Scene-adaptive spatially channeled imaging Mueller polarimeter.

A spatially adaptive Mueller matrix imaging polarimeter is described, simulated, and demonstrated with preliminary experiments. The system uses a spatial light modulator (SLM) in the polarization state generator (PSG) to create spatial carriers that controlled by the pattern written to the SLM. The polarization state analyzer (PSA) is a commercial division of focal plane imaging polarimeter. The PSG/PSA pair form a 9-channeled partial Mueller matrix polarimeter that measures a 3 × 3 sub-matrix of the Mueller matrix. We demonstrate that adapting the PSG modulation to the spatial frequency structure of the scene can reduce channel crosstalk and improve reconstruction accuracy. Initial experiments are performed that demonstrate the SLM's ability to produce sufficient modulation diversity to create the desired channel structure. Though there are several experimental challenges to obtain accurate Mueller matrix imagery, we demonstrate a system that adapts to the particular scene spatial frequency structure.

Multi-harmonic reconstruction of photoelastic modulator-based Mueller polarimeters using the complex Q-matrix.

Analysis of data generated by Mueller matrix polarimeters using two photoelastic modulators has been evolving with the improvements in data acquisition and digital signal processing (DSP). Historical processing of the temporal data generated by these devices has involved isolating the frequencies via hardware signal processing (e.g., lock-in amplifiers) or the numerical computation of Fourier integrals of recorded temporal data. Both avenues have their advantages, but the DSP aspects of the latter provide greater flexibility in choice of harmonics for processing. While conventional processing uses one harmonic for each desired Mueller matrix element, recent work has demonstrated that theoretical improvements are possible by coherently combining the information in multiple harmonic channels for each element. We demonstrate some recent progress in DSP that enables these polarimeters' data to be more fully exploited by addressing two key issues in the Fourier domain: spectral leakage and phase recovery. Adequately addressing these issues enables numerical analysis of the temporal data in the complex Fourier domain and delivers Mueller matrix results in which spectral phase information is used to recover the matrix elements and determine their signs automatically. We explore the application of this complex analysis and how the precision and accuracy of the results are affected by common experimental and DSP limitations compared to the usual magnitude-only analysis in the Fourier domain. The multi-harmonic method can provide a theoretical factor of 1.3-1.7 improvement in instrumental precision, and our experimental results approach that theoretical range.

Spectral-temporal channeled spectropolarimetry using deep-learning-based adaptive filtering.

Channeled spectropolarimetry (CSP) employing low-pass channel extraction filters suffers from cross talk and spectral resolution loss. These are aggravated by empirically defining the shape and scope of the filters for different measured. Here, we propose a convolutional deep-neural-network-based channel filtering framework for spectrally-temporally modulated CSP. The network is trained to adaptively predict spectral magnitude filters (SMFs) that possess wide bandwidths and anti-cross-talk features that adapt to scene data in the two-dimensional Fourier domain. Mixed filters that combine the advantages of low-pass filters and SMFs demonstrate superior performance in reconstruction accuracy.

Transcending conventional snapshot polarimeter performance via neuromorphically adaptive filters.

A channeled Stokes polarimeter that recovers polarimetric signatures across the scene from the modulation induced channels is preferrable for many polarimetric sensing applications. Conventional channeled systems that isolate the intended channels with low-pass filters are sensitive to channel crosstalk effects, and the filters have to be optimized based on the bandwidth profile of scene of interest before applying to each particular scenes to be measured. Here, we introduce a machine learning based channel filtering framework for channeled polarimeters. The machines are trained to predict anti-aliasing filters according to the distribution of the measured data adaptively. A conventional snapshot Stokes polarimeter is simulated to present our machine learning based channel filtering framework. Finally, we demonstrate the advantage of our filtering framework through the comparison of reconstructed polarimetric images with the conventional image reconstruction procedure.

Nonseparable modulation strategy for channeled spatiotemporal Stokes polarimeters.

Spatiotemporally modulated polarimeters have shown promising imaging performance by leveraging the tradeoff between spatial bandwidth and temporal bandwidth to outperform polarimeters that use spatial or temporal modulation alone. However, the existing separable modulation strategy, in which the spatial carriers are generated independently from the temporal carriers, makes such devices sensitive to the systematic errors of the rotation element inevitably. In this paper, we propose two novel strategies that have spatiotemporal modulation that is inherently mixed. The method enables different elements of the Mueller matrix to be used to create the carriers, reducing the effects of systematic errors in different ways. We present the indepth comparison of the channel structure and the reconstruction accuracy of each modulation strategy in various bandwidth scenarios under the presence of systematic error. Simulation results show that the nonseparable modulation can provide higher reconstruction accuracy of polarimetric information as compared to the separable strategy.

Spectral-temporal hybrid modulation for channeled spectropolarimetry.

Channeled spectropolarimeters (CSPs) are capable of estimating spectrally resolved Stokes parameters from a single modulated spectrum. However, channel crosstalk and subsequent spectral resolution loss reduce the reconstruction accuracy and limit the systems' scope of application. In this paper, we propose a spectral-temporal modulation strategy with the aim of extending channel bandwidth and improving reconstruction accuracy by leveraging the hybrid carriers and allocating channels in the two-dimensional Fourier domain that yield optimal performance. The scheme enables spectral bandwidth and temporal bandwidth to be traded off, and provides flexibility in selecting demodulation strategies based on the features of the input. We present an in-depth comparison of different systems' performances in various input features under the presence of noise. Simulation results show that the hybrid-modulation strategy offers the best comprehensive performance as compared to the conventional CSP and dual-scan techniques.

Structured decomposition of a multi-snapshot nine-reconstructables Mueller matrix polarimeter.

Snapshot channeled polarimeters forgo temporal modulation in favor of modulating polarization information in either space or wavenumber. We have recently introduced methodologies for describing both channeled and partial polarimeters. In this paper, we focus on the nine-reconstructables design, which limits the resolution loss by reducing the number of carriers. The architecture offers a number of favorable trade-offs: a factor of 5.44 increase in spatial bandwidth or a factor of 3.67 increase in spectral bandwidth, for a smaller amount of temporal bandwidth loss as dictated by the number of snapshots taken. The multi-snapshot structured decomposition given here allows one to analytically shape the measured space with optimal noise characteristics and minimum system complexity. A two-snapshot system can measure a premeditated set of 14 reconstructables; we provide the null space for the subset of optimal systems that also achieve better SNR than the baseline single-snapshot system. A three-snapshot system can measure all 16 Mueller elements while offering an overall 26.3% or 50.4% better bandwidth-SNR figure of merit for the spectral and spatial systems, respectively. Finally, four-snapshot systems provide diminishing returns, but may be more implementable.

Imaging dynamic scenes with a spatio-temporally channeled polarimeter.

Most channeled polarimeters modulate the intensity in a single independent domain such as space, time, or wavenumber. Recently we proposed and modeled a concept for a system modulated simultaneously in space and time [Opt. Lett.43, 2768 - 2771 (2018)] and demonstrated that superior performance could be obtained by trading off spatial and temporal bandwidth in the system. Here we present results from a prototype realization of such a system and demonstrate quantitatively that the spatial modulation transfer function of the imager can be improved by choosing the appropriate modulation strategy for a given scene spatial and temporal bandwidth. We demonstrate that a hybrid modulation system can achieve the high spatial frequency performance of a time modulated system for static scenes, or it can achieve the high temporal frequency performance of a spatially modulated system for rapidly varying scenes, and it can out perform both systems for scenes with intermediate bandwidth in both domains. Moreover, the physical system implementation is essentially the same for each system type, which in principle allows the reconstruction strategy to be selected in real-time by choosing the appropriate reconstruction filters.

Multi-carrier channeled polarimetry for photoelastic modulator systems.

Photoelastic modulator-based polarimeters use multi-carrier modulation schemes that are more complicated than the single carriers of rotating optics. Current state-of-the-art reconstruction implementations favor mathematical simplicity by using significantly abridged subsets of channels. In this Letter, we extend our generalized channeled polarimetry principles to address the challenges associated with multi-carrier modulation schemes. We demonstrate the performance forfeited by existing systems through the use of an incomplete set of information channels, as well as propose a set of more optimal system parameters that achieve better reconstruction noise characteristics. The overall improvement corresponds to a better sensitivity of up to a factor of six.

Perceptually uniform color space for visualizing trivariate linear polarization imaging data.

The visualization of polarimetric data is often done by color mapping the linear parameters using the three channels in the HSV color space. Because this color space is not an accurate model of human color perception, the resulting visualization mixes the perceptual channels and contains nonuniformity. To the best of our knowledge, we present a new mapping strategy that reliably and accurately depicts reality by placing the polarization parameters directly into the perceptually uniform channels of CAM02-UCS. This mapping also ensures that regions of high polarization will be more visible, even when the measured irradiance is low.

Channeled spatio-temporal Stokes polarimeters.

We present the analysis and design of spatio-temporal channeled Stokes polarimeters. We extend our recent work on optimal pixelated polarizer arrays by utilizing temporal carrier generation, resulting in polarimeters that achieve super-resolution via the tradeoff between spatial bandwidth and temporal bandwidth. Utilizing the channel space description, we present a linear-Stokes design and two full-Stokes imaging polarimeter designs that have the potential to operate at the full frame rate of the imaging sensor of the system by using hybrid spatio-temporal carriers. If the objects are not spatially bandlimited, the achievable temporal bandwidth is more difficult to analyze; however, a spatio-temporal tradeoff still exists.

Optimal bandwidth and systematic error of full-Stokes micropolarizer arrays.

In this paper, we present the first in-depth analysis of the bandwidth tradeoffs, error performance, and noise resiliency of full-Stokes micropolarizer array (MPA) designs. By applying our Fourier domain tools that provide a systematic way for arranging information carriers and allocating bandwidth, we develop a number of new full-Stokes MPA layouts and compare them to the existing full-Stokes MPAs in the literature, all of which use 2×2 pixel unit cells to build the MPA. We compare the reconstruction accuracy afforded by these traditional designs with the generalized 2×L family of MPAs, a 3×3 tiling, as well as a 2×2×3 layout that uses multiple snapshots and trades off temporal resolution for spatial resolution. Of those systems, the hybrid spatiotemporally modulated 2×2×3 MPA provisions the most bandwidth and provides the highest reconstruction accuracy, while the modified 2×L family remains the best performing single-snapshot MPA. Additionally, we study the degradation of reconstruction accuracy under the presence of systematic error in MPA fabrication. We find that reducing the amount of correlated error is by far the largest factor in ensuring robust performance.

Focal plane filter array engineering I: rectangular lattices.

Focal planes arrays (FPA) measure values proportional to an integrated irradiance with little sensitivity to wavelength or polarization in the optical wavelength range. The measurement of spectral properties is often achieved via a spatially varying color filter array. Recently spatially varying polarization filter arrays have been used to extract polarization information. Although measurement of color and polarization utilize separate physical methods, the underlying design and engineering methodology is linked. In this communication we derive a formalism which can be used to design any type of periodic filter array on a rectangular lattice. A complete system description can be obtained from the number of unit cells, the pixel shape, and the unit cell geometry. This formalism can be used to engineer the channel structure for any type of periodic tiling of a rectangular lattice for any type of optical filter array yielding irradiance measurements.

Optimal bandwidth micropolarizer arrays.

Currently, the best performing micropolarizer array is the 2×4 pattern introduced by LeMaster and Hirakawa. In this Letter, we extend the available set of patterns with the aim of improving reconstruction quality by leveraging the Fourier domain and designing information carriers that yield optimal bandwidth. First, the family of 2×L patterns widens the optimization space of the 2×4 pattern by facilitating variable allocation of bandwidth for channels surrounding polarization and intensity carriers. Second, the 2×2×N patterns present an intriguing option for use within a hybrid spatiotemporal modulation scheme, in which the multiple temporal measurements enable maximum theoretical spatial resolution of reconstructed Stokes parameters.

Adapting the HSV polarization-color mapping for regions with low irradiance and high polarization.

Many mappings from polarization into color have been developed so that polarization information can be displayed. One of the most common of these maps the angle of linear polarization into color hue and degree of linear polarization into color saturation, while preserving the irradiance information from the polarization data. While this strategy enjoys wide popularity, there is a large class of polarization images for which it is not ideal. It is common to have images where the strongest polarization signatures (in terms of degree of polarization) occur in regions of relatively low irradiance: either in shadow in reflective bands or in cold regions in emissive bands. Since the irradiance is low, the chromatic properties of the resulting images are generally not apparent. Here we present an alternate mapping that uses the statistics of the angle of polarization as a measure of confidence in the polarization signature, then amplifies the irradiance in regions of high confidence, and leaves it unchanged in regions of low confidence. Results are shown from an LWIR and a visible spectrum imager.

Design of channeled partial Mueller matrix polarimeters.

In this paper, we introduce a novel class of systems called channeled partial Mueller matrix polarimeters (c-pMMPs). Their analysis benefits greatly by drawing from the concepts of generalized construction of channeled polarimeters as described by the modulation matrix. The modulation matrix resembles that of the data reduction method of a conventional polarimeter, but instead of using Mueller vectors as the bases, attention is focused on the Fourier properties of the measurement conditions. By leveraging the understanding of the measurement's structure, its decomposition can be manipulated to reveal noise resilience and information about the polarimeter's ability to measure the aspect of polarization that are important for any given task. We demonstrate the theory with a numerical optimization that designs c-pMMPs for the task of monitoring the damage state of a material as presented earlier by Hoover and Tyo [Appl. Opt.46, 8364 (2007)APOPAI0003-693510.1364/AO.46.008364]. We select several example systems that produce a fewer-than-full-system number of channels yet retain the ability to discriminate objects of interest. Their respective trade-offs are discussed.

Structured decomposition design of partial Mueller matrix polarimeters.

Partial Mueller matrix polarimeters (pMMPs) are active sensing instruments that probe a scattering process with a set of polarization states and analyze the scattered light with a second set of polarization states. Unlike conventional Mueller matrix polarimeters, pMMPs do not attempt to reconstruct the entire Mueller matrix. With proper choice of generator and analyzer states, a subset of the Mueller matrix space can be reconstructed with fewer measurements than that of the full Mueller matrix polarimeter. In this paper we consider the structure of the Mueller matrix and our ability to probe it using a reduced number of measurements. We develop analysis tools that allow us to relate the particular choice of generator and analyzer polarization states to the portion of Mueller matrix space that the instrument measures, as well as develop an optimization method that is based on balancing the signal-to-noise ratio of the resulting instrument with the ability of that instrument to accurately measure a particular set of desired polarization components with as few measurements as possible. In the process, we identify 10 classes of pMMP systems, for which the space coverage is immediately known. We demonstrate the theory with a numerical example that designs partial polarimeters for the task of monitoring the damage state of a material as presented earlier by Hoover and Tyo [Appl. Opt.46, 8364 (2007)10.1364/AO.46.008364APOPAI1559-128X]. We show that we can reduce the polarimeter to making eight measurements while still covering the Mueller matrix subspace spanned by the objects.

Generalized channeled polarimetry.

Channeled polarimeters measure polarization by modulating the measured intensity in order to create polarization-dependent channels that can be demodulated to reveal the desired polarization information. A number of channeled systems have been described in the past, but their proposed designs often unintentionally sacrifice optimality for ease of algebraic reconstruction. To obtain more optimal systems, a generalized treatment of channeled polarimeters is required. This paper describes methods that enable handling of multi-domain modulations and reconstruction of polarization information using linear algebra. We make practical choices regarding use of either Fourier or direct channels to make these methods more immediately useful. Employing the introduced concepts to optimize existing systems often results in superficial system changes, like changing the order, orientation, thickness, or spacing of polarization elements. For the two examples we consider, we were able to reduce noise in the reconstruction to 34.1% and 57.9% of the original design values.