Mueller Matrix Polarimeter Research Articles

Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic error.

The relationship between system condition and signal-to-noise ratio (SNR) in reconstructed Stokes parameter images is investigated for rotating compensator, variable retardance, and rotating analyzer Stokes vector (SV) polarimeters. A variety of optimal configurations are presented for each class of systems. The operation of polarimeters is discussed in terms of a four-dimensional conical vector space; and the concept of nonorthogonal bases, frames, and tight frames is introduced to describe the operation of SV polarimeters. Although SNR is an important consideration, performance of a polarimeter in the presence of errors in the calibration and alignment of the optical components is also important. The relationship between system condition and error performance is investigated, and it is shown that an optimum system from the point of view of SNR is not always an optimum system with respect to error performance. A detailed theory of error performance is presented, and the error of a SV polarimeter is shown to be related to the stability and condition number of the polarization processing matrices. The rms error is found to fall off as the inverse of the number of measurements taken. Finally, the concepts used to optimize SV polarimeters are extended to be useful for full Mueller matrix polarimeters.

Depolarization effects in the human eye

We have studied the effects of depolarization in the living human eye by using a spatially resolved Mueller-matrix polarimeter [Opt. Lett. 24 (1999) 64]. Results show that the degree of polarization for the central part of double-pass images is about 0.85 and 0.70 for 2 mm and 5 mm of pupil, respectively. This parameter decreases towards the tails of the image. In the plane of the pupil, the degree of polarization also depends on the analyzed area, and it has been related to the different components of the light coming back from the retina. Values of polarizance suggest that the eye presents a slight polarizing power mainly due to the existence of both circular birefringence and dichroic properties. Polarizance is also larger at the central part of double-pass images (about 0.25 on average) and decreases along the radius. In addition, it has been shown that the major retinal layer where the light is reflected does not depend on the state of polarization of the incident light.

Polarimetry using liquid-crystal variable retarders: theory and calibration

A Mueller-matrix polarimeter in transmission mode using two electronically controlled liquid-crystal variable retarders has been developed. Its design, theory and calibration are described. Although liquid crystals have been proposed earlier, this paper is focused on the process of the calculation of the Mueller matrix by a matrix-inversion method, oriented to static systems and in vitro samples. By driving the retarders with appropriate voltages, nine independent pairs of polarization states can be produced (incomplete polarimetry), while the other additional seven pairs are obtained by placing two quarter-wave plates (in the input and output optical paths respectively). This configuration allows extraction of 16 independent measurements of intensity. The Mueller matrix of the sample is calculated from them. The results of Mueller matrices for air, a linear polarizer and a quarter-wave plate are presented. Additional polarization parameters such as retardation, ellipticity or degree of polarization were also computed and some applications of the system are proposed.

Measurements of linear diattenuation and linear retardance spectra with a rotating sample spectropolarimeter

A technique to measure linear diattenuation and retardance spectra of infrared materials in transmission is described. A sample is rotated between two stationary linear polarizers in the sample compartment of a Fourier transform infrared spectrometer. The intensity modulation that results from the rotation of the sample is Fourier analyzed, and the linear diattenuation and linear retardance of the sample are calculated from the Fourier series coefficients for each wavelength. The advantages of this technique include immunity of the measurement to instrumental polarization, to circular diattenuation, and to circular retardance. The rotating sample polarimeter does not require retarders. Compensation for systematic errors from polarizers with diattenuation less than one is included in the data reduction. This technique is useful for the calibration of retarders and polarizers and hence for the bootstrap calibration of more elaborate polarimeters such as Mueller matrix polarimeters. We present as an example of t technique the caliration spectra 3-14 µm of an infrared quasi-achromatic retarder whose fast axis orientation oscillates with wavelength.

Mueller matrix dual-rotating retarder polarimeter

A computer-controlled Mueller matrix polarimeter with dual rotating retarders is described. Bulk properties of optical materials are determined by controlling the input-polarization state and measuring the output-polarization state. The Mueller matrix of a sample is obtained from polarimetric measurements, and polarization properties, i.e., diattenuation and retardance as well as depolarization, are extracted from the Mueller matrix. Further, fundamental electro- and magneto-optical material properties such as the electro-optical tensor coefficients may be obtained from Mueller matrices measured with applied fields. The polarimeter is currently configured to operate over the 3- to 12-microm spectral region.

Error analysis of a Mueller matrix polarimeter

An error analysis of a Mueller matrix polarimeter with dual rotating retarders is presented. Errors in orientational alignment of three of the four polarization elements are considered. Errors that are due to nonideal retardation elements are also included in the analysis. Compensation for imperfect retardation elements is possible with the equations derived, and the equations permit a calibration of the polarimeter for azimuthal alignment of polarization elements. An analytical treatment is given and is followed by numerical examples. The latter should prove useful in the laboratory in comparing precalibrated experimental results with theoretical predictions.