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) [1]. 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∘, we predict a sensitivity of 0.5% for diattenuation and 0.3∘ 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.
Highlights
Polarimeters characterize the polarization properties of materials
It is likely that the measurement is more sensitive when the sample under test (SUT) exhibits strong polarization properties, and the retardance and diattenuation are not decoupled in calculating the repeatability of either of them
The Mueller pupil matrix of an arbitrary non-depolarizing SUT is predicted before it is converted to a Jones pupil matrix
Summary
Polarimeters characterize the polarization properties of materials. They find application in, for instance, optical samples [2], cancer non-invasive screening tools [3] in clinics, hyper-numerical-aperture lithography [4,5,6,7,8] where controlled polarization enhances the contrast and enabling smaller structures to be written on the wafer.Inherited from standard interferometry [9], the double-pass configuration detecting the phase shift between its two arms has been developed for sensing applications such as dilatometric measurement [10] and pH monitoring [11]. A doublepass layout enables angle-resolved measurements, whereby the polarization response of a sample for a range of polar angles and all azimuths can be measured in a synchronous approach. This simplifies the measurement setup and saves time compared to, otherwise, an apparatus with a function of rotating a solid angle over a certain range. While experimental demonstrations have validated the concept of doublepass polarimetry in angle-resolved polarization measurements [2], repeatability analysis to tolerances of the double-pass polarimeter has not been studied systematically. The present work attempts to fill this gap by providing a detailed sensitivity analysis of the polarimeter repeatability
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