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Development of the surface dipole model of light scattering at plane boundaries perturbed by roughness.

The so-called surface dipole model of light scattering at slightly rough layer interfaces of optical coatings is discussed with particular reference to its limitations. It is shown how these limitations can be overcome and the model developed in microscopic rather than in its present macroscopic terms. In the new more detailed description, the surface dipole moments required to represent the effects of interfacial roughness are related to the electric field of the radiation via a tensor. The form of this relationship is derived by an approximate method for specified cases. A more precise numerical procedure for obtaining the values of the tensor elements is also described.