Abstract

A relation from vector scattering theory has been used to predict the angular distribution of scattered light from optical surfaces as a function of the wavelength, optical constants of the material, and spectral density function. For calculations of one-dimensional (two-dimensional) scattering, the spectral density function of the surface roughness is obtained from the Fourier transform (Hankel transform) of the autocovariance function, which in turn is determined from surface-profile data. Measured statistics presented for various types of optical surfaces indicate that there are three basic components of surface structure: long-range waviness, short-range random roughness, and periodicity; one or more of which may be present on a given surface. Averaged and unaveraged surfaceprofile data for the same surface are shown to be consistent. Experimental data are presented that yield an exponential autocovariance function, and give a reasonably good fit to a Poisson distribution of zero crossings. Finally, angular scattering values calculated using measured surface statistics with vector scattering theory are compared to scattering values measured on the same surface. The shapes of the measured and calculated curves are similar, but the magnitudes are not. However, the rms surface roughnesses calculated from total integrated scattering measurements are in excellent agreement with values measured directly on these same surfaces.

© 1979 Optical Society of America

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  1. H. E. Bennett and J. O. Porteus, J. Opt. Soc. Am. 51,123 (1961); H. E. Bennett, ibid., 53, 1389 (1963); J. 0. Porteus, ibid. 53, 1395 (1963).
  2. J. M. Bennett, Appl. Opt. 15, 2705 (1976).
  3. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford, 1963); J. A. Holzer and C. C. Sung, J. Appl. Phys. 47, 3363 (1976).
  4. J. M. Elson and R. H. Ritchie, Phys. Status Solidi B 62, 461 (1974); V. Celli, A. Marvin, and F. Toigo, Phys. Rev. B 11, 1779 (1975); A. A. Maradudin and D. L. Mills, ibid. 11, 1392 (1975); J. M. Elson, ibid. 12, 2541 (1975); J. M. Elson, Appl. Opt. 16, 2872 (1977).
  5. J. Eastman and P. W. Baumeister, Opt. Commun. 12,418 (1974); P. J. Chandley, Opt. Quantum Electron. 8, 329 (1976); J. C. Leader, McDonnell Aircraft Company, Report No. MCAIR 71-013, 1971 (unpublished).
  6. P. J. Chandley, Opt. Quantum Electron. 8, 323 (1976).
  7. J. C. Stover, Appl. Opt. 14, 1796 (1975).
  8. I. J. Hodgkinson, J. Phys. E, 3,300 (1970); 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, DC, April 1976); M. Kubo, Acta Imeko 21, 115 (1964); M. Kubo, Rev. Sci. Instrum. 36, 236 (1965); J. A. Greenwood and J. B. P. Williamson, Proc. Roy. Soc. Lond. A 295, 300 (1966); J. B. P. Williamson, Proc. Inst. Mech. Eng. 182, 21 (1967); T. R. Thomas and S. D. Probert, J. Phys. D. 3, 277 (1970); D. J. Whitehouse and J. F. Archard, Proc. Roy. Soc. Lond. A 316, 97 (1970); C. J. Pellerin, J. Christensen, R. C. Jerner, and J. H. Peavey, J. Vac. Sci. Technol. 12, 496 (1975); J. Renau and J. A. Collinson, Bell System Tech. J. 44, 2203 (1965); J. Peklenik, Proc. Inst. Mech. Eng. 182, 108 (1967).
  9. D. Gloge, E. L. Chinnock, and H. E. Earl, Bell System Tech. J. 48, 511 (1969); I. J. Hodgkinson, J. Phys. E, 3, 341 (1970); R. P. Edwin, ibid., 6, 55 (1973); D. Heitman and V. Permien, Opt. Commun. 23, 131 (1977); B. P. Hildebrand, R. L. Gordon, and E. V. Allen, Appl. Opt. 13, 177 (1974).
  10. E. L. Church and J. M. Zavada, Appl. Opt. 14, 1788 (1975).
  11. E. L. Church, H. A. Jenkinson, and J. M. Zavada, Opt. Eng. 16, 360 (1977).
  12. Equation (5.1) in the paper by Elson and Ritchie in Ref. 4. In this reference the surface factor is given as |ζk|2/L2.
  13. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1966), p. 272.
  14. The complex dielectric constant is related to the complex index of refraction n̄ = n + ik where n is the real part of the refractive index and k the extinction coefficient by the relation ∊1 = n2k2 and ∊2 = 2nk. The extinction coefficient is not to be confused with the surface wave vector k which is used throughout the paper.
  15. To a good approximation the second and third terms in the denominator can be neglected relative to the first term, and sin2θ in the A term can be neglected relative to ∊l. If the log of the optical factor is plotted versus θ for a given wavelength, the factor multiplying cos2θ, (equations) merely shifts the curve vertically and does not affect the angular dependence of the function.
  16. J. M. EBson, J. Opt. Soc. Am. 66, 682 (1976).
  17. Y. W. Lee, Statistical Theory of Communication (Wiley, New York, 1960), pp. 73–74.
  18. R. B. Blackman and J. W. Tukey, Bell System Tech. J. 37, 485 (1958), see especially, p. 499.
  19. J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley, New York, 1971), pp. 314–321.
  20. See Ref. 19, pp. 311–312. Equation (13) is equivalent to Eq. (9.98) in Ref. 19. This equation and Eq. (9.95) in Ref. 19 are equally good definitions of the auto-covariance function, especially when used with lag windows.
  21. See Ref. 18, pp. 228–231.
  22. See Ref. 19, pp. 83, 173.
  23. See Ref. 19, pp. 376–377.
  24. See Ref. 19, p. 22.
  25. See Ref. 17, p. 177.
  26. J. L. Doob, Stochastic Processes (Wiley, New York, 1953), p. 233.
  27. J. C. Leader, J. Appl. Phys. 42, 4808 (1971).
  28. Manufactured by Rank Precision Industries, Ltd., Leicester, England.
  29. Manufactured by Ernst Fr. Weinz WEKA-OHG, 658 Idar-Oberstein 2, Germany.
  30. J. H. Dancy and J. M. Bennett, "Study of Diamond Styluses for a Talystep Profilometer," in High Energy Laser Mirrors and Windows, Annual Report No. 9, NWC TP5988, NWC TP5988, (Naval Weapons Center, China Lake, California 1977), pp. 133-144.
  31. H. E. Bennett and J. L. Stanford, J. Res. Natl. Bur. Stand. (U.S.) 80A, 643 (1976); P. C. Archibald and H. E. Bennett, "Scattering from Infrared Missile Domes," in Proceedings of Seminar on Optics in Missile Engineering, January 16–18, 1978, Los Angeles, California, Vol. 133, (Society of Photo-Optical Instrumentation Engineers, Bellingham, Washington, 1978); also, Opt. Eng. 17, 647 (Nov/Dec 1978).
  32. R. W. Dietz and J. M. Bennett, Appl. Opt. 5, 881 (1966).
  33. R. Anderson and J. M. Bennett, "Properties of KCI Optical Elements Forged Between Optically Polished Dies," in Proceedings of the High Power Laser Optical Components and Component Materials Meeting, (Defense Advanced Research Projects Agency, Arlington, Virginia, 1977), p. 177.
  34. T. T. Saito, Appl. Opt. 14, 1773 (1975); J. B. Arnold, P. J. Steger, and T. T. Saito, ibid. 14, 1777 (1975).
  35. J. M. Blakely and D. L. Olson, J. Appl. Phys. 39, 3476 (1968).
  36. W. J. Choyke, W. D. Partlow, E. P. Supertzi, F. J. Venskytis, and G. B. Brandt, Appl. Opt. 16, 2013 (1977).
  37. Frederick Scmid, U. S. Patent No. 3,898,051, Crystal Growing, 5 Aug. 1975.

Anderson, R.

R. Anderson and J. M. Bennett, "Properties of KCI Optical Elements Forged Between Optically Polished Dies," in Proceedings of the High Power Laser Optical Components and Component Materials Meeting, (Defense Advanced Research Projects Agency, Arlington, Virginia, 1977), p. 177.

Baumeister, P. W.

J. Eastman and P. W. Baumeister, Opt. Commun. 12,418 (1974); P. J. Chandley, Opt. Quantum Electron. 8, 329 (1976); J. C. Leader, McDonnell Aircraft Company, Report No. MCAIR 71-013, 1971 (unpublished).

Beckmann, P.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford, 1963); J. A. Holzer and C. C. Sung, J. Appl. Phys. 47, 3363 (1976).

Bendat, J. S.

J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley, New York, 1971), pp. 314–321.

Bennett, H. E.

H. E. Bennett and J. L. Stanford, J. Res. Natl. Bur. Stand. (U.S.) 80A, 643 (1976); P. C. Archibald and H. E. Bennett, "Scattering from Infrared Missile Domes," in Proceedings of Seminar on Optics in Missile Engineering, January 16–18, 1978, Los Angeles, California, Vol. 133, (Society of Photo-Optical Instrumentation Engineers, Bellingham, Washington, 1978); also, Opt. Eng. 17, 647 (Nov/Dec 1978).

H. E. Bennett and J. O. Porteus, J. Opt. Soc. Am. 51,123 (1961); H. E. Bennett, ibid., 53, 1389 (1963); J. 0. Porteus, ibid. 53, 1395 (1963).

Bennett, J. M.

J. M. Bennett, Appl. Opt. 15, 2705 (1976).

J. H. Dancy and J. M. Bennett, "Study of Diamond Styluses for a Talystep Profilometer," in High Energy Laser Mirrors and Windows, Annual Report No. 9, NWC TP5988, NWC TP5988, (Naval Weapons Center, China Lake, California 1977), pp. 133-144.

R. Anderson and J. M. Bennett, "Properties of KCI Optical Elements Forged Between Optically Polished Dies," in Proceedings of the High Power Laser Optical Components and Component Materials Meeting, (Defense Advanced Research Projects Agency, Arlington, Virginia, 1977), p. 177.

R. W. Dietz and J. M. Bennett, Appl. Opt. 5, 881 (1966).

Blackman, R. B.

R. B. Blackman and J. W. Tukey, Bell System Tech. J. 37, 485 (1958), see especially, p. 499.

Blakely, J. M.

J. M. Blakely and D. L. Olson, J. Appl. Phys. 39, 3476 (1968).

Brandt, G. B.

W. J. Choyke, W. D. Partlow, E. P. Supertzi, F. J. Venskytis, and G. B. Brandt, Appl. Opt. 16, 2013 (1977).

Chandley, P. J.

P. J. Chandley, Opt. Quantum Electron. 8, 323 (1976).

Chinnock, E. L.

D. Gloge, E. L. Chinnock, and H. E. Earl, Bell System Tech. J. 48, 511 (1969); I. J. Hodgkinson, J. Phys. E, 3, 341 (1970); R. P. Edwin, ibid., 6, 55 (1973); D. Heitman and V. Permien, Opt. Commun. 23, 131 (1977); B. P. Hildebrand, R. L. Gordon, and E. V. Allen, Appl. Opt. 13, 177 (1974).

Choyke, W. J.

W. J. Choyke, W. D. Partlow, E. P. Supertzi, F. J. Venskytis, and G. B. Brandt, Appl. Opt. 16, 2013 (1977).

Church, E. L.

E. L. Church and J. M. Zavada, Appl. Opt. 14, 1788 (1975).

E. L. Church, H. A. Jenkinson, and J. M. Zavada, Opt. Eng. 16, 360 (1977).

Dancy, J. H.

J. H. Dancy and J. M. Bennett, "Study of Diamond Styluses for a Talystep Profilometer," in High Energy Laser Mirrors and Windows, Annual Report No. 9, NWC TP5988, NWC TP5988, (Naval Weapons Center, China Lake, California 1977), pp. 133-144.

Dietz, R. W.

R. W. Dietz and J. M. Bennett, Appl. Opt. 5, 881 (1966).

Doob, J. L.

J. L. Doob, Stochastic Processes (Wiley, New York, 1953), p. 233.

Earl, H. E.

D. Gloge, E. L. Chinnock, and H. E. Earl, Bell System Tech. J. 48, 511 (1969); I. J. Hodgkinson, J. Phys. E, 3, 341 (1970); R. P. Edwin, ibid., 6, 55 (1973); D. Heitman and V. Permien, Opt. Commun. 23, 131 (1977); B. P. Hildebrand, R. L. Gordon, and E. V. Allen, Appl. Opt. 13, 177 (1974).

Eastman, J.

J. Eastman and P. W. Baumeister, Opt. Commun. 12,418 (1974); P. J. Chandley, Opt. Quantum Electron. 8, 329 (1976); J. C. Leader, McDonnell Aircraft Company, Report No. MCAIR 71-013, 1971 (unpublished).

EBson, J. M.

J. M. EBson, J. Opt. Soc. Am. 66, 682 (1976).

Elson, J. M.

J. M. Elson and R. H. Ritchie, Phys. Status Solidi B 62, 461 (1974); V. Celli, A. Marvin, and F. Toigo, Phys. Rev. B 11, 1779 (1975); A. A. Maradudin and D. L. Mills, ibid. 11, 1392 (1975); J. M. Elson, ibid. 12, 2541 (1975); J. M. Elson, Appl. Opt. 16, 2872 (1977).

Gloge, D.

D. Gloge, E. L. Chinnock, and H. E. Earl, Bell System Tech. J. 48, 511 (1969); I. J. Hodgkinson, J. Phys. E, 3, 341 (1970); R. P. Edwin, ibid., 6, 55 (1973); D. Heitman and V. Permien, Opt. Commun. 23, 131 (1977); B. P. Hildebrand, R. L. Gordon, and E. V. Allen, Appl. Opt. 13, 177 (1974).

Hodgkinson, I. J.

I. J. Hodgkinson, J. Phys. E, 3,300 (1970); 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, DC, April 1976); M. Kubo, Acta Imeko 21, 115 (1964); M. Kubo, Rev. Sci. Instrum. 36, 236 (1965); J. A. Greenwood and J. B. P. Williamson, Proc. Roy. Soc. Lond. A 295, 300 (1966); J. B. P. Williamson, Proc. Inst. Mech. Eng. 182, 21 (1967); T. R. Thomas and S. D. Probert, J. Phys. D. 3, 277 (1970); D. J. Whitehouse and J. F. Archard, Proc. Roy. Soc. Lond. A 316, 97 (1970); C. J. Pellerin, J. Christensen, R. C. Jerner, and J. H. Peavey, J. Vac. Sci. Technol. 12, 496 (1975); J. Renau and J. A. Collinson, Bell System Tech. J. 44, 2203 (1965); J. Peklenik, Proc. Inst. Mech. Eng. 182, 108 (1967).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1966), p. 272.

Jenkinson, H. A.

E. L. Church, H. A. Jenkinson, and J. M. Zavada, Opt. Eng. 16, 360 (1977).

Leader, J. C.

J. C. Leader, J. Appl. Phys. 42, 4808 (1971).

Lee, Y. W.

Y. W. Lee, Statistical Theory of Communication (Wiley, New York, 1960), pp. 73–74.

Olson, D. L.

J. M. Blakely and D. L. Olson, J. Appl. Phys. 39, 3476 (1968).

Partlow, W. D.

W. J. Choyke, W. D. Partlow, E. P. Supertzi, F. J. Venskytis, and G. B. Brandt, Appl. Opt. 16, 2013 (1977).

Piersol, A. G.

J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley, New York, 1971), pp. 314–321.

Porteus, J. O.

H. E. Bennett and J. O. Porteus, J. Opt. Soc. Am. 51,123 (1961); H. E. Bennett, ibid., 53, 1389 (1963); J. 0. Porteus, ibid. 53, 1395 (1963).

Ritchie, R. H.

J. M. Elson and R. H. Ritchie, Phys. Status Solidi B 62, 461 (1974); V. Celli, A. Marvin, and F. Toigo, Phys. Rev. B 11, 1779 (1975); A. A. Maradudin and D. L. Mills, ibid. 11, 1392 (1975); J. M. Elson, ibid. 12, 2541 (1975); J. M. Elson, Appl. Opt. 16, 2872 (1977).

Saito, T. T.

T. T. Saito, Appl. Opt. 14, 1773 (1975); J. B. Arnold, P. J. Steger, and T. T. Saito, ibid. 14, 1777 (1975).

Scmid, Frederick

Frederick Scmid, U. S. Patent No. 3,898,051, Crystal Growing, 5 Aug. 1975.

Spizzichino, A.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford, 1963); J. A. Holzer and C. C. Sung, J. Appl. Phys. 47, 3363 (1976).

Stanford, J. L.

H. E. Bennett and J. L. Stanford, J. Res. Natl. Bur. Stand. (U.S.) 80A, 643 (1976); P. C. Archibald and H. E. Bennett, "Scattering from Infrared Missile Domes," in Proceedings of Seminar on Optics in Missile Engineering, January 16–18, 1978, Los Angeles, California, Vol. 133, (Society of Photo-Optical Instrumentation Engineers, Bellingham, Washington, 1978); also, Opt. Eng. 17, 647 (Nov/Dec 1978).

Stover, J. C.

J. C. Stover, Appl. Opt. 14, 1796 (1975).

Supertzi, E. P.

W. J. Choyke, W. D. Partlow, E. P. Supertzi, F. J. Venskytis, and G. B. Brandt, Appl. Opt. 16, 2013 (1977).

Tukey, J. W.

R. B. Blackman and J. W. Tukey, Bell System Tech. J. 37, 485 (1958), see especially, p. 499.

Venskytis, F. J.

W. J. Choyke, W. D. Partlow, E. P. Supertzi, F. J. Venskytis, and G. B. Brandt, Appl. Opt. 16, 2013 (1977).

Zavada, J. M.

E. L. Church, H. A. Jenkinson, and J. M. Zavada, Opt. Eng. 16, 360 (1977).

E. L. Church and J. M. Zavada, Appl. Opt. 14, 1788 (1975).

Other

H. E. Bennett and J. O. Porteus, J. Opt. Soc. Am. 51,123 (1961); H. E. Bennett, ibid., 53, 1389 (1963); J. 0. Porteus, ibid. 53, 1395 (1963).

J. M. Bennett, Appl. Opt. 15, 2705 (1976).

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford, 1963); J. A. Holzer and C. C. Sung, J. Appl. Phys. 47, 3363 (1976).

J. M. Elson and R. H. Ritchie, Phys. Status Solidi B 62, 461 (1974); V. Celli, A. Marvin, and F. Toigo, Phys. Rev. B 11, 1779 (1975); A. A. Maradudin and D. L. Mills, ibid. 11, 1392 (1975); J. M. Elson, ibid. 12, 2541 (1975); J. M. Elson, Appl. Opt. 16, 2872 (1977).

J. Eastman and P. W. Baumeister, Opt. Commun. 12,418 (1974); P. J. Chandley, Opt. Quantum Electron. 8, 329 (1976); J. C. Leader, McDonnell Aircraft Company, Report No. MCAIR 71-013, 1971 (unpublished).

P. J. Chandley, Opt. Quantum Electron. 8, 323 (1976).

J. C. Stover, Appl. Opt. 14, 1796 (1975).

I. J. Hodgkinson, J. Phys. E, 3,300 (1970); 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, DC, April 1976); M. Kubo, Acta Imeko 21, 115 (1964); M. Kubo, Rev. Sci. Instrum. 36, 236 (1965); J. A. Greenwood and J. B. P. Williamson, Proc. Roy. Soc. Lond. A 295, 300 (1966); J. B. P. Williamson, Proc. Inst. Mech. Eng. 182, 21 (1967); T. R. Thomas and S. D. Probert, J. Phys. D. 3, 277 (1970); D. J. Whitehouse and J. F. Archard, Proc. Roy. Soc. Lond. A 316, 97 (1970); C. J. Pellerin, J. Christensen, R. C. Jerner, and J. H. Peavey, J. Vac. Sci. Technol. 12, 496 (1975); J. Renau and J. A. Collinson, Bell System Tech. J. 44, 2203 (1965); J. Peklenik, Proc. Inst. Mech. Eng. 182, 108 (1967).

D. Gloge, E. L. Chinnock, and H. E. Earl, Bell System Tech. J. 48, 511 (1969); I. J. Hodgkinson, J. Phys. E, 3, 341 (1970); R. P. Edwin, ibid., 6, 55 (1973); D. Heitman and V. Permien, Opt. Commun. 23, 131 (1977); B. P. Hildebrand, R. L. Gordon, and E. V. Allen, Appl. Opt. 13, 177 (1974).

E. L. Church and J. M. Zavada, Appl. Opt. 14, 1788 (1975).

E. L. Church, H. A. Jenkinson, and J. M. Zavada, Opt. Eng. 16, 360 (1977).

Equation (5.1) in the paper by Elson and Ritchie in Ref. 4. In this reference the surface factor is given as |ζk|2/L2.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1966), p. 272.

The complex dielectric constant is related to the complex index of refraction n̄ = n + ik where n is the real part of the refractive index and k the extinction coefficient by the relation ∊1 = n2k2 and ∊2 = 2nk. The extinction coefficient is not to be confused with the surface wave vector k which is used throughout the paper.

To a good approximation the second and third terms in the denominator can be neglected relative to the first term, and sin2θ in the A term can be neglected relative to ∊l. If the log of the optical factor is plotted versus θ for a given wavelength, the factor multiplying cos2θ, (equations) merely shifts the curve vertically and does not affect the angular dependence of the function.

J. M. EBson, J. Opt. Soc. Am. 66, 682 (1976).

Y. W. Lee, Statistical Theory of Communication (Wiley, New York, 1960), pp. 73–74.

R. B. Blackman and J. W. Tukey, Bell System Tech. J. 37, 485 (1958), see especially, p. 499.

J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley, New York, 1971), pp. 314–321.

See Ref. 19, pp. 311–312. Equation (13) is equivalent to Eq. (9.98) in Ref. 19. This equation and Eq. (9.95) in Ref. 19 are equally good definitions of the auto-covariance function, especially when used with lag windows.

See Ref. 18, pp. 228–231.

See Ref. 19, pp. 83, 173.

See Ref. 19, pp. 376–377.

See Ref. 19, p. 22.

See Ref. 17, p. 177.

J. L. Doob, Stochastic Processes (Wiley, New York, 1953), p. 233.

J. C. Leader, J. Appl. Phys. 42, 4808 (1971).

Manufactured by Rank Precision Industries, Ltd., Leicester, England.

Manufactured by Ernst Fr. Weinz WEKA-OHG, 658 Idar-Oberstein 2, Germany.

J. H. Dancy and J. M. Bennett, "Study of Diamond Styluses for a Talystep Profilometer," in High Energy Laser Mirrors and Windows, Annual Report No. 9, NWC TP5988, NWC TP5988, (Naval Weapons Center, China Lake, California 1977), pp. 133-144.

H. E. Bennett and J. L. Stanford, J. Res. Natl. Bur. Stand. (U.S.) 80A, 643 (1976); P. C. Archibald and H. E. Bennett, "Scattering from Infrared Missile Domes," in Proceedings of Seminar on Optics in Missile Engineering, January 16–18, 1978, Los Angeles, California, Vol. 133, (Society of Photo-Optical Instrumentation Engineers, Bellingham, Washington, 1978); also, Opt. Eng. 17, 647 (Nov/Dec 1978).

R. W. Dietz and J. M. Bennett, Appl. Opt. 5, 881 (1966).

R. Anderson and J. M. Bennett, "Properties of KCI Optical Elements Forged Between Optically Polished Dies," in Proceedings of the High Power Laser Optical Components and Component Materials Meeting, (Defense Advanced Research Projects Agency, Arlington, Virginia, 1977), p. 177.

T. T. Saito, Appl. Opt. 14, 1773 (1975); J. B. Arnold, P. J. Steger, and T. T. Saito, ibid. 14, 1777 (1975).

J. M. Blakely and D. L. Olson, J. Appl. Phys. 39, 3476 (1968).

W. J. Choyke, W. D. Partlow, E. P. Supertzi, F. J. Venskytis, and G. B. Brandt, Appl. Opt. 16, 2013 (1977).

Frederick Scmid, U. S. Patent No. 3,898,051, Crystal Growing, 5 Aug. 1975.

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