Structured decomposition design of partial Mueller matrix polarimeters
01 Jul 2015-Journal of The Optical Society of America A-optics Image Science and Vision (Optical Society of America)-Vol. 32, Iss: 7, pp 1302-1312
TL;DR: This paper considers the structure of the Mueller matrix and the ability to probe it using a reduced number of measurements, and develops analysis tools and an optimization method 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.
Abstract: 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.
Citations
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TL;DR: This work demonstrates post-processing compressions of the full Mueller matrix that preserve detection performance and the J-optimal Channelized Quadratic Observer method for optimizing polarimetric measurements demonstrates equivalent AUC values for the full Muller matrix and 6 J-CQO optimized measurements.
Abstract: Prior work demonstrated significant contrast in visible wavelength Mueller matrix images for healthy and pre-cancerous regions of excised cervical tissue. This work demonstrates post-processing compressions of the full Mueller matrix that preserve detection performance. The purpose of this post-processing is to understand polarimetric measurement utility for computing mathematical observers and designing future imaging protocols. The detection performance of the full Mueller matrix, and both linear and non-linear parameters of the Mueller matrix will be compared. The area under the receiver operating characteristic (ROC) curve, otherwise known as the AUC, is the gold standard metric to quantify detection performance in medical applications. An AUC = 1 is perfect detection and AUC = 0.5 is the performance of guessing. Either the scalar retardance or the 3 smallest eigenvalues of the coherency matrix yield an average AUC of 0.94 or 0.93, respectively. When these four non-linear parameters are used simultaneously the average AUC is 0.95. The J-optimal Channelized Quadratic Observer (J-CQO) method for optimizing polarimetric measurements demonstrates equivalent AUC values for the full Muller matrix and 6 J-CQO optimized measurements. The advantage of this optimization is that only 6 measurements, instead of 16 for the full Mueller matrix, are required to achieve this AUC.
50 citations
TL;DR: It is shown that an incomplete, nine-element Mueller matrix with a row and a column missing, obtained in a partial polarimetry experiment, can be completed to a full, 16-elementueller matrix, provided depolarization is absent experimentally.
Abstract: Conventional generalized ellipsometry instrumentation is capable of measuring 12 out of the 16 elements of the Mueller matrix of the sample. The missing column (or row) of the experimental partial Mueller matrix can be analytically determined under additional assumptions. We identify the conditions necessary for completing the partial Mueller matrix to a full one. More specifically, such a completion is always possible if the sample is nondepolarizing; the fulfillment of additional conditions, such as the Mueller matrix exhibiting symmetries or being of a special two-component structure, are necessary if the sample is depolarizing. We report both algebraic and numerical procedures for completing the partial 12-element Mueller matrix in all tractable cases and validate them on experimental examples.
20 citations
TL;DR: In this article, the Stokes-Mueller formula was used to improve the performance of the ROPI method by rotating the polarizer mechanically and using Mueller matrix based polarization information processing for precise control of the illumination polarization angle.
13 citations
TL;DR: In this article, a machine learning based channel filtering framework for channeled polarimeters is proposed, where the machines are trained to predict anti-aliasing filters according to the distribution of the measured data adaptively.
Abstract: 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.
6 citations
01 Jan 2016
TL;DR: In this paper, the trade-off between noise and bandwidth in spatio-temporal channeled Mueller matrix polarimetric systems has been investigated, and cost functions are developed to jointly optimize systems with good bandwidth and noise performance.
Abstract: Polarimetric systems design has seen recent utilization of linear systems theory for system descriptions. Although noise optimal systems have been shown, bandwidth performance has not been addressed in depth generally and is particularly lacking for Mueller matrix (active) polarimetric systems. Bandwidth must be considered in a systematic way for remote sensing polarimetric systems design. The systematic approach facilitates both understanding of fundamental constraints and design of higher bandwidth polarimetric systems. Fundamental bandwidth constraints result in production of polarimetric “artifacts” due to channel crosstalk upon Mueller matrix reconstruction. This dissertation analyzes bandwidth trade-offs in spatio-temporal channeled Mueller matrix polarimetric systems. Bandwidth is directly related to the geometric positioning of channels in the Fourier (channel) space, however channel positioning for polarimetric systems is constrained both physically and by design parameters like domain separability. We present the physical channel constraints and the constraints imposed when the carriers are separable between space and time. Polarimetric systems are also constrained by noise performance, and there is a trade-off between noise performance and bandwidth. I develop cost functions which account for the trade-off between noise and bandwidth for spatio-temporal polarimetric systems. The cost functions allow a systems designer to jointly optimize systems with good bandwidth and noise performance. Optimization is implemented for a candidate spatio-temporal system design, and high temporal bandwidth systems resulting from the optimization are presented. Systematic errors which impact the bandwidth performance and mitigation strategies for these systematic errors are are also presented.
6 citations
References
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TL;DR: The concept of correlation and regression may be applied not only to ordinary one-dimensional variates but also to variates of two or more dimensions as discussed by the authors, where the correlation of the horizontal components is ordinarily discussed, whereas the complex consisting of horizontal and vertical deviations may be even more interesting.
Abstract: Concepts of correlation and regression may be applied not only to ordinary one-dimensional variates but also to variates of two or more dimensions. Marksmen side by side firing simultaneous shots at targets, so that the deviations are in part due to independent individual errors and in part to common causes such as wind, provide a familiar introduction to the theory of correlation; but only the correlation of the horizontal components is ordinarily discussed, whereas the complex consisting of horizontal and vertical deviations may be even more interesting. The wind at two places may be compared, using both components of the velocity in each place. A fluctuating vector is thus matched at each moment with another fluctuating vector. The study of individual differences in mental and physical traits calls for a detailed study of the relations between sets of correlated variates. For example the scores on a number of mental tests may be compared with physical measurements on the same persons. The questions then arise of determining the number and nature of the independent relations of mind and body shown by these data to exist, and of extracting from the multiplicity of correlations in the system suitable characterizations of these independent relations. As another example, the inheritance of intelligence in rats might be studied by applying not one but s different mental tests to N mothers and to a daughter of each
6,122 citations
TL;DR: This paper unify the formulation of these different approaches using transformation theory and an eigenvector analysis of the covariance or coherency matrix of the scattering matrix for target decomposition theory in radar polarimetry.
Abstract: In this paper, we provide a review of the different approaches used for target decomposition theory in radar polarimetry. We classify three main types of theorem; those based on the Mueller matrix and Stokes vector, those using an eigenvector analysis of the covariance or coherency matrix, and those employing coherent decomposition of the scattering matrix. We unify the formulation of these different approaches using transformation theory and an eigenvector analysis. We show how special forms of these decompositions apply for the important case of backscatter from terrain with generic symmetries.
2,369 citations
TL;DR: In this paper, the authors decompose a Mueller matrix into a sequence of three matrix factors: a diattenuator, followed by a retarder, then followed by depolarizer.
Abstract: We present an algorithm that decomposes a Mueller matrix into a sequence of three matrix factors: a diattenuator, followed by a retarder, then followed by a depolarizer. Those factors are unique except for singular Mueller matrices. Based on this decomposition, the diattenuation and the retardance of a Mueller matrix can be defined and computed. Thus this algorithm is useful for performing data reduction upon experimentally determined Mueller matrices.
1,220 citations
TL;DR: 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 and the concept of nonorthogonal bases, frames, and tight frames is introduced to describe the operation of SV polarimeters.
Abstract: 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.
318 citations
Journal Article•
TL;DR: In this paper, the authors propose an approach unifiee a l'algebre de la polarisation en utilisant les groupes unitaires speciaux SU(2) et SU(4) and leurs homomorphismes respectifs.
298 citations