Angel YanguasGil, Brent A. Sperling, John R. Abelson
Theory of light scattering from selfaffine surfaces: Relationship between surface morphology and effective medium roughness
Physical Review B 84 (2011) 085402
Using RayleighRice scattering theory we have studied the influence of surface morphology on the optical response of selfaffine surfaces. We have established a mathematical relationship between the surface roughness (d) as determined by spectroscopic ellipsometry (SE) using the effective medium approximation (EMA) and the parameters controlling the morphology of the surface: rootmeansquare roughness (w), correlation length (xi), and roughness (Hurst) exponent (alpha). These three parameters affect the roughness value measured by ellipsometry. However, when the correlation length is smaller than the wavelength, the dependence is contained in a single parameter w delta that is proportional to the product of the surface roughness and the local slope delta = w/xi(alpha). The fact that the local slope of a surface increases only very slowly during growth explains the linear dependence experimentally found between w as measured by scanningprobe microscopy and the vertical roughness determined by the effective medium approach.
Cited Articles

Franta D., Ohlídal I.,
Comparison of effective medium approximation and Rayleigh–Rice theory concerning ellipsometric characterization of rough surfaces,
Optics Communications 248 (2005) 459–467 
Franta D., Ohlídal I.,
Ellipsometric parameters and reflectances of thin films with slightly rough boundaries,
Journal of Modern Optics 45 (1998) 903–934