Polarimetry comprises a set of noninvasive and nondesctructive optical techniques that demonstrated their great interest in biophotonics due to its capability to obtain relevant information from biological samples in a noninvasive and nondestructive way. Various polarimetric observables, derived from the Mueller matrix of a sample, are used to probe the efficacy of these techniques in pathology detection or different biological structures classification. The physical properties of a sample related to polarization can be categorized in three groups: retardance, dichroism and depolarization. In this work, we propose the study of the polarimetric observables linked to these physical properties for the identification of different structures within an ex-vivo cow brain sample by means of different pseudo-coloration methods. In particular, we study pseudo-coloration functions based on the Gaussian and Cauchy probabilistic functions. These probabilistic functions allow us to compute the probability of a given part of a sample to belong to a particular class (i.e. healthy or pathological or different structures inside the same sample) where, this probability depends on the polarimetric observables obtained from the studied sample. Our investigation encompasses a study of different observables and methodologies to find the optimal approach for brain tissue identification (identification of gray and white matter in ex-vivo cow brain) and, which may be of interest in multiple biomedical scenarios such as early pathology detection and diagnosis or enhanced visualization of different structures for clinical applications.
In this study we analyze the effect of experimental errors on the optimization and calibration method of a Mueller matrix imaging polarimeter based on liquid crystal variable retarders. The study is carried out through numerical simulations, where the optimized Mueller matrix polarimeter is simulated considering misalignments of the polarimetric components, and variations in the induced retardance of the LCVRs. However, the final measurement error does not depend only on non-ideal elements, but also depends on the noise, in the irradiance measurements, and the accuracy of the calibration method. Thus, the eigenvalue calibration method is used in the simulations, including random variations in the irradiance matrix. The tolerances of the optimization and calibration method are analyzed, and the results are presented.
We present the optimization and calibration of a Mueller matrix imaging polarimeter. The polarimeter is intended to be used as a compact tool for biomedical diagnosis, in particular for skin examination. The device uses a pixelated-polarization camera along with a fixed variable retarder for the polarization state analyzer, minimizing the number of elements used in the device for Full-Mueller matrix measurements. For the polarization state generator the device uses an LED as light source, and a polarizer followed by a pair of LCVRs to generate any polarization state over the Poincare sphere. With this system the polarization properties of a sample can be obtained with a total of 8 measurements to extract the 16 elements of the Mueller matrix. We study the optimization strategies by minimizing the condition number of the instrument matrix, to maximize the signal to noise ratio, and reducing the effect of experimental errors on the optimization. As a compact and transportable tool, the polarimeter will be used in different environments, so an auto-calibration method is also required. In this work we explore the necessary conditions to successfully use the Eigenvalue calibration method in a polarized-camera and liquid crystals based polarimeter. The study presented will help to measure the Mueller matrix of a sample with high accuracy and precision levels, needed for the study of biological samples.
Polarimetric techniques have widely demonstrated their potential in biophotonics due to its capability to obtain relevant information from biological samples in a noninvasive and nondestructive way. Different polarimetric observables, obtained from the Mueller matrix of a sample, are used to explore the potential of these techniques in pathology detection or different biological structures classification. The physical properties of a sample related to polarization can be divided in three main groups: retardance, dichroism and depolarization. In this work, we propose the study of the polarimetric observables related to these physical properties for the identification of different structures in a biological sample by means of different pseudo-coloration methods. In particular, we study pseudo-coloration functions based on the Gaussian and Cauchy probabilistic functions. These probabilistic functions allow us to compute the probability of a given part of a sample to belong to a particular class (i.e. healthy or pathological or different structures in the same sample) where, this probability depends on the polarimetric observables obtained from the studied sample. We present a study of the different observables and methods to find the best approach for brain tissue identification (identification of gray and white matter in ex-vivo cow brain) and, which may be of interest in multiple biomedical scenarios such as early pathology detection and diagnosis or enhanced visualization of different structures for clinical applications.
Stokes polarimeters measure some or all the Stokes parameters of a light beam. To reduce the effect of noise in the measurements made on the final calculated Stokes parameters, a polarimeter can be optimized by minimizing the condition number of the characteristic or instrument matrix. However, this optimization does not guarantee the best stability in the presence of experimental errors in the polarimeter configuration. This is particularly important for polarimeters using liquid-crystal variable retarders, which have we have found have errors in the retardance as a function of position in the aperture of the liquid-crystal cell, and fast axis angles as a function of the applied voltage, so even the best aligned of this type of system will have these errors. We have found that different optimized polarimeter configurations can have very different sensitivity to experimental errors. In this work, we present an analysis of a number of different optimized systems to find the most stable configuration with respect to experimental errors. In particular, we consider the variation of the volume of the solid formed in the Poincaré sphere by the Stokes vector values used in each polarimeter configuration.
In many astrophysical processes, the complete characterization of the polarization properties of radiation gives important information about the source or the interaction between radiation and matter. Stokes imaging polarimeters based on liquid crystal variable retarders (LCVRs) are widely used to determine the polarization state of radiation. But these devices have errors due to the nature of the liquid crystals that induce an inhomogeneous retardance over the complete aperture, and their fast-axis position depends on the applied voltage. We present the analysis of the impact of variations in the retardance and orientation of the LCVRs, in the optimization of a Stokes imaging polarimeter. An optimized Stokes polarimeter based on two LCVRs, was simulated. First considering individual errors in the retardance and orientation, then one million cases were simulated adding random errors in both LCVRs. The condition number was calculated to analyze the effect in the optimization of the polarimeter. Also, a Stokes imaging polarimeter was calibrated, to verify experimentally the effect of these errors in a real polarimeter. For the calibration the instrument matrix and condition number were calculated individually in every pixel of the image. The results show that these errors lead to polarimetric measurements different from the ideal and to a poorly optimized polarimeter, demonstrating that a condition number optimization of the instrument matrix and a calibration are not sufficient to guarantee accurate polarimetric measurements.
We present a method to measure the polarization of light scattered on structured surfaces, through the implementation of a Mueller-matrix polarimeter, using focused illumination. Typically the scattered light has been measured using an incident beam with a diameter on the order of a few cm for surfaces with scales of the order of microns, mainly to avoid problems with the speckle pattern of light, however in this way it is not possible to obtain information on local variations in the polarization effects presented on the surface. Therefore, we use an incident spot size of a few microns to illuminate and analyze the local variations in the polarization state produced by the sample. First, we will begin by describing the instrumentation of the polarimeter, which uses Liquid Crystal Variable Retarders (LCVRs) to control the incident and detected polarization states. Our device implements a calibration and data extraction method, which allows us to reduce the experimental error in the instrument to obtain efficient measurements. We use as a sample, a reflective structured surface with dimensions of 15 microns and we use an incident beam size of 5 microns to perform a preliminary qualitative interpretation and comparison of results of experimental cases with results of numerical calculation based on the Kirchhoff approximation of light scattering, including polarization effects, the simulations has been previously verified with other methods. We conclude about the advantages of measuring the polarization effect in the scattering pattern from one point to another in the studied sample.
The design and construction of a Full-Stokes Imaging polarimeter is presented. The device uses a telescope optical system and a polarization state analyzer (PSA) to obtain polarimetric images on a CCD. The PSA employs two liquid crystal variable retarders (LCVR) and a linear polarizer to measure the four Stokes parameters. The Stokes polarimetry method used in this paper is based on the application of six combinations of retardance values on the LCVRs. A well-known method is used to extract all the Stokes vector parameters from this intensity data. Due to experimental errors, a calibration is necessary. The calibration method used in this paper, also calculates the errors in the experimental set-up by fitting the experimental intensity measurements for the calibration samples to a theoretical polarimeter with errors. In this case, we used incident 45° polarized light to control the output polarization, and six calibration samples. The errors calculated in the method include the axes alignment errors and the errors in the retardance values of both LCVRs. The acquisition of Stokes images used a telescope optical system with a CCD camera.
A comparison between two experimental techniques to characterize retardance as a function of applied voltage of liquid
crystal variable retarders (LCVR) is presented. In the first method the variable retarder was rotated between two
polarizers with their transmission axes parallel, and the retardance was calculated from the Fourier series coefficients for
each applied voltage. The second method involved using two polarizers with their transmission axes perpendicular to
each other, the variable retarder was placed between the polarizers with its optical axis at 45° from the horizontal, and a
final stage known as "phase unwrapping" is used on experimental data to obtain the voltage-retardance function. With
these two experimental methods, the voltage-retardance relationship was obtained.
To verify the accuracy of this characterization a second experiment involving the production of specific polarization
states was performed as the basis of a Mueller polarimeter. A method based on measuring the optical signal resulting
from the application of a predetermined set of fixed values of retardance in each retarder was used. 16 elements of the
Mueller matrix of a polarizer with its transmission axis at 0° and 90° were measured, and the results are compared to the
expected theoretical values.
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