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Optimal ellipsometric parameter measurement strategies based on four intensity measurements in presence of additive Gaussian and Poisson noise.

The two ellipsometric parameters of an isotropic sample can be measured with simplified polarimetry setups that acquire at least four intensity measurements. However, these measurements are perturbed by noise and the measurement strategy has to be optimized, in order to limit noise propagation. We determine two different measurement strategies that are optimal for both white Gaussian additive noise and Poisson shot noise. The first one involves a polarization state generator (PSG) with a single state of polarization and a polarization state analyzer (PSA) with four states. The second one involves both PSG and PSA having two states. The total estimation variances obtained with both strategies are demonstrated to be minimal, of equal values, and independent of the ellipsometric parameters to be measured. They are based on simple optical elements and could simplify and accelerate ellipsometric measurements.