Precision of Brewster-angle methods for optical thin films

We compare the precision of the Abeles Brewster-angle method for thin films, in which coated and uncoated regions of the substrate are illuminated by p-polarized light and Hacskaylo’s Brewster-angle method, in which a small fraction of s-polarized light is admitted. Hacskaylo’s Brewster-angle method has been reported to yield a higher precision, but this is not supported by our analysis. Approximate expressions that we derive for the precision and the direct iterative solutions both show that the precision of the two Brewster-angle methods is the same when the limiting factor is ability to detect the irradiance match.