The problem of relating the specimen ψ and Δ to the instrument readings and component imperfections is solved by a general technique without any restriction on the nature of the imperfections. Thus, for the first time, small incoherent effects in the ellipsometer can be treated. The solution is explicit and is given in terms of the properties of the ideal ellipsometer and the Mueller imperfection matrices of the optical devices. After deriving the general solution, we consider a conventional ellipsometric arrangement. Arrays of coupling constants are introduced which clearly show the effect of imperfections on ψ and Δ. Also, we indicate in a schematic way the elements that remain effective after averaging over two and four zones. Component depolarization is discussed and the matrix elements contributing to it are found. Besides allowing all previous results to be obtained, some new conclusions of this analysis are: a small depolarization of the polarizer light output affects ψ (0.15° error in ψ for 1% depolarization) and this effect remains after two- and four-zone averaging. The effect of both coherent and incoherent p ↔ s cross scattering by the cell windows cancels if a two-zone average is taken. The same applies for the coherent and incoherent cross scattering by the specimen-surface roughness or by surface optical activity. For the compensator, cross scattering caused by birefringence and optical activity cancels only if a four-zone average is taken.
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