Optimizing precision of fixed-polarizer, rotating-polarizer, sample, and fixed-analyzer spectroscopic ellipsometry

General equations describing the theoretical uncertainty in measurements of the complex reflectance ratio, rho, are given for fixed-polarizer, rotating-polarizer, sample, and fixed-analyzer (PP(r)SA) ellipsometers operating under shot-noise-limited (SNL) and detector-noise-limited (DNL) conditions. Optimum values of the fixed-polarizer and fixed-analyzer azimuths are calculated as a function of ellipsometric parameters (psi and D) for SNL and DNL systems. The uncertainty of complex reflectance ratio, calculated from the optimum values of the fixed polarizer and analyzer azimuths, decreases linearly in psi as psi --> 0 under the SNL condition but approaches arbitrary large under the DNL condition. This suggests that a compensator is not needed under the SNL condition to achieve high precision on dielectric surfaces but that measurements at small psi values should be avoided under the DNL condition. A discrepancy of the fixed polarizer or analyzer azimuth from its optimum value for various D is discussed with psi = 5 degrees and 45 degrees under the SNL condition.