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

Abstract

We consider imaging systems that measure the three first elements of the Stokes vector and deduce from them the degree of linear polarization and the angle of polarization. They require the acquisition of at least three intensity measurements, but performing more measurements is often thought to improve the estimation precision. We show that if the total acquisition time is fixed, the optimal number of measurements depends on the type of noise that affects the image: the estimation variance increases with the number of measurements N when the noise is additive; it is independent of N in the presence of Poisson shot noise and decreases with N when the angles of the analyzers fluctuate. In general, the optimal number of measurements results from a compromise on the robustness of these different types of perturbations.

Enpolarization and depolarization of light scattered from chromatic complex media

“…A sophisticated formalism was proposed [5] which gathers both polarization and coherence of light, and allows detailed investigation of polarized data. Within this framework, numerous experiments were driven and have shown great agreement with the predictions [6][7][8][9].…”

Fully tunable active polarization imager for contrast enhancement and partial polarimetry

“…To have a more concrete understanding of the performance improvement, we will use the following criterion: It represents the sum of estimated variances of the N Ω estimated coefficients [34,35]. When using the method described in [19], one obtains C 15.2, whereas using the method described in the present paper, one obtains C 5.3: the estimation variance is thus reduced by about a factor 3.…”

A Low Cost CMOS Polarimetric Ophthalmoscope Scheme for Cerebral Malaria Diagnostics

“…Although this spatial resolution loss by a factor of N could be alleviated by examining the intensity values of neighboring pixels and adopting interpolation algorithms, it will become extremely difficult even unreliable for a large value of N . In addition, in a recently appeared literature [12], Goudail et al indicate that some noise is independent of even increases with N such as additive noise, and the optimum value of N results from a compromise between the robustness to different noise sources. Here we choose an N value of 4 with the micropolarizers' transmission axis orientations denoted as (θ 1 , θ 2 , θ 3 , θ 4 ) and the intensity measurements can be expressed in matrix form:…”