A least squares method for the precise nulling of an arbitrary ellipsometer arrangement is presented, and the standard errors of the null settings are calculated. The general expressions obtained are applied to the most common null ellipsometers, i.e., the PCSA and PSCA arrangements. For these ellipsometers we arrive at simple closed formulas that show the influence of the noise of the detected light, the extinction ratio of the ellipsometer, and the reflectivity and ellipsometric angles of the sample. In addition, coupling is discussed. It is shown, especially for the PSCA ellipsometer, that coupling has little effect on precision if the least squares method is used.
© 1981 Optical Society of America
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