Error propagation in polarimetric demodulation

Abstract

The polarization analysis of the light is typically carried out using modulation schemes. The light of unknown polarization state is passed through a set of known modulation optics and a detector is used to measure the total intensity passing the system. The modulation optics is modified several times and, with the aid of such several measurements, the unknown polarization state of the light can be inferred. How to find the optimal demodulation process has been investigated in the past. However, since the modulation matrix has to be measured for a given instrument and the optical elements can present problems of repeatability, some uncertainty is present in the elements of the modulation matrix and/or covariances between these elements. We analyze in detail this issue, presenting analytical formulae for calculating the covariance matrix produced by the propagation of such uncertainties on the demodulation matrix, on the inferred Stokes parameters and on the efficiency of the modulation process. We demonstrate that, even if the covariance matrix of the modulation matrix is diagonal, the covariance matrix of the demodulation matrix is, in general, non-diagonal because matrix inversion is a nonlinear operation. This propagates through the demodulation process and induces correlations on the inferred Stokes parameters.

Estimation precision of the degree of linear polarization and of the angle of polarization in the presence of different sources of noise

“…We will consider three different types of perturbations: additive noise that is independent of the measured intensity, Poisson shot noise, and noise due to imperfect knowledge of the parameters of the measurement system. It should be noted that these issues have already been addressed by many authors in the more complex cases of full Stokes and Mueller measurements [5][6][7][8][9][10][11][12][13]. Restricting ourselves to the case of linear Stokes measurements will make it possible to obtain closed-form solutions for the estimation variances that clearly exhibit the influence of the number of measurements.…”

Analysis of Seeing-Induced Polarization Cross-Talk and Modulation Scheme Performance

“…It therefore makes sense to derive the expressions for the expectation value and variance of I i -respectively, E(I i ) and σ 2 (I i ) -as these provide important information about the quality of the observations (see also Asensio Ramos & Collados 2008). As we anticipated earlier in this section, E(x(t)) = 0.…”

“…A separate question -also of fundamental importance for observational spectro-polarimetery -concerns the effects of polarization calibration errors on the degree of polarization cross-talk affecting an observation. This subject has been exhaustively treated by Asensio Ramos & Collados (2008), and therefore it will not be addressed here.…”

Metasurface Polarimeter on Optical Fiber Facet by Nano-Transfer to UV-Curable Hybrid Polymer

“…A2-A3 for comparison. The uncertainty on the polarization measurements (red error bars) is calculated from uncertainty in the intensity measurements and from error propagation through the calibration process using the general error propagation formula [30]. The uncertainty of the degree of polarization (DOP) is calculated from the uncertainty of the Stokes parameters [31].…”