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

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.     

Determination of the Polarization Characteristics of Objects by the Method of Three Probing Polarizations

A method of three probing polarizations for determining the polarization characteristics of objects by measuring their Mueller complete and incomplete matrices has been developed. The conditions of optimal implementation of the method from the viewpoint of minimizing the error in measurement of the Mueller matrix elements have been investigated.     

Structure of Deterministic Mueller Matrices and Their Reconstruction in the Method of Three Input Polarizations

The method of reconstruction of complete deterministic Mueller matrices for the structures of incomplete matrices, which are measured in the method of three input polarizations, has been developed. The method is based on reconstruction of the corresponding Jones matrices for the given structures of incomplete Mueller matrices.     

Mueller matrix differential decomposition

We present a Mueller matrix decomposition based on the differential formulation of the Mueller calculus. The differential Mueller matrix is obtained from the macroscopic matrix through an eigenanalysis. It is subsequently resolved into the complete set of 16 differential matrices that correspond to the basic types of optical behavior for depolarizing anisotropic media. The method is successfully applied to the polarimetric analysis of several samples. The differential parameters enable one to perform an exhaustive characterization of anisotropy and depolarization. This decomposition is particularly appropriate for studying media in which several polarization effects take place simultaneously.     

Polarization state and Mueller matrix measurements in terahertz-time domain spectroscopy

We derive the complete formulae governing the polarization state measurement in terahertz-time domain spectroscopy (THz-TDS) by using a rotatable THz polarizer. Four Stokes parameters can be uniquely obtained by spectrally-resolved measurement in THz-TDS. Further, we propose a new approach to measure the Mueller matrix of a pure birefringent material, using THz-TDS, by rotating the material under test. Based on the above techniques, we successfully measured the Mueller matrices of a quartz crystal in the frequency domain.     

Determination of local polarization properties of biological samples in the presence of diattenuation by use of Mueller optical coherence tomography

A unique feature of polarization-sensitive Mueller optical coherence tomography is that, by measuring Jones or Mueller matrices, it can reveal the complete polarization properties of biological samples, even in the presence of diattenuation. We map local polarization properties for the first time to our knowledge by using polar decomposition in combination with least-squares fitting to differentiate measured integrated Jones matrices with respect to depth. We also introduce the new concept of dual attenuation coefficients to characterize diattenuation per unit infinitesimal length in tissues. We experimentally verify the algorithm using measurements of a section of porcine tendon and the septum of a rat heart.     

Two-dimensional depth-resolved Mueller matrix characterization of biological tissue by optical coherence tomography

We built a polarization-sensitive optical coherence tomographic system and measured the two-dimensional depth-resolved full 4 x 4 Mueller matrix of biological tissue for what is believed to be the first time. The Mueller matrix measurements, which we made by varying the polarization states of the light source and the detector, yielded a complete characterization of the polarization property of the tissue sample. The initial experimental results indicated that this new approach reveals some tissue structures that are not perceptible in standard optical coherence tomography.     

Transformation matrices for the Mueller-Jones formalism

The Mueller-Jones (MJ) or pure Mueller matrix formulation has been reported by using two different matrix transformations in a condensed representation. The possibility to find other transformation matrices is explored. A complete set of unitary operators (R) is found to be closely related with the MJ matrices and with the evolution of pure states on the Poincaré sphere surface. We propose an alternative deduction for the condensed representation of the MJ matrices, obtained by using the Kronecker product operation and use of R unitary matrices as a tool to combine different Mueller matrices and changes of polarized states on the Poincarè sphere surface. Finally, it is shown explicitly that the columns of the transformation matrices are the eigenvectors of the MJ matrix associated to a non-depolarizing optical system and a corollary is established as a criterion to differentiate a Mueller matrix from an MJ matrix.     

Complete determination of the conical Mueller matrix for one-dimensional rough metallic surfaces

We present results of the complete determination of the Mueller matrix for the light scattered by a one-dimensional random rough metallic surface under a conical or out-the-plane of incidence geometry. We present and apply a reduced method for its complete determination. This reduced method considers only 16 intensity-polarized measurements instead of the 36 intensity-polarized measurements recently reported. Effects related with the enhanced backscattering were observed.     

Three linear probe polarization method in Mueller polarimetry with a source of arbitrary ellipticity

This is a study of the effect of the ellipticity of the polarization of radiation at the inlet of the shaping polarizer in the probe channel of a Mueller polarimeter operating with three linear probe polarizations on the accuracy with which the incomplete Mueller matrix is determined (without a fourth beam). It is shown that the appearance of and variations in the ellipticity cause a change in the conditions for optimization of the set of polarizations of the probe radiation from the standpoint of minimizing the measurement error. In the case of linear polarization (zero ellipticity), the measurement error is the same as the error when four probe polarizations are used. This allows measurement of the complete Mueller matrix and makes this version of the polarimeter especially promising, because in the input channel of the polarimeter, a single polarizing element, i.e., a linear polarizer with a controllable azimuthal orientation, can be used as the polarization transducer. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 6, pp. 875–880, November–December, 2008.     

Hybrid complete Mueller polarimeter based on phase modulators

Optical properties of matter as diattenuation, retardance and depolarization can be evaluated using polarimetric techniques. In this paper, the analysis and implementation of a complete Mueller polarimeter is presented. The system is constituted of a polarization state generator (PSG) and a polarization state analyzer (PSA), which are controlled and synchronized through a computer program. The PSG comprises a dual liquid crystal variable retarder system while the PSA is based on a two-photoelastic modulator setup. Using air and common polarizing optics as test samples for calibration at 633 nm, the hybrid instrument met a good precision when the Mueller matrices of those optical elements were measured.     

Numerical study of the characterization of forward scattering Mueller matrix patterns of turbid media with triple forward scattering assumption

We propose a triple forward scattering model to numerically investigate the forward scattering Mueller matrix of a turbid medium. The calculated results show that the Mueller matrix based on the triple scattering model can completely describe the basic symmetries and azimuthal structures of the forward scattering Mueller matrix of a turbid medium. The results show that the forward scattering Mueller matrix is characterized with special symmetric structure compared with backscattering Mueller matrix patterns. The method will extend the investigation to light scattering mechanism from cells and to diagnosis of diabetes and other blood related diseases.     

Schemes for complete compensation for polarization mode dispersion up to second order

The required structure and elements of polarization mode dispersion (PMD) compensators for complete second-order compensation are investigated by use of a general PMD vector formalism of concatenated PMD elements based on Mueller matrices and Stokes vectors. The investigation shows that two- and three-stage compensators with five independent parameters can compensate for polarization-dependent chromatic dispersion as well as the depolarization component of second-order PMD.     

随机介质背散射二维Mueller矩阵的数值模拟与分析

推导了随机介质背散射Mueller矩阵的直接计算公式,并运用矢量Monte Carlo方法进行了数值模拟.结果表明随机介质背散射二维Mueller矩阵方位关系随散射系数的减小而增强,而与微粒大小关系不大;Mueller矩阵元素绝对值的空间分布随径向呈近似指数规律衰减,矩阵元素的方位变化具有周期性.对称系统的二维Mueller矩阵的花样图中仅有7幅独立,其余9幅可通过对称、旋转变换得到.     

Calculations of Backscattering Mueller Matrices for Turbid Media with a Sphere Queue Model

A sphere queue model is introduced to calculate Mueller matrices of turbid media. Combined with the single scattering approximation, the backscattering Mueller matrices of turbid media can be computed rapidly by Mie theory. The numerical results agree with the azimuthal dependences of backscattering Mueller matrices＇ patterns from turbid media, which indicates that the major contribution to the Mueller matrices＇ patterns comes from the single scattering of the sphere queue, and the multiple scattering considered as a high-order correction does not change the patterns. The numerical analysis reveals that the contrast of Mueller matrices＇ patterns will decrease with increase of the concentration of media and the distance from the incident point.     

Ultrafast holographic Stokesmeter for polarization imaging in real time

We propose an ultrafast holographic Stokesmeter using a volume holographic substrate with two sets of two orthogonal gratings to identify all four Stokes parameters of the input beam. We derive the Mueller matrix of the proposed architecture and determine the constraints necessary for reconstructing the complete Stokes vector. The speed of this device is determined primarily by the channel spectral bandwidth (typically 100 GHz), corresponding to a few picoseconds.     

Recovery of the Complete Mueller Matrix of an Arbitrary Object in the Method of Three Input Polarizations

The problem of the recovery of the complete Mueller matrix of an arbitrary object by additionally measuring the matrix elements whose values are not determined in base measuring cycles of the method of three input polarizations is considered. We suggest a number of methods for recovering the complete matrix of dependent and independent recovery and for carrying out two base measuring cycles of the method of three input polarizations. A comparative analysis of the accuracy characteristics of the proposed methods has been performed.     

Two-dimensional depth-resolved Mueller matrix of biological tissue measured with double-beam polarization-sensitive optical coherence tomography

A double-beam polarization-sensitive system based on optical coherence tomography was built to measure the Mueller matrix of scattering biological tissue with high spatial resolution. The Jones matrix of a sample can be determined with a single scan and subsequently converted into an equivalent nondepolarizing Mueller matrix. As a result, the system can be used to measure the Mueller matrix of an unstable sample, such as soft tissue. The polarization parameters of a porcine tendon, including magnitude and orientation of birefringence and diattenuation, were extracted by decomposition of the measured Mueller matrix.     

Mueller matrix for characterization of one-dimensional rough perfectly reflecting surfaces in a conical configuration

Theoretical results of the use of a Mueller matrix to characterize a one-dimensional rough perfectly reflecting, single-scattering surface in a conical configuration are presented. The conical Mueller matrix (CMM) is derived from the known Mueller matrix of this kind of surface in the plane of incidence [the plane Mueller matrix (PMM)]. The key argument is that, as the PMM is considered to be a Mueller-Jones matrix, an appropriate rotation of the complex amplitude matrix provides the conic Mueller matrix.     

Equivalence between the Mueller Regge model and the multiperipheral model

It is proven that a large class of pionization Mueller Regge models are equivalent to the multiperipheral model. An orthogonal similarity transformation is found which allows one to transform in either direction between equivalent multiperipheral and Mueller models. Models with charge are discussed and the problem of constructing charge conserving Mueller models is solved.