Russell A. Chipman

Interpretation of Mueller matrices based on polar decomposition

We present an algorithm that decomposes a Mueller matrix into a sequence of three matrix factors: a diattenuator, followed by a retarder, then followed by a depolarizer. Those factors are unique except for singular Mueller matrices. Based on this decomposition, the diattenuation and the retardance of a Mueller matrix can be defined and computed. Thus this algorithm is useful for performing data reduction upon experimentally determined Mueller matrices.

Homogeneous and inhomogeneous Jones matrices

The classification of polarization properties of polarization elements is studied to derive data-reduction equations for extracting the diattenuation, retardance, and other polarization properties from their Jones matrices. Polarization elements, and Jones matrices as well, are divided into two classes: homogeneous, with orthogonal eigenpolarizations, and inhomogeneous, with nonorthogonal eigenpolarizations. The basic polarization properties, diattenuation and retardance, of homogeneous polarization elements are straightforward and well known; these elements are characterized by their eigenvalues and eigenpolarizations. Polarization properties of inhomogeneous polarization elements are not so evident. By applying polar decomposition, the definitions of diattenuation and retardance are generalized to inhomogeneous polarization elements, providing an understanding of their polarization characteristics. Furthermore, an inhomogeneity parameter is introduced to describe the degree of inhomogeneity in a polarization element. These results are then adapted to degenerate polarization elements, which have only one linearly independent eigenpolarization.

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.

Mueller matrix imaging polarimetry

The design and operation of a Mueller matrix imaging polarimeter is presented. The instrument is configurable to make a wide variety of polarimetric measurements of optical systems and samples. In one configuration, it measures the polarization properties of a set of ray paths through a sample. The sample may comprise a single element, such as a lens, polarizer, retarder, spatial light modulator, or beamsplitter, or an entire optical system containing many elements. In a second configuration, it measures an optical systems point spread matrix, a Mueller matrix relating the polarization state of a point object to the distribution of intensity and polarization across the image. The instrument is described and a number of example measurements are provided that demonstrate the Mueller matrix imaging polarimeters unique measurement capability.

Phase-only modulation of a twisted nematic liquid crystal TV by use of the eigenpolarization states

We present the eigenpolarization states of a commercially available liquid-crystal television display and show that phase-only modulation can be achieved over a large dynamic range of video voltages for several bias voltage settings if the eigenpolarization states are used. A set of operating curves using these polarization states is given for the device.

Dual-photoelastic-modulator-based polarimetric imaging concept for aerosol remote sensing

A dual-photoelastic-modulator- (PEM-) based spectropolarimetric camera concept is presented as an approach for global aerosol monitoring from space. The most challenging performance objective is to measure degree of linear polarization (DOLP) with an uncertainty of less than 0.5% in multiple spectral bands, at moderately high spatial resolution, over a wide field of view, and for the duration of a multiyear mission. To achieve this, the tandem PEMs are operated as an electro-optic circular retardance modulator within a high-performance reflective imaging system. Operating the PEMs at slightly different resonant frequencies generates a beat signal that modulates the polarized component of the incident light at a much lower heterodyne frequency. The Stokes parameter ratio q = Q/I is obtained from measurements acquired from each pixel during a single frame, providing insensitivity to pixel responsivity drift and minimizing polarization artifacts that conventionally arise when this quantity is derived from differences in the signals from separate detectors. Similarly, u = U/I is obtained from a different pixel; q and u are then combined to form the DOLP. A detailed accuracy and tolerance analysis for this polarimeter is presented.

Depolarization index and the average degree of polarization

Two single number metrics for depolarization of samples are contrasted: (1) the average degree of polarization of the exiting light averaged over the Poincaré sphere and (2) the depolarization index of Gill and Berbenau [Opt. Acta 32, 259-261 (1985); 33, 185-189 (1986)1. The depolarization index is a geometric measure that varies from 0 for the ideal depolarizer to 1 for nondepolarizing Mueller matrices. The average degree of polarization also varies from 0 to 1 and characterizes the typical level of depolarization. Although the depolarization index is very often close to the average degree of polarization, these two metrics can differ by more than 0.5 for certain Mueller matrices.

Optimization of Mueller matrix polarimeters in the presence of error sources

Methods are presented for optimizing the design of Mueller matrix polarimeters and and in particular selecting the retardances and orientation angles of polarization components to ensure accurate reconstruction of a samples Mueller matrix in the presence of error sources. Metrics related to the condition number and to the singular value decomposition are used to guide the design process for Mueller matrix polarimeters with the goal of specifying polarization elements, comparing polarimeter configurations, estimating polarimeter errors, and compensating for known error sources. The use of these metrics is illustrated with analyses of two example polarimeters: a dual rotating retarder polarimeter, and a dual variable retarder polarimeter.

Polarimetric characterization of liquid-crystal-on-silicon panels

Mueller matrix imaging polarimetry of liquid-crystal-on-silicon (LCoS) panels provides detailed information useful for the diagnosis of LCoS problems and to understand the interaction of LCoS panels with other projector components. Data reduction methods are presented for the analysis of LCoS Mueller matrix images yielding contrast ratio, efficiency, spatial uniformity, and the calculation of optimum trim retarders. The effects of nonideal retardance, retardance orientation, and depolarization on LCoS system performance are described. The white-state and dark-state Mueller matrix images of an example LCoS panel are analyzed in terms of LCoS performance metrics typical for red-green-blue wavelengths of 470, 550, and 640 nm. Variations of retardance, retardance orientation, and depolarization are shown to have different effects on contrast ratio, efficiency, and brightness. Thus Mueller matrix images can diagnose LCoS problems in a way different from radiometric testing. The calculation of optimum trim retarders in the presence of spatial variations is discussed. The relationship of the LCoS retardance in single-pass (from front to back) to the double-pass retardance (from entrance to exit) is established and used to clarify coordinate system issues related to Mueller matrices for reflection devices.

Mueller matrix retinal imager with optimized polarization conditions.

A new Mueller matrix polarimeter was used to image the retinas of normal subjects. Light from a linearly polarized 780 nm laser was passed through a system of variable retarders and scanned across the retina. Light returned from the eye passed through a second system of retarders and a polarizing beamsplitter to two confocal detection channels. Optimization of the polarimetric data reduction matrix was via a condition number metric. The accuracy and repeatability of polarization parameter measurements were within +/- 5%. The magnitudes and orientations of retardance and diattenuation, plus depolarization, were measured over 15 degrees of retina for 15 normal eyes.