Research On Optimal Measurement Methods For Polarimetry Of Stokes Vector And Mueller Matrix

As one of the basic characteristics of the optics,polarization has the significant advantages in such conditions that the intensity and spectrum information do not work better.Therefore,its acquisitions and measurements are widely used in various fields,such as the object identification,remote sensing,and medical diagnosis etc.Among these polarization information,the Stokes vector characterizes the polarization state of the lightwave,while the Mueller matrix characterizes the polarization property of the material.Moreover,The conbination of Stokes and Mueller is always used to study the interaction between lightwave and meterial related to the polarization.Indeed,almost polarization parameters are deduced from the Stokes vector or the Mueller matrix,such as the degree of polarization,the angle of polarization,and the ellipsometric param-eters etc.However,due to the disturbation of environmental noises,the precision of the Stokes-Mueller measurement is limited,and thus the accuracy and effectiveness of these applications is reduced.In practice,for different measurement systems,the mea-surement error is mainly caused by the inverse model of intensity,moreover,the noise is amplified by the measurement matrix.Therefore,based on the statistic of noises,op-timizing the measurement matrix and reducing the noise propagation are two key issues in the fields of polarimetric measurement.In this thesis,by analyzing the modulation effect of measurement matrix on the noise propagation,we study the optimal measurement strategies based on the Stokes-Mueller formalism,in order to reduce the estimation variance and improve the mea-surement precision.The main works of this thesis include:1.We systematically investigate the optimization of full Stokes polarimeters based on linear division-of-focal-plane(DoFP)cameras,and determine their fundamental pre-cision limits in the presence of different types of noise.Besides,considering that the spatial resolution is divided by two with respect to the pixel pitch in each direction,which is the main drawback of DoFP linear polarization cameras,we determine the optiaml parameter settings that minimize estimation variance in each spatial resolu-tion mode,so that precision,spatial resolution,and acquisition time can be optimally and dynamically balanced to implement the imaging solution best adapted to a given application.This work can be considered as a complement to the existing Stokes po-larimeters.2.Based on the measurement redundancy,we propose a general theory of simul-taneous estimation of Stokes vector and instrumental autocalibration of polarization imagers.We illustrate it on the example of retardance autocalibration in a large class of polarization imagers and analyze the corresponding validity domains of input states for retardance autocalibration and Stokes estimation.Besides,we show that although all these architectures can yield optimal estimation precision of the Stokes vector if they are properly configured,they do not have the same autocalibration capacity and have to be specifically optimized for that purpose.Both the theory and experiment verify the possibility and the validity of dynamically calibration for retardance.3.Since the measurement of ellipsometric parameters only relate to partial ele-ments in Mueller matrix,we optimize the measurement strategy to minimize the total estimation variance for these elements,in order to furtherly increase the measurement precision of ellipsometric parameters.Compared with the previous strategies,the opti-mal solution effectively decreases the eatimation variance and thus statistically improve the measurement precision by about 25%in presence of different types of noise.More-over,the optimal solutions do not depend on the ellipsometric parameters to be mea-sured.This work makes excellent additions to the incomplete Mueller polarimeters.4.The Mueller matrix of isotropic materials is block-diagonal and only contains four different unknown parameters.It should thus be possible to reduce the number of intensity measurements to four.We determine the measurement strategies that are optimal for different types of noise.The corresponding polarization state generation part only contains a linear polarizer with fixed direction of 45°.Therefore,both the precision and the efficiency of measurement for these Mueller matrices with special structure is improved.This work complements the existing theory of Mueller measurements.