Increasing signal-to-noise ratio in over-determined Mueller matrices.

This work investigates how the signal-to-noise ratio (SNR) of an over-determined Mueller matrix can be improved by changing the method of calculation. Specifically, our investigation focused on comparing SNRs achieved using the vector methodology from the field of partial Mueller polarimetry, and the matrix methodology. We use experimentally derived measurements from an investigation into the time-varying signal produced by the Mueller matrix of an electro-optic Bismuth Silicon Oxide (BSO) crystal undergoing cyclical impact of a Helium plasma ionisation wave. Our findings show that the vector methodology is superior to the matrix methodology, with a maximum SNR of 7.54 versus 4.97. We put forth that the superiority of the vector methodology is due to its greater flexibility, which results in the Mueller matrix being calculated with better condition matrices, and higher levels of SNR in the intensity measurements used for calculation.

Optimizing Mueller polarimetry in noisy systems through over-determination.

Mueller polarimetry measurements are increasingly being used to image highly dynamic and short-lived phenomena such as plasma discharges. For phenomena such as these, exposure times below 1 µs must be used. Unfortunately, these low exposure times significantly reduce the signal-to-noise ratio, making accurate and consistent measurements difficult. To overcome this limitation, we investigated increasing the number of Stokes vectors produced from a polarization state analyzer and polarization state generator, a process known as over-determination. To conduct our analysis, we used results from physical experiments using Stokes vectors generated by liquid crystal variable retarders. These results were then verified using data from simulations. First, we conclude that increasing the degree of over-determination is a simple and effective way of dealing with this noise; however, we also convey that choosing the best scheme is not an entirely trivial process. Second, we demonstrate that over-determination gives rise to hitherto inaccessible information that allows for the quantification of statistical noise and, crucially, the pinpointing of the origin of systematic error, a highly beneficial process that has been lacking until now.

Structural circular birefringence and dichroism quantified by differential decomposition of spectroscopic transmission Mueller matrices from Cetonia aurata.

Transmission Mueller-matrix spectroscopic ellipsometry is applied to the cuticle of the beetle Cetonia aurata in the spectral range 300-1000 nm. The cuticle is optically reciprocal and exhibits circular Bragg filter features for green light. By using differential decomposition of the Mueller matrix, the circular and linear birefringence as well as dichroism of the beetle cuticle are quantified. A maximum value of structural optical activity of 560°/mm is found.

Sum decomposition of Mueller-matrix images and spectra of beetle cuticles.

Spectral Mueller matrices measured at multiple angles of incidence as well as Mueller matrix images are recorded on the exoskeletons (cuticles) of the scarab beetles Cetonia aurata and Chrysina argenteola. Cetonia aurata is green whereas Chrysina argenteola is gold-colored. When illuminated with natural (unpolarized) light, both species reflect left-handed and near-circularly polarized light originating from helicoidal structures in their cuticles. These structures are referred to as circular Bragg reflectors. For both species the Mueller matrices are found to be nondiagonal depolarizers. The matrices are Cloude decomposed to a sum of non-depolarizing matrices and it is found that the cuticle optical response, in a first approximation can be described as a sum of Mueller matrices from an ideal mirror and an ideal circular polarizer with relative weights determined by the eigenvalues of the covariance matrices of the measured Mueller matrices. The spectral and image decompositions are consistent with each other. A regression-based decomposition of the spectral and image Mueller matrices is also presented whereby the basic optical components are assumed to be a mirror and a circular polarizer as suggested by the Cloude decomposition. The advantage with a regression decomposition compared to a Cloude decomposition is its better stability as the matrices in the decomposition are determined a priori. The origin of the depolarizing features are discussed but from present data it is not possible to conclude whether the two major components, the mirror and the circular polarizer are laterally separated in domains in the cuticle or if the depolarization originates from the intrinsic properties of the helicoidal structure.

Mid-infrared Mueller ellipsometer with pseudo-achromatic optical elements.

The purpose of this article is to present a new broadband Mueller ellipsometer designed to work in the mid-infrared range, from 3 to 14 µm. The Mueller ellipsometer, which can be mounted in reflection or in transmission configuration, consists of a polarization state generator (PSG), a sample holder, and a polarization state analyzer (PSA). The PSG consists of one linear polarizer and a retarder sequentially rotated to generate a set of four optimal polarization states. The retarder consists of a biprism made of two identical Fresnel rhombs disposed symmetrically and joined by an optical contact, giving the ensemble a "V" shape. Retardation is induced by the four total internal reflections that the beam undergoes when it propagates through the biprism. Total internal reflection allows the generation of a quasi-achromatic retardation. The PSA is identical to the PSG, but with its optical elements mounted in reverse order. After a measurement run, the instrument yields a set of sixteen independent values, which is the minimum amount of data required to calculate the Mueller matrix of the sample. The design of the Mueller ellipsometer is based on the optimization of an objective criterion that allows for minimizing the propagation of errors from raw data to the Mueller matrix of the sample. The pseudo-achromatic optical elements ensure a homogeneous quality of the measurements for all wavelengths. The performance of the Mueller ellipsometer, in terms of precision and accuracy, is discussed and illustrated with a few examples.

Retrieval of a non-depolarizing component of experimentally determined depolarizing Mueller matrices.

The measurement of the Mueller matrix when the probing beam is placed on the boundary between two (or more) regions of the sample with different optical properties may lead to a depolarization in the Mueller matrix. The depolarization is due to the incoherent superposition of the optical responses of different sample regions in the probe beam. Despite of the depolarization, the measured Mueller matrix has information enough to subtract a Mueller matrix corresponding to one of the regions of sample provided that this subtracted matrix is non-depolarizing. For clarity, we will call these non-depolarizing Mueller matrices of one individual region of the sample simply as the non-depolarizing components. In the framework of the theory of Mueller matrix algebra, we have implemented a procedure allowing the retrieval of a non-depolarizing component from a depolarizing Mueller matrix constituted by the sum of several non-depolarizing components. In order to apply the procedure, the Mueller matrices of the rest of the non-depolarizing components have to be known. Here we present a numerical and algebraic approaches to implement the subtraction method. To illustrate our method as well as the performance of the two approaches, we present two practical examples. In both cases we have measured depolarizing Mueller matrices by positioning an illumination beam on the boundary between two and three different regions of a sample, respectively. The goal was to retrieve the non-depolarizing Mueller matrix of one of those regions from the measured depolarizing Mueller matrix. In order to evaluate the performance of the method we compared the subtracted matrix with the Mueller matrix of the selected region measured separately.