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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 22, Iss. 20 — Oct. 15, 1983
  • pp: 3207–3219

Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation length, and roughness cross-correlation properties

J. M. Elson, J. P. Rahn, and J. M. Bennett  »View Author Affiliations


Applied Optics, Vol. 22, Issue 20, pp. 3207-3219 (1983)
http://dx.doi.org/10.1364/AO.22.003207


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Abstract

Previously published vector equations describing angle-resolved scattering from single-layer- and multilayer-coated optics have been integrated numerically and analytically over all angles in the reflecting hemisphere to obtain numerical results and analytical expressions for total integrated scattering (TIS). The effects of correlation length, polarization, angle of incidence, roughness height distribution, scattered light missed by the collecting hemisphere, and roughness cross-correlation properties of the multilayer stack on the TIS expression are considered. Background material on TIS from optics coated with single opaque reflecting layers is given for completeness and comparison to corresponding multilayer TIS results. It is shown that errors can occur in calculating the true rms surface roughness from actual TIS measurements; ways to correct these errors are discussed.

© 1983 Optical Society of America

History
Original Manuscript: November 10, 1982
Published: October 15, 1983

Citation
J. M. Elson, J. P. Rahn, and 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)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-22-20-3207


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References

  1. H. Davies, Proc. IEE London 101, 209 (1954).
  2. H. E. Bennett, J. O. Porteus, J. Opt. Soc. Am. 51, 123 (1961). [CrossRef]
  3. J. O. Porteus, J. Opt. Soc. Am. 53, 1394 (1963). [CrossRef]
  4. J. M. Eastman, “Surface Scattering in Optical Interference Coatings,” Dissertation, U. Rochester, Rochester, N.Y. (1974).
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), p. 379.
  6. J. M. Elson, Phys. Rev. B 12, 2541 (1975);J. M. Elson, Proc. Soc. Photo-Opt. Instrum. Eng. 240, 296 (1981). [CrossRef]
  7. The angle-resolved scattering equations pertaining to surfaces coated with single opaque reflecting films are given in the present notation in Ref. 6. These equations have been obtained previously byD. E. Barrick, Radar Cross Section Handbook (Plenum, New York, 1970), Chap. 9 and subsequently by numerous other workers using various methods.
  8. J. M. Elson, J. M. Bennett, J. Opt. Soc. Am. 69, 31 (1979). [CrossRef]
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  10. H. E. Bennett, Opt. Eng. 17, 480 (1978). [CrossRef]
  11. For properties of G(τ) and g(k), see, e.g., J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley, New York, 1971), p. 18.
  12. J. M. Bennett, J. H. Dancy, Appl. Opt. 20, 1785 (1981). [CrossRef] [PubMed]
  13. H. Raether, “Surface Plasmons and Roughness,” in Surface Polaritons, V. M. Agranovich, D. L. Mills, Eds. (North-Holland, Amsterdam, 1982), Chap. 9.
  14. J. M. Bennett, J. P. Rahn, P. C. Archibald, D. L. Decker, “Specifying the Surface Finish of Diamond-Turned Optics—A Study of the Relation Between Surface Profiles and Scattering,” in Technical Digest, Workshop on Optical Fabrication and Testing (Optical Society of America, Washington, D.C., 1981).
  15. A two-Gaussian autocorrelation function was used in earlier work by J. M. Elson, J. P. Rahn, J. M. Bennett, Appl. Opt. 19, 669 (1980). [CrossRef] [PubMed]
  16. J. M. Elson, J. Opt. Soc. Am. 69, 48 (1979). [CrossRef]

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