, J. O.

Probert, S. D.

T. R. Thomas, S. D. Probert, J. Phys. D 3, 277 (1970).
[CrossRef]

Radhakrishnan, V.

V. Radhakrishnan, Wear 23, 339 (1973).
[CrossRef]

Ritchie, R. H.

J. M. Elson, R. H. Ritchie, Phys. Status Solidi B 62, 461 (1974).
[CrossRef]

Saito, T. T.

Sharples, F. P.

Soileau, M. J.

Spizzichino, A.

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

Stanford, J. L.

H. E. Bennett, J. L. Stanford, “Structure-Related Optical Characteristics of Thin Metallic Films in the Visible and Ultraviolet,” presented at Workshop Seminar on Standardization in Spectrophotometry and Luminescence Measurements, Gaithersburg, Md., 19–20 Nov. 1975;Proceedings to be published in J. Res. Natl. Bur. Stand.

Stover, J. C.

Teague, E. C.

R. D. Young, E. C. Teague, in Properties of Electrodeposits: Their Measurement and Significance, R. Sard, H. Leidheiser, F. Ogburn, Eds., Proceedings of Symposium of Corrosion, Electrodeposition, and Electronics Division at 146th (Oct. 1974) Mtg. of Electrochemical Society (Electrochemical Society, Princeton, N.J., 1975), pp. 22–49.

E. C. Teague, “Evaluation, Revision and Application of the NBS Stylus/Computer System for the Measurement of Surface Roughness,” NBS Technical Note 902 (U.S. Department of Commerce, Washington, D.C., April1976).

Thomas, T. R.

T. R. Thomas, S. D. Probert, J. Phys. D 3, 277 (1970).
[CrossRef]

Toigo, F.

See, for example, V. Celli, A. Marvin, F. Toigo, Phys. Rev. B 11, 1779 (1975); A. A. Maradudin, D. L. Mills, Phys. Rev. B 11, 1392 (1975); J. M. Elson, Phys. Rev. B. 12, 2541 (1975); J. M. Elson in High Energy Laser Mirrors and Windows (Semi-Annual Report No. 6, ARPA Order 2175, Naval Weapons Center, China Lake, Calif., May1975), pp. 125–138.
[CrossRef]

Tolansky, S.

S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Clarendon Press, Oxford, 1948).

S. Tolansky, Surface Microtopography (John Wiley, Interscience Division, New York, 1960).

Tukey, J. W.

R. B. Blackman, J. W. Tukey, Bell Syst. Tech. J. 37, 185, 485 (1958).

Wang, V.

Whitehouse, D. J.

D. J. Whitehouse, J. F. Archard, Proc. R. Soc. (London) A316, 97 (1970).

Williamson, J. B. P.

J. A. Greenwood, J. B. P. Williamson, Proc. R. Soc. (London) A295, 300 (1966).

Young, R. D.

R. D. Young, E. C. Teague, in Properties of Electrodeposits: Their Measurement and Significance, R. Sard, H. Leidheiser, F. Ogburn, Eds., Proceedings of Symposium of Corrosion, Electrodeposition, and Electronics Division at 146th (Oct. 1974) Mtg. of Electrochemical Society (Electrochemical Society, Princeton, N.J., 1975), pp. 22–49.

Appl. Opt. (4)

Bell Syst. Tech. J. (1)

R. B. Blackman, J. W. Tukey, Bell Syst. Tech. J. 37, 185, 485 (1958).

Biometrika (1)

See, for example, the window function D1(ρ) given in Ref. 29 and also in M. S. Bartlett, Biometrika 37, 1 (1950), Eq. (18).

Brit. J. Appl. Phys. (1)

J. A. Greenwood, Brit. J. Appl. Phys. 17, 1621 (1966).
[CrossRef]

J. Opt. Soc. Am. (5)

J. Phys. D (1)

T. R. Thomas, S. D. Probert, J. Phys. D 3, 277 (1970).
[CrossRef]

J. Phys. E. (1)

I. J. Hodgkinson, J. Phys. E. 3, 300 (1970).
[CrossRef]

J. Vac. Sci. Technol. (2)

C. J. Pellerin, J. Christensen, R. C. Jerner, J. H. Peavey, J. Vac. Sci. Technol. 12, 496 (1975).
[CrossRef]

R. M. Anderson, G. W. Neudeck, J. Vac. Sci. Technol. 8, 454 (1971).
[CrossRef]

Phys. Rev. (1)

H. E. Bennett, J. M. Bennett, E. J. Ashley, R. J. Motyka, Phys. Rev. 165, 755 (1968).
[CrossRef]

Phys. Rev. B (1)

See, for example, V. Celli, A. Marvin, F. Toigo, Phys. Rev. B 11, 1779 (1975); A. A. Maradudin, D. L. Mills, Phys. Rev. B 11, 1392 (1975); J. M. Elson, Phys. Rev. B. 12, 2541 (1975); J. M. Elson in High Energy Laser Mirrors and Windows (Semi-Annual Report No. 6, ARPA Order 2175, Naval Weapons Center, China Lake, Calif., May1975), pp. 125–138.
[CrossRef]

Phys. Status Solidi B (1)

J. M. Elson, R. H. Ritchie, Phys. Status Solidi B 62, 461 (1974).
[CrossRef]

Proc. R. Soc. (London) (2)

J. A. Greenwood, J. B. P. Williamson, Proc. R. Soc. (London) A295, 300 (1966).

D. J. Whitehouse, J. F. Archard, Proc. R. Soc. (London) A316, 97 (1970).

Res. Dev. (1)

D. W. Freyberg, Res. Dev. 25, 41 (May1974).

Wear (1)

V. Radhakrishnan, Wear 23, 339 (1973).
[CrossRef]

Other (13)

A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957).

R. D. Young, E. C. Teague, in Properties of Electrodeposits: Their Measurement and Significance, R. Sard, H. Leidheiser, F. Ogburn, Eds., Proceedings of Symposium of Corrosion, Electrodeposition, and Electronics Division at 146th (Oct. 1974) Mtg. of Electrochemical Society (Electrochemical Society, Princeton, N.J., 1975), pp. 22–49.

S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Clarendon Press, Oxford, 1948).

S. Tolansky, Surface Microtopography (John Wiley, Interscience Division, New York, 1960).

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

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

H. E. Bennett, J. L. Stanford, “Structure-Related Optical Characteristics of Thin Metallic Films in the Visible and Ultraviolet,” presented at Workshop Seminar on Standardization in Spectrophotometry and Luminescence Measurements, Gaithersburg, Md., 19–20 Nov. 1975;Proceedings to be published in J. Res. Natl. Bur. Stand.

J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley-Interscience, New York, 1971), p. 311.

E. C. Teague, “Evaluation, Revision and Application of the NBS Stylus/Computer System for the Measurement of Surface Roughness,” NBS Technical Note 902 (U.S. Department of Commerce, Washington, D.C., April1976).

J. M. Bennett in High Energy Laser Mirrors and Windows (Semi-Annual Report No. 4, ARPA Order 2175, Naval Weapons Center, China Lake, Calif., Mar.1974), pp. 9–19.

J. M. Bennett, J. M. Elson in High Energy Laser Mirrors and Windows (Semi-Annual Report No. 5, ARPA Order 2175, Naval Weapons Center, China Lake, Calif., Sept.1974), pp. 4–14.

J. M. Bennett, J. M. Elson in High Energy Laser Mirrors and Windows (Semi-Annual Report Nos. 7 and 8, ARPA Order 2175, Naval Weapons Center, China Lake, Calif., July1976), pp. 149–165 1976).

The lateral resolution of 2 μm sets a short wavelength limit for scattering calculated from the surface statistics.

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Figures (20)

Fig. 1
Fig. 1

Schematic of the feco scanning interferometer. Symbols are: A, 75-W xenon arc; L1 and L3, collimating lenses; L2 and L4, focusing lenses; B, TiO2-coated beam splitter; I, interferometer; S, slit; P, dense flint dispersing prism (constant deviation spectrograph consists of S, L3, P, and L4). feco fringes are detected by slow scan TV camera; data reduction and processing are done by the signal averager and minicomputer.

Fig. 2
Fig. 2

Photograph of feco scanning interferometer. The sample is in the upper right center, TV camera at left, signal averager and minicomputer in upper center, and teletype at right.

Fig. 3
Fig. 3

Interferometer drift correction. (a) Wavelengths of the 256th scan line taken after every seventh scan. The points are fitted to a quadratic curve using the least-squares method. (b) Deviations of points in (a) from smooth curve. Average deviation is ±0.46 Å. Constants of the quadratic curve are used to correct all 512 data points.

Fig. 4
Fig. 4

Effect of drift correction on surface height measurements for machined copper. Upper curve is raw data without drift correction. One of the lower curves is same trace after correction. Other curve is another scan with a smaller drift correction. Curves are slightly displaced to show excellent agreement of surface structure.

Fig. 5
Fig. 5

Single-stage replica electron micrographs of (a) 1600-Å thick silver film on polished fused quartz and (b) same polished fused quartz surface but without silver. The total area in each micrograph is equal to the area included in one scan line of the TV camera. The large black spots in (a) are artifacts on the micrograph.

Fig. 6
Fig. 6

Photograph of the feco fringe, TV scanning camera trace, and autocovariance function for an 18.6-Å rms roughness polished fused quartz surface. Data average of 51 scans.

Fig. 7
Fig. 7

Height and slope distribution functions: for the same fused quartz surface.

Fig. 8
Fig. 8

Photograph, TV scan, and autocovariance function for a 9.4-Å rms polished CaF2 surface. Data average of 8 scans.

Fig. 9
Fig. 9

Height and slope distribution functions for the same CaF2 surface.

Fig. 10
Fig. 10

Photograph, TV scan, and autocovariance function for a 19.1-Å rms electroless nickel mirror. Data average of 10 scans.

Fig. 11
Fig. 11

Height and slope distribution functions for the same electroless nickel surface.

Fig. 12
Fig. 12

Photograph, TV scan, and autocovariance function for a 22.5-Å rms single-point diamond-machined copper surface. Data average of 10 scans.

Fig. 13
Fig. 13

Height and slope distribution functions for the same machined copper surface.

Fig. 14
Fig. 14

Photograph, TV scan, and autocovariance function for a 28.7-Å rms polished potassium chloride surface. Data average of 8 scans.

Fig. 15
Fig. 15

Height and slope distribution functions for the same KCl surface.

Fig. 16
Fig. 16

Cumulative probability distribution plots derived from the measured histograms in Figs. 7, 9,11, 13, and 15. Superposed points are ○ fused quartz, △ CaF2, ▽ electroless Ni, □ machined Cu; single curve ao-15-11-2705-i001 KCl. Lower scale is for KCl data, upper scale for four superposed curves. Arrows are the zero and 1/e points on the abscissas, where the heights equal the scanning camera values of rms roughness times ± 2 .

Fig. 17
Fig. 17

Photograph, TV scan, and autocovariance function for a holographic grating with a 21-μm spacing and 103-Å groove depth. Single scan.

Fig. 18
Fig. 18

Height and scan slope distribution functions for the same grating surface.

Fig. 19
Fig. 19

Relation between visual measurements of rms roughness and values obtained from scanning camera data.

Fig. 20
Fig. 20

Relation between rms slope determined from scanning camera data and visual measurements of rms roughness.

Tables (4)

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Table I Techniques for Measuring Optical Figure and Surface Waviness

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Table II Techniques for Measuring Roughness of Optically Polished Surfaces; Roughness Less Than 100 Å rms

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Table III Techniques for Measuring the Roughness of Ground, Polished and Machined Surfaces; Roughness Greater Than 100 Å rms

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Table IV Comparison of rms Surface Roughness Determined from Visual Interferometric Measurements and from Total Integrated Scattering Measurements

Equations (7)

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F = λ N Δ λ = π ( R R ) 1 / 4 1 - ( R R ) 1 / 2 ,
N = λ / ( λ - λ ) ,
λ = λ o + B C - x ,
δ = ( N / 2 ) Δ λ ,
G ( ρ ) lim L 1 L 0 L z ( x ) z ( x + ρ ) d x ,
G ( ρ ) = 1 L - ρ 0 L - ρ z ( x ) z ( x + ρ ) d x .
G ( ρ ) = G ( m ρ o ) = 1 M n = 1 M - m z ( n ρ o ) z ( n ρ o + m ρ o ) , ρ = ( 0 , 1 , 2 , M - 1 ) ρ o ; G ( ρ ) = 0 , ρ M ρ o .

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