We have recently extended the concepts of generalized channeled polarimetry to keep proper account of all the multi-carrier harmonics generated by Photoelastic Modulators (PEMs). In order to build a Mueller matrix polarimeter out of such devices, the system needs to include at least four PEMs, each modulating at a different frequency. In our previous treatment, we have deliberately deferred the concept of multi-carrier harmonics of different PEMs mixing within the same channel. Despite the choice being a reasonable one due to the difficulty of precisely controlling PEMs' mechanical resonance properties due to manufacturing tolerances and temperature dependence, there are instances where having mixed channels enables a significantly better reconstruction SNR. Here, we revisit the omission by quantifying the additional performance that can be achieved with mixed channels, and explore the bounds on the level of frequency shift control required to ensure the predicted performance. We demonstrate that deliberate design of mixed channels is particularly beneficial when reconstructing with a low number of channels. Conversely, the level of control required to ensure an accurate enough alignment of higher harmonics leads to diminishing returns when reconstructing with a high number of channels.
Channeled polarimeters modulate the Stokes parameters onto harmonic carriers of a particular independent domain such as time, space, wavenumber, or angle of incidence. Because the modulation creates many channels within the frequency sampling space of the detector array, channel bandwidth is crucial for this type of device. Much researches has been conducted to exploit more bandwidth in polarimeters that modulate in space, time, or wavenumber along. Our group and others have provided previous theoretical designs for hybrid-domain modulation strategies in order to extend the distance between channels in the Fourier domain through a bandwidth tradeoff approachin order to provide a wider channel bandwidth than systems utilize only one of the corresponding domains. This paper will present results from a a spatio-temporally modulated Stokes polarimeter. The system trades off the bandwidth between space and time to obtain further channel separations. In this work, we demonstrate the system implementation and the experiment results. The experiment compared the spatio-temporal hybrid domain modulated Stokes polarimeter with the spatial and temporal domain only modulated Stokes polarimeter to verify the prediction from the theoretical work. The experimental results indicated that comparing to the spatial and temporal domain only modulated Stokes polarimeters the hybrid-domain modulated polarimeter provides a better image reconstruction and contrast on signals with moderate bandwidth extension. We also consider adaptive reconstruction methods that allow the reconstruction filters to be tailored to the input data. This strategy will allow the bandwidth of the system to be optimally exploited for any particular task.
The method for mapping linear polarization imaging variables to the color channels of hue, saturation, and value in the HSV color space is a common technique for the visualization of polarization imaging data. This method utilizes the structural similarities between polarization vision and color vision so that the full linear polarization information is depicted in a single image. Recent developments have attempted to address issues, arising from the fact that the HSV color space is not an accurate model of human color vision, by mapping the polarization channels of intensity, degree, and angle to the color channels of lightness, colorfulness, and hue defined in the perceptually uniform color space CAM02-UCS. While the theoretical benefits of this method have been demonstrated using metrics of perceptual uniformity and channel independence, the practical benefits to human observers has not been studied. In this user study, the two methods are compared using a series of forced-choice questions on the perceived magnitude differences in DoLP value to determine 1) which method produces fewer errors, 2) which method produces a more linear scale in degree of polarization perception, 3) whether the perception of degree of polarization is independent of intensity and angle of polarization.
Recently we have presented theoretical predictions and numerical modeling that show that a more advanced processing scheme can significantly improve the performance of photoelastic modulator (PEM)-based Mueller polarimeters. Of note, by simply including all of the multi-carrier harmonics rather than a hand-selected subset thereof, the sensitivity of the system can be enhanced by up to a factor of six in certain elements of the Mueller matrix. This paper extends our work on PEM-based Mueller polarimeters to PEM-based partial Mueller systems with 2 PEMs, one PEM each in the generator and analyser. Our findings clearly demonstrates significant performance improvement through the use of a substantially large set of multi-carrier harmonics rather than a hand-selected subset. We also present results from our experimental PEM testbed system that verifies the numerical findings.
Collected sources for the different types of visualizations used in the field of polarization imaging are not extensive. Here, we survey and review the different visualization techniques in passive polarimetric imaging. Analysis of the methods is done by applying various concepts from the field of visualization. We provide recommendations for choosing a visualization based on the data structure, spatial frequency, and analysis goals.
Quantum key distribution (QKD) is a method for establishing secure cryptographic keys between two parties who share an optical, “quantum” channel and an authenticated classical channel. To share such keys across the globe, space-based links are required and in the near term these will take the form of trusted node, key management satellites. We consider such channels between two nanosatellite spacecraft for polarization entanglement-based QKD, and the optical channel is described in detail. Quantum channels between satellites are useful for balancing keys within constellations of trusted node QKD satellites and, in the future, may have applications in long-distance qubit exchange between quantum computers and in fundamental physics experiments. The nanosatellite mission proposed uses an optical link with 80-mm diameter optical terminals. If such a link could be maintained with 10-μrad pointing accuracy, then this would allow QKD to be performed for satellite separations up to around 400 km. A potential pointing and tracking system is also described although currently this design would likely limit the satellite separation to 100 to 150 km.
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.
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.
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.
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.
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.
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.
Polarimeters operate by making polarization-dependent alterations in the intensity of the optical ﬁeld. Modulated polarimeters introduce controlled ﬂuctuations as a function of time, spatial position, wavelength, angle of incidence, or any other independent variable. These ﬂuctuations create channels in frequency space that can be used to carry the polarimetric information. Since polarimeters are then inherently multiplexed information systems, issues of noise, bandwidth, channel cross-talk, and system conditioning become immediately important. This paper reviews much of the work over the past two decades on polarimeter design, and presents some of the most recent work on hybrid and non-periodic modulation schemes that hold out potential for maximizing system bandwidth.
In prior work,1,2 we introduced methods to treat channeled systems in a way that is similar to Data Reduction Method (DRM), by focusing attention on the Fourier content of the measurement conditions. Introduction of Q enabled us to more readily extract the performance of the system and thereby optimize it to obtain reconstruction with the least noise. The analysis tools developed for that exercise can be expanded to be applicable to partial Mueller Matrix Polarimeters (pMMPs), which were a topic of prior discussion as well. In this treatment, we combine the principles involved in both of those research trajectories and identify a set of channeled pMMP families. As a result, the measurement structure of such systems is completely known and the design of a channeled pMMP intended for any given task becomes a search over a finite set of possibilities, with the additional channel rotation allowing for a more desirable Mueller element mixing.
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.
"Linear systems" is a broad and important area in many scientific and engineering disciplines, and it is especially important in optics because it forms the basis for Fourier optics, diffraction theory, image-quality assessment, and many other areas. This Field Guide provides the practicing optical engineer with a reference for the basic concepts and techniques of linear systems, including Fourier series, continuous and discrete Fourier transforms, convolution, sampling and aliasing, and MTF/PSF using the language, notation, and applications from optics, imaging, and diffraction.
Nighttime active SWIR imaging has resolution, size, weight, and power consumption advantages over passive MWIR and LWIR imagers for applications involving target identification. We propose that the target discrimination capability of active SWIR systems can be extended further by exerting polarization control over the illumination source and imager, i.e. through active polarization imaging. In this work, we construct a partial Mueller matrix imager and use laboratory derived signatures to uniquely identify target materials in outdoor scenes. This paper includes a description of the camera and laser systems as well as discussion of the reduction and analysis techniques used for material identification.
We have developed a tool to simulate reconstruction behavior of a snapshot Mueller matrix channeled spectropolarimeter
in presence of noise. A shortcoming of channeled spectropolarimeters is that with a large number
of channels, each channel has to be narrow, which limits the reconstruction accuracy and provides a bandlimit
constraint on the object. The concept of making partial Mueller matrix measurements can be extended to a channeled
system by considering polarimeter designs that make irrelevant Mueller matrix elements unreconstructable,
while decreasing the number of channels and subsequently increasing the bandwidth available to each channel.
This tool optimizes the distribution of the available bandwidth towards the polarization elements that we care
about most. A generic linear systems model of a spectropolarimeter with four variable retarders allows us to
construct a matrix that maps Mueller matrix elements into corresponding channels. A pseudo-inverse of that
matrix enables the reconstruction of Mueller matrix elements from channels. By specifying a mask vector, we can
control the subjective importance of each of the reconstructed elements and weigh their error contribution accordingly.
Finally, searching the design space allows us to find a design that maximizes the Signal-to-Noise-Ratio
(SNR) for a specific partial Mueller matrix measurement task.
The goal of this study is to develop a spectropolarimeter for purposes of assessing polarization signatures in
skin scattering on a regional scale. Prior research has that certain skin lesions have identifiable polarization
signatures;1-3 however, those studies were limited to single lesion evaluation and are not convenient for screening
patients with many suspicious legions. As a precursor to the future instrument, a simple actively illuminated
Stokes spectropolarimeter was constructed to gather preliminary data about expected signatures and the required
performance (resolution, wavelength, polarization state, etc.). This spectropolarimeter consists of a rotating
retarder and a hyperspectral camera4 that scans through wavelengths by means of a Liquid Crystal Tunable
Filter (LCTF). Data is captured in a serial fashion, where LCTF scans through eight wavelengths at each of the
four retarder orientations. With a single acquisition taking 23 seconds to complete, it makes the issue of image
registration very important. After proper alignment, the acquired images reveal that wavelength-dependent
polarization signatures exist on a regional scale. In particular, it was found that polarization factors such as
Degree of Linear Polarization (DoLP) tend to suppress many uninteresting skin features like wrinkles and skin
texture, while capturing information that is not necessarily apparent in the intensity image.