Bandwidth and Noise in Spatio-temporally Modulated Mueller Matrix Polarimeters

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 also presented. Finally, a portable imaging Mueller matrix system is built and analyzed based on the theoretical bandwidth analysis and system bandwidth optimization. Temporal bandwidth performance is improved by 300% over a conventional dual rotating retarder Mueller matrix polarimeter. Reconstruction results from the physical instrument are presented, and issues with the implemented system design are discussed.