Error Analysis for Repeatability Enhancement of a Dual-Rotation Mueller Matrix Ellipsometer

Abstract

Since the Mueller matrix ellipsometer has been used as a highly accurate tool for thin film measurement, the error analysis and repeatability enhancement of such a tool are of great importance. The existence of the Poisson–Gaussian mixed noise and the random bias of the trigger signal in the optical measurement system may reduce the repeatability and accuracy of a measurement. Utilizing the probabilistic analysis, the random errors in the Mueller matrix measurements are quantified. A quantitative analysis on the instrument matrix has been carried out to assess the individual effects for different error sources. We proposed a general optimal instrument matrix which is capable of minimizing the estimation variance for both Gaussian additive noise and Poisson shot noise. Besides, a peak-matching algorithm is proposed to compress the repeatability errors due to the bias of the trigger signal and the limited sampling frequency. The effectiveness of the proposed methods is shown using both virtual simulations and experiments carried out on our self-developed instrument, which potentially paves a way to reduce the requirements on motor performance, acquisition card resolution, and trigger accuracy, which are critical to cost reduction.