J. Scott Tyo

Review of passive imaging polarimetry for remote sensing applications

Imaging polarimetry has emerged over the past three decades as a powerful tool to enhance the information available in a variety of remote sensing applications. We discuss the foundations of passive imaging polarimetry, the phenomenological reasons for designing a polarimetric sensor, and the primary architectures that have been exploited for developing imaging polarimeters. Considerations on imaging polarimeters such as calibration, optimization, and error performance are also discussed. We review many important sources and examples from the scientific literature.

Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic error

The relationship between system condition and signal-to-noise ratio (SNR) in reconstructed Stokes parameter images is investigated for rotating compensator, variable retardance, and rotating analyzer Stokes vector (SV) polarimeters. A variety of optimal configurations are presented for each class of systems. The operation of polarimeters is discussed in terms of a four-dimensional conical vector space; and the concept of nonorthogonal bases, frames, and tight frames is introduced to describe the operation of SV polarimeters. Although SNR is an important consideration, performance of a polarimeter in the presence of errors in the calibration and alignment of the optical components is also important. The relationship between system condition and error performance is investigated, and it is shown that an optimum system from the point of view of SNR is not always an optimum system with respect to error performance. A detailed theory of error performance is presented, and the error of a SV polarimeter is shown to be related to the stability and condition number of the polarization processing matrices. The rms error is found to fall off as the inverse of the number of measurements taken. Finally, the concepts used to optimize SV polarimeters are extended to be useful for full Mueller matrix polarimeters.

Noise equalization in Stokes parameter images obtained by use of variable-retardance polarimeters

An imaging variable retardance polarimeter was developed and tested by Tyo and Turner [Proc. SPIE 3753, 214 (1999)]. The signal-to-noise ratio (SNR) in the reconstructed polarization images obtained with this system varied for the four Stokes parameters. The difference in SNR is determined to be due to differences in the Euclidean lengths of the rows of the synthesis matrix used to reconstruct the Stokes parameters from the measured intensity data. I equalize (and minimize) the lengths of the rows of this matrix by minimizing the condition number of the synthesis matrix, thereby maximizing the relative importance of each of the polarimeter measurements. The performance of the optimized system is demonstrated with simulated data, and the SNR is shown to increase from a worst case of -3.1 dB for the original settings to a worst case of +5.0 dB for the optimized system.

Spectrally adaptive infrared photodetectors with bias-tunable quantum dots

Quantum-dot infrared photodetectors (QDIPs) exhibit a bias-dependent shift in their spectral response. In this paper, a novel signal-processing technique is developed that exploits this bias-dependent spectral diversity to synthesize measurements that are tuned to a wide range of user-specified spectra. The technique is based on two steps: The desired spectral response is first optimally approximated by a weighted superposition of a family of bias-controlled spectra of the QDIP, corresponding to a preselected set of biases. Second, multiple measurements are taken of the object to be probed, one for each of the prescribed biases, which are subsequently combined linearly with the same weights. The technique is demonstrated to produce a unimodal response that has a tunable FWHM (down to Δλ~0.5 μm) for each center wavelength in the range 3–8 μm, which is an improvement by a factor of 4 over the spectral resolution of the raw QDIP.

Variable-retardance, Fourier-transform imaging spectropolarimeters for visible spectrum remote sensing

An imaging, variable-retardance, Fourier-transform spectropolarimeter is presented that is capable of creating spectropolarimetric images of scenes with independent characterization of spatial, spectral, and polarimetric information. The device has a spectral resolution of approximately 225 cm(-1), making it truly hyperspectral in nature. Images of canonical targets such as spheres and cylinders obtained in a laboratory setup are presented. The results demonstrate the capability of developing systems to collect spectropolarimetric data of field images by use of the concept of pushbroom scanning and serial collection of polarimetric information. Further development of a parallelized collection strategy would allow the collection of near-real-time images of real-world targets.

Total elimination of sampling errors in polarization imagery obtained with integrated microgrid polarimeters.

Microgrid polarimeters operate by integrating a focal plane array with an array of micropolarizers. The Stokes parameters are estimated by comparing polarization measurements from pixels in a neighborhood around the point of interest. The main drawback is that the measurements used to estimate the Stokes vector are made at different locations, leading to a false polarization signature owing to instantaneous field-of-view (IFOV) errors. We demonstrate for the first time, to our knowledge, that spatially band limited polarization images can be ideally reconstructed with no IFOV error by using a linear system framework.

Interpolation strategies for reducing IFOV artifacts in microgrid polarimeter imagery

Microgrid polarimeters are composed of an array of micro-polarizing elements overlaid upon an FPA sensor. In the past decade systems have been designed and built in all regions of the optical spectrum. These systems have rugged, compact designs and the ability to obtain a complete set of polarimetric measurements during a single image capture. However, these systems acquire the polarization measurements through spatial modulation and each measurement has a varying instantaneous field-of-view (IFOV). When these measurements are combined to estimate the polarization images, strong edge artifacts are present that severely degrade the estimated polarization imagery. These artifacts can be reduced when interpolation strategies are first applied to the intensity data prior to Stokes vector estimation. Here we formally study IFOV error and the performance of several bilinear interpolation strategies used for reducing it.

Band limited data reconstruction in modulated polarimeters

Data processing for sequential in time polarimeters based on the Data Reduction Matrix technique yield polarization artifacts in the presence of time varying signals. To overcome these artifacts, polarimeters are designed to operate at higher and higher speeds. In this paper we describe a band limited reconstruction algorithm that allows the measurement and processing of temporally varying Stokes parameters without artifacts. An example polarimeter consisting of a rotating retarder and polarizer is considered, and conventional processing methods are compared to a band limited reconstruction algorithm for the example polarimeter. We demonstrate that a significant reduction in error is possible using these methods.

The effects of thermal equilibrium and contrast in LWIR polarimetric images

Long-wave infrared (LWIR) polarimetric signatures provide the potential for day-night detection and identification of objects in remotely sensed imagery. The source of optical energy in the LWIR is usually due to thermal emission from the object in question, which makes the signature dependent primarily on the target and not on the external environment. In this paper we explore the impact of thermal equilibrium and the temperature of (unseen) background objects on LWIR polarimetric signatures. We demonstrate that an object can completely lose its polarization signature when it is in thermal equilibrium with its optical background, even if it has thermal contrast with the objects that appear behind it in the image.

Design and optimization of partial Mueller matrix polarimeters.

Mueller matrix polarimeters (MMPs) are designed to probe the polarization properties of optical scattering processes. When using a MMP for a detection, discrimination, classification, or identification task, a user considers certain elements of the Mueller matrix. The usual way of performing this task is to measure the full Mueller matrix and discard the unused elements. For polarimeter designs with speed, miniaturization, or other constraints, it may be desirable to have a system with reduced dimensionality that measures only elements of the Mueller matrix that are important in a particular application as efficiently as possible. In this paper, we develop a framework that allows partial MMPs to be analyzed. Quantitative metrics are developed by considering geometrical relationships between the space spanned by a particular MMP and the space occupied by the scene components. The method is generalized to allow the effects of noise to be considered. The results are general and can also be used to optimize complete and overspecified MMPs for performing specific tasks, as well.