Polarized light interaction with inhomogeneous linear birefringent crystalline medium in single scattering approach has been built. Mueller matrix of the medium has been calculated theoretically. Polarization characteristics of the scattered light behind the screen have been investigated.
The analysis of Mueller matrix measurement errors, total and for each of the matrix elements, for time-sequential Mueller polarimeter in the case of utilizing different types of Stokes polarimeters in receiving channel are carried out. The consideration concerns of two types of Stokes polarimeters: polarimeter based on four angular orientations of retarder and polarimeter based on phenomenological definition of the Stokes vector. It has been shown that the measurement errors depend on the type of anisotropy characterizing the studied object and the azimuth of linear anisotropy. This gives the extra opportunities for the reduction of errors of the Mueller matrix measurements.
The analysis of dependence of total errors for objects with different anisotropy and error distribution over elements of experimental Mueller matrix for dynamic (dual rotating retarder-DRR) polarimeter is carried out. These results discloses new direction and matter of optimization of the Mueller matrix measurement.
The analysis of the experiment results of measurements of the Mueller matrices shows that the values of error of each matrix element do not equal each other and depend on the anisotropy types of studied objects. However, this fact did not receive an appropriate attention in the literature yet. At the same time, this feature can be used for polarimeter optimization in measuring of objects with specific polarization behavior (linear amplitude or phase anisotropy). For the estimation of the Mueller matrix measurement error is usually used the total error, that is a square root of sum of squares of all matrix element error). As analysis have shown this is not always justified. The goal of this work is to analyze error distribution over experimental Mueller matrix elements for the serial probing polarimeter in its four input polarization mode. The analysis is carried out for the three cases: (1) uniformly precise Stokes measurements, (2) uniformly precise Fourier measurements, (3) non-uniformly precise Fourier measurements. These results disclose new aspects of the Mueller matrix measurement tools optimization and the Mueller matrix measurement strategies.
It is theoretically known, that there exists a reciprocal correspondence between Mueller and Jones matrix formalisms for deterministic objects. However, in practice, it is mostly failed to determine a Jones matrix corresponding an experimental Mueller matrix of the deterministic object. The reason of such situation is a presence of experimental errors of Mueller matrix measurements. In essence, there is no the systematic study of measurement error influence on results of analysis of information containing in Mueller matrix in polarization literature existed now. In the paper the method of finding of a deterministic Mueller matrix closest (the difference between its element values do not exceed a value of average measurement error) in some sense to initial experimental one is offered and for which the correspondent Jones matrix could be found. Our choice for the deterministic Mueller matrix is based on four anisotropy mechanisms: linear and circular amplitude (dichroism) anisotropy and linear and circular phase (birefrigent) anisotropy.
Analysis of existing approaches to the problem of the physical realizability of experimentally obtained Mueller matrix has been carried out. The more physically clear approach has been suggested to answer the question whether experimentally obtained Mueller matrix is physically realizable with given experimental error. This method has been illustrated for Mueller matrices existed in polarimetric literature (Ramsey, Howell, etc). This method has been applied for the set of experimental Mueller matrices we have obtained as well.
Mueller matrix formalism has been used for the analysis of polarization properties for microalgae with different content and structure of cells' wall. Using microalgae from different systematic groups: Cyanobacteria (murein cells' wall)--Anabaena hassalii (Kuetz) Wittr., Microcystis aeruginosa Kuetz. emend. Elenk., and Chlorophyta (cellulose)--Ankistradesmus fusiformas Corda. The dependence of obtained polarization properties of microalgae from morphological peculiarities of cells and its sizes was discussed.
It is known that the fact that symmetry of studied object permit reduction of the number of independent parameters of Mueller matrix of the object was firstly noted by F. Perrin. This work was carried out in scope of so-called direct problem of polarimetry. In the present paper the analysis of number of Mueller matrix independent parameters for nondepolarizing and input-independent classes of objects in scope of inverse problem of polarimetry is carried out.
The full polarization elements parameter optimization is conducted to minimize the determination error of Mueller matrix elements and to accelerate the measurement. The optimal retarders rotating frequency ratio is found. Expressions for the Mueller matrix elements is given in terms of components of the signal Fourier decomposition for the dynamic Muller-polarimeter (which scheme was proposed by R. Azzam in 1978) with arbitrary parameters. Muller- polarimeter with optimal parameters is shown to have the measurement error in 1.7 times less than Mueller-polarimeter with parameter chosen in traditional manner. The correspondent computer simulation is conducted to confirm theoretical study.
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