Israel J. Vaughn

Noise reduction in a laser polarimeter based on discrete waveplate rotations

While several analyses of polarimeter noise-reduction have been published, little data has been presented to support the analytical results, particularly for a laser polarimeter based on measurements taken at discrete, independent rotation angles of two birefringent waveplates. This paper derives and experimentally demonstrates the reduction of both system and speckle noise in this type of laser polarimeter, achieved by optimizing the rotation angles of the waveplates by minimizing the condition numbers of the appropriate matrix equation. Results are demonstrated experimentally in signal-to-noise ratio (SNR) variations for a range of materials and spatial bandwidths. Use of optimal waveplate angles is found to improve the average SNR of the normalized Mueller matrix over speckle by a factor of up to 8 for a non-depolarizing material, but to provide little improvement for a depolarizing material. In the limit of zero spatial bandwidth, the average SNR of the normalized Mueller matrix over speckle is found to be greater than one for a non-depolarizing material and less than one for a depolarizing material.

Classification using active polarimetry

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.

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.

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.

A portable imaging Mueller matrix polarimeter based on a spatio-temporal modulation approach: theory and implementation

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.

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.

Bandwidth and crosstalk considerations in a spatio-temporally modulated polarimeter

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.

Overview of visualization strategies for polarimetric imaging data

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.

Channel-first design of modulated polarimeters

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.

A nine-channeled partial Mueller matrix polarimeter

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.