Abstract

A theoretical method is described for calculating the angular scattering curve for any given thin-film multilayer in which the various surfaces and interfaces are assumed to be rough. The energy that is scattered in any particular direction depends on two factors. The first is solely a function of the characteristics of the ideal multilayer and the observation conditions. The second depends on the roughnesses of the various surfaces, that is, on their autocorrelation and cross-correlation functions. The expressions that are obtained are completely general because no restrictive hypothesis has been developed on the relationship that may exist between the roughnesses of the various interfaces. The principal features of the apparatus used for the scattering measurements are briefly described. Next, several results of calculation and measurement are given as illustrations. The measurements show that polished surfaces of high optical quality often show marked anisotropy.

© 1981 Optical Society of America

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  12. P. Giacomo, "Les couches réflechissantes multidiélectriques appliquées à l'interférométrie de Fabry–Perot. Etude théorique et expérimentale des couches réelles," Rev. Opt. Theor. Instrum. 35, 317–354, 442–467 (1956).

1980

1979

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

S. J. Gourley and P. H. Lissberger, "Optical scattering in multilayer thin films," Opt. Acta 26, 117–143 (1979).

C. K. Carniglia, "Scalar scattering theory for multilayer optical coatings," Opt. Eng. 18, 104–115 (1979).

1977

1976

J. M. Bennett, "Measurement of the rms roughness, autocovariance function and other statistical properties of optical surfaces using a FECO scanning interferometer," Appl. Opt. 11, 2705–2721 (1976); J. Eastman and P. Baumeister, "The microstructure of polished optical surfaces," Opt. Commun. 12, 418–420 (1974).

1975

1970

E. Körger and E. Kretschmann, "Scattering of light by slightly rough surfaces on thin films including plasma resonance emission," Z. Phys. 237, 1–15 (1970).

1965

1956

P. Giacomo, "Les couches réflechissantes multidiélectriques appliquées à l'interférométrie de Fabry–Perot. Etude théorique et expérimentale des couches réelles," Rev. Opt. Theor. Instrum. 35, 317–354, 442–467 (1956).

Bennett, J. M.

Berning, P. H.

P. H. Berning, "Theory and calculations of optical thin films," in Physics of Thin Films, G. Hass, ed. (Academic, New York, 1963), Vol. 1, pp. 69–121.

Carniglia, C. K.

C. K. Carniglia, "Scalar scattering theory for multilayer optical coatings," Opt. Eng. 18, 104–115 (1979).

Eastman, J. M.

J. M. Eastman, "Surface scattering in optical interference coatings," Ph.D. Thesis (University of Rochester, Rochester, New York, 1974) (unpublished).

Elson, J. M.

Giacomo, P.

P. Giacomo, "Les couches réflechissantes multidiélectriques appliquées à l'interférométrie de Fabry–Perot. Etude théorique et expérimentale des couches réelles," Rev. Opt. Theor. Instrum. 35, 317–354, 442–467 (1956).

Gourley, S. J.

S. J. Gourley and P. H. Lissberger, "Optical scattering in multilayer thin films," Opt. Acta 26, 117–143 (1979).

Körger, E.

E. Körger and E. Kretschmann, "Scattering of light by slightly rough surfaces on thin films including plasma resonance emission," Z. Phys. 237, 1–15 (1970).

Kretschmann, E.

Kröger, E.

Lissberger, P. H.

S. J. Gourley and P. H. Lissberger, "Optical scattering in multilayer thin films," Opt. Acta 26, 117–143 (1979).

Nicodemus, F. E.

Rahn, J. P.

Appl. Opt.

J. Opt. Soc. Am.

Opt. Acta

S. J. Gourley and P. H. Lissberger, "Optical scattering in multilayer thin films," Opt. Acta 26, 117–143 (1979).

Opt. Eng.

C. K. Carniglia, "Scalar scattering theory for multilayer optical coatings," Opt. Eng. 18, 104–115 (1979).

Rev. Opt. Theor. Instrum.

P. Giacomo, "Les couches réflechissantes multidiélectriques appliquées à l'interférométrie de Fabry–Perot. Etude théorique et expérimentale des couches réelles," Rev. Opt. Theor. Instrum. 35, 317–354, 442–467 (1956).

Z. Phys.

E. Körger and E. Kretschmann, "Scattering of light by slightly rough surfaces on thin films including plasma resonance emission," Z. Phys. 237, 1–15 (1970).

Other

J. M. Eastman, "Surface scattering in optical interference coatings," Ph.D. Thesis (University of Rochester, Rochester, New York, 1974) (unpublished).

P. H. Berning, "Theory and calculations of optical thin films," in Physics of Thin Films, G. Hass, ed. (Academic, New York, 1963), Vol. 1, pp. 69–121.

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