Error in determining Mueller matrix elements and its effect on solution of the inverse problem of polarimetry

Abstract

We present an analysis of the errors in measurement of the Mueller matrix elements in polarimeters that are a combination of different types of Stokes polarimeters in the detection channel and controllable polarization converters in the probing channel. As polarization converters for the probing radiation, we consider a phase plate having four different angular positions in measuring the complete Mueller matrix and a linear polarizer having different angular positions in measuring the structural parts of an incomplete 4 × 3 Mueller matrix.We have shown that the error in determining the Mueller matrix elements is distributed nonuniformly over the matrix. The nature of the error distribution over the elements and its values are different for different combinations of detection and probing channels of the polarimeter, and depend on the anisotropy of the test object. The latter dictates the choice of the optimal layout for a Mueller polarimeter for studying media with the same or different types of anisotropy and the choice of Mueller matrix elements used to solve the inverse problem of determining the anisotropy parameters.Introduction. Study of the properties of anisotropic media is a problem which is efficiently solved using the Mueller matrix method. At this time there are a wide variety of polarimeter layouts for measuring the structural parts of complete and incomplete Mueller matrices for different types of media and objects over a broad range of probing radiation wavelengths [1][2][3]. Recently a number of matrix models have been proposed for analysis of the polarization properties of media based on the measured Mueller matrices [4-6]. As a rule, the polarimeter layout is chosen based on the experimental conditions. In particular, for scanning measurements, optimal layouts have a minimal number of polarization elements which have high uniformity for large aperture [7]. In this case, the number of necessary changes in the parameters of the polarization converters should be minimal to ensure an acceptable measurement time. For spectral polarimetric studies, it is undesirable to use polarization elements with pronounced dispersion properties (crystalline phase plates, etc.). For nonscanning polarization measurements, except perhaps in cases when the nature of the possible changes in the polarization state of the radiation after interaction with the test object is known and limited (for example, when radiation interacts with a medium which is characterized by optical activity, only the azimuth of the orientation of the polarization ellipse changes, etc.), the motivation for the choice of polarimeter layout came from the required minimum measurements for determination of the unknown polarization characteristics. Moreover, we know that the individual Stokes parameters and Mueller matrix elements in the general case are measured with different accuracies [8]. Furthermore, the error in determination of the same Stokes parameter is different for different Stokes polarimeter layouts [9,10]. This provides a basis for as...