Inversion of reflection ellipsometric data

The dielectric constant of an isotropic homogeneous layer on an isotropic substrate is shown to satisfy a quintic equation, with the coefficients determined by |ρ|(2) and Re(ρ), where ρ = r(p)/r(s) is found ellipsometrically. This algebraic equation eliminates many (but not all) of the nonphysical roots in the inversion of ellipsometric data. A simple form is obtained if the angle of incidence is equal to the Brewster angle of the substrate. The problem of inversion for thin films is also discussed.