Tolerance analysis of non-depolarizing double-pass polarimetry

TL;DR

This paper presents a comprehensive tolerance analysis of a double-pass polarimeter, combining Mueller matrix calibration and Zernike polynomial expansion to predict sensitivities and guide improvements in polarization measurement accuracy.

Contribution

It introduces a numerical approach integrating eigenvalue calibration and Zernike polynomials to analyze and enhance polarimeter sensitivity considering hardware tolerances.

Findings

Achieved a sensitivity of 0.5% for diattenuation.

Predicted a 0.3° sensitivity for retardance.

Validated numerical predictions with experimental data.

Abstract

Double-pass polarimetry measures the polarization properties of a sample over a range of polar angles and all azimuths. Here, we present a tolerance analysis of all the optical elements in both the calibration and measurement procedures to predict the sensitivities of the double-pass polarimeter. The calibration procedure is described by a Mueller matrix based on the eigenvalue calibration method (ECM). Our numerical results from the calibration and measurement in the Mueller matrix description with tolerances limited by systematic and stochastic noise from specifications of commercially available hardware components are in good agreement with previous experimental observations. Furthermore, by using the orientation Zernike polynomials (OZP) which are an extension of the Jones matrix formalism, similar to the Zernike polynomials wavefront expansion, the pupil distribution of the polarization properties of non-depolarizing samples under test are expanded. Using polar angles ranging up to 25$^{\circ}$, we predict a sensitivity of 0.5% for diattenuation and 0.3$^{\circ}$ for retardance using the root mean square (RMS) of the corresponding OZP coefficients as a measure of the error. This numerical tool provides an approach for further improving the sensitivities of polarimeters via error budgeting and replacing sensitive components with those having better precision.