Visualizing polarimetric imaging data is a difficult task due to its multidimensional nature, and there have been many different approaches to develop techniques for displaying this information. Currently, there is no method for producing effective visualizations, or evaluating their performance in accomplishing their intended goals. A task-based design process can be used to make sure that the unavoidable biases that occur in these visual representations match the biases required for effectively interpreting the information, relationships, and features within the data. As the field of polarimetric imaging grows and extends into other fields, some standardization of effective visualization techniques may be beneficial in communication and continued growth.
Multi-domain modulated polarimeters combine carriers on different domains to exploit the bandwidth of the measurement system. However, the inevitable systematic errors in polarimeters will degrade their bandwidth performance, so we developed a new type of multi-domain modulated polarimeter. Compared with conventional polarimeters and our previous separable designs, this new type of system can avoid some of the negative effects (such as the emergence of extraneous channels) caused by the systematic errors. To illustrate the advantages and disadvantages of both systems, both types of Stokes polarimeters are designed based on the same channel structure and their performance is simulated under systematic errors.
Current visualization techniques for mapping polarization data to a color coordinates defined by the Hue,
Saturation, Value (HSV) color representation are analyzed in the context of perceptual uniformity. Since HSV is
not designed to be perceptually uniform, the extent of non-uniformity should be evaluated by using robust color
difference formulae and by comparison to the state-of-the-art uniform color space CAM02-UCS. For mapping just
angle of polarization with HSV hue, the results show clear non-uniformity and implications for how this can
misrepresent the data. UCS can be used to create alternative mapping techniques that are perceptually uniform.
Implementing variation in lightness may increase shape discrimination within the scene. Future work will be
dedicated to measuring performance of both current and proposed methods using psychophysical analysis.
We recently defined a new formalism for engineering spatial information channels for focal plane filter arrays (FPFAs) in a general way for any physical light property measured via irradiance including spectral bands, polarimetric bands, and general coherence. The formalism encompasses color filter arrays, micropolarizer arrays, and microantenna arrays over a pixelated irradiance sensor. The formalism derives the physical channels available from the parameters of the unit cell used to tile the focal plane array: the unit cell geometry, the filter transmission functions, the number of unit cells, and the unit cell filter weights. We also recently showed that switching the polarization measuring properties in time over a fixed micropolarizer array would perform well compared with snapshot systems, even given increased noise due to doubling the temporal framerate. We present preliminary results on the extension of our FPFA framework to include temporal effects. Instead of a 2D unit cell which completely defines the system channels, a 3D unit cell consisting of 3D attenuation functions on a 3D rectangular lattice in (x,y,t) is defined, and specific examples are shown for micropolarizer array systems with a ferroelectric variable retarder; and a color filter array system utilizing tunable etalons for color filter modulation.
Designing polarimetric systems directly in the channel space has provided insight into how to design new types
of polarimetric systems, including systems which use carriers in hybrid domains of space, time, or spectrum.
Utilizing linear systems theory, we present a full Stokes imaging polarimeter design which has the potential to
operate at half the frame rate of the imaging sensor of the system by utilizing a hybrid spatio-temporal carrier
design. The design places channels on the faces and the edges of the Nyquist cube resulting in the potential
for half the Nyquist limit to be achieved, provided that the spatial frequency of the objects being imaged are
bandlimited to less than 0.25 cycles per pixel. If the objects are not spatially bandlimited, then the achievable
temporal bandwidth is more difficult to analyze. However, a spatio-temporal tradeoff still exists allowing for
increased temporal bandwidth. We present the design of a “Fast Stokes’’ polarimeter and some simulated images
using this design.
We have recently introduced channeled-partial Mueller matrix polarimeters as a potential design for measuring a
limited number of Mueller elements for remote sensing discrimination. Because in such systems the polarization
information is modulated in space or spectrum, the corresponding carrier domain ends up sharing two different
types of information, thus leading to a reduction of bandwidth for each. In this work, we concentrate
on an efficient nine-channel/nine-reconstructables design, which limits the associated resolution loss by limiting
the overall complexity of the system. Employing structured decomposition techniques allows us to produce a
system description that provides an analytically deducible set of reconstructables that include 𝑚00, any two
linear combinations of the elements within the diattenuation vector, any two linear combinations of the elements
within the polarizance vector, as well as the linear combinations specified by the Kronecker product of the
diattenuation and polarizance vectors. Finally, we optimize the available polarimeter parameters to align the
nine reconstructables with the desirables derived from sample data, while maintaining the ability to discriminate
between different objects.
Micropolarizer arrays are occasionally used in partial Stokes, full Stokes, and Mueller matrix polarimeters. When treating modulated polarimeters as linear systems, specific assumptions are made about the Dirac delta functional forms generated in the channel space by micropolarizer arrays. These assumptions are 1) infinitely fine sampling both spatially and temporally and 2) infinite array sizes. When these assumptions are lifted and the physical channel shapes are computed, channel shapes become dependent on both the physical pixel area and shape, as well as the array size. We show that under certain circumstances the Dirac delta function approximation is not valid, and give some bounding terms to compute when the approximation is valid, i.e., which array and pixel sizes must be used for the Dirac delta function approximation to hold. Additionally, we show how the physical channel shape changes as a function of array and pixel size, for a conventional 0°, 45°, −45°, 90° superpixel micropolarizer array configuration.
While active polarimeters have been shown to be successful at improving discriminability of the targets of interest from their background in a wide range of applications, their use can be problematic for cases with strong bandwidth constraints. In order to limit the number of performed measurements, a number of successive studies have developed the concept of partial Mueller matrix polarimeters (pMMPs) into a competitive solution. Like all systems, pMMPs need to be calibrated in order to yield accurate results. In this treatment we provide a method by which to select a limited number of reference objects to calibrate a given pMMP design. To demonstrate the efficacy of the approach, we apply the method to a sample system and show that, depending on the kind of errors present within the system, a significantly reduced number of reference objects measurements will suffice for accurate characterization of the errors.
We present the design and prototyping results for an ultra-wideband rotating polarization modulator that consists of a stack of quartz plates. The plate thicknesses and orientations were optimized such that after rotation of the modulator to 6 different angles before a polarization analyzer, the full Stokes vector can be optimally determined at all wavelengths from 300 to 2500 nm. Additional optimization parameters include minimal variation of the retardance with incidence angle and temperature, and the suppression of polarized spectral fringes for a spectral resolution of 10,000. The prototype modulator's design was re-optimized after the production and measurement of each individual quartz plate. We present the performance of the as-built prototype. To eliminate aliasing with inherent temporal variations of the source, the modulator can be used together with a polarizing beam-splitter (dual-beam" approach). Because of the large sinusoidal spectral variations of the polarization modulation, this modulator can also be considered a "spectral modulator for channeled spectropolarimetry". Therefore, at each modulation state, spectrally resolved polarization information can also be extracted directly, although at limited spectral resolution. We use this modulator as an example of a "multi-domain polarization modulator", and outline a general approach for optimally storing polarization information in all available measurement dimensions (temporal, spatial, spectral), and rendering the overall polarization measurement independent from systematic effects in any of these dimensions.
Imaging polarimeters have been largely used for remote sensing tasks, and most imaging polarimeters are division of time or division of space Stokes polarimeters. Imaging Mueller matrix polarimeters have just begun to be constructed which can take data quickly enough to be useful. We have constructed a Mueller matrix (active) polarimeter utilizing a hybrid modulation approach (modulated in both time and space) based on a micropo- larizer array camera and rotating retarders. The hybrid approach allows for an increase in temporal bandwidth (instrument speed) at the expense of spatial bandwidth (sensor resolution). We present the hybrid approach and associated reconstruction schemes here. Additionally, we introduce the instrument design and some preliminary results and data from the instrument.
Recently we designed and built a portable imaging polarimeter for remote sensing applications.1 Polarimetric imaging operators are a class of linear systems operators in the Mueller matrix reconstruction space, resulting in a set of measurement channels.2 The nature of remote sensing requires channel crosstalk to be minimized for either general Mueller matrix reconstruction or task specific polarimetric remote sensing. We illustrate crosstalk issues for a spatio-temporally modulated Mueller matrix reconstruction operator, and show how to minimize channel crosstalk by maximizing bandwidth between channels. Specifically channel cancellation allows increases in channel bandwidth. We also address the impact that systematic deviations from the ideal operators and i.i.d. noise have on the system channel structure.
Axially symmetric polarized beams have attracted great interest recently in the field of optics. There have been several viable proposals concerning axially symmetric polarizers, also referred to as radial polarizers. In contrast, proposals for axially symmetric wave plates have strong dependence on wavelength. Moreover, the structure of the axially symmetric wave plates inherently introduces spatial dispersion. As a solution to these problems, we propose an achromatic axially symmetric wave plate based on internal Fresnel reflection that does not introduce spatial dispersion. It is possible to generate the achromatic axially symmetric polarized beam. In this paper, we show the principle of the achromatic axially symmetric wave plate and the evaluation results of the optical element using a Mueller matrix polarimeter.
Active (Mueller matrix) remote sensing is an under-utilized technique for material discrimination and classication.
A full Mueller matrix instrument returns more information than a passive (Stokes) polarimeter; Mueller
polarimeters measure depolarization and other linear transformations that materials impart on incident Stokes
vectors, which passive polarimeters cannot measure. This increase in information therefore allows for better
classication of materials (in general). Ideally, material classication over the entire polarized BRDF is desired,
but sets of Mueller matrices for dierent materials are generally not separable by a linear classier over elevation
and azimuthal target angles. We apply non-linear support vector machines (SVM) to classify materials over
BRDF (all relevant angles) and show variations in receiver operator characteristic curves with scene composition
and number of Mueller matrix channels in the observation.
Imaging polarimeters have currently and historically been largely used for remote sensing tasks. They have also
been used to evaluate the defects and calibrate the polarization of liquid crystal displays. A particular type of
polarimeter that has a great deal of unrealized potential is the microgrid array linear Stokes polarimeter. This
type of polarimeter is not often used because of reconstruction errors. If these errors could be minimized, or
mitigated via proper algorithmic reconstruction, then they have advantages over other types of polarimeters,
mainly calibration (not much is needed) and proper operation over wide wavelength bands (due to the use of
wire grid linear polarizers). In the paper I analyze the imaging equation of the microgrid Stokes polarimeter,
using the full vectorial electric field.