Computational Polarimetry: A Bayesian Framework for Polarimetric System Design
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Date
2019-09-10
Authors
Haider, Shahid
Journal Title
Journal ISSN
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Publisher
University of Waterloo
Abstract
In this thesis, we propose a novel polarimetric system design framework that computationally evaluates a design to solve an optical problem. It does this by explicitly formulating the logical connections and dependencies in the design of the components in a polarimetric system (i.e the components chosen affect the choice of their parameters; the parameters of each component affects the measurements, and the system design requirements and constraints affect them all) in a Bayesian network. With this Bayesian network formulation, for the first time, prior knowledge of components, system component parameters, and measurement processes can be explicitly modelled in conjunction with system design requirements and constraints in a unified way for the design of polarimetric systems. With this prior knowledge of system processes, component behaviour, and design requirements and constraints, we can design polarimetric systems to achieve design objectives while reducing the effects of stochastic and deterministic error.
We demonstrate these capabilities in this thesis by first designing a single linear polariser, polarisation angle estimation system to produce a desired and measurable angular sensitivity given prior knowledge of component behaviour and prior knowledge of stochastic and deterministic error sources. Using the Computational Polarimetry Framework, we were able to estimate ideal linear polariser orientations under various orthodox and unorthodox design conditions to achieve minimal and desired levels of measurable angular sensitivities. An unintentional consequence of this system was producing stable parameter configurations where the system performance is optimal over tens of degrees.
Next, we used the Computational Polarimetry Framework to estimate the optical activity of a sample using spirally polarised beams and a spatial detector array. The computational optical rotary dispersion (CORD) system incorporated prior knowledge of the beam polarisation distribution, the measurement system, and the measurement process to arrive at an inference model to estimate a sample's optical activity. This system was able to estimate accurate optical activities under synthetic conditions with varying amounts of stochastic error to a lower detectable limit of two millidegrees. The system was able to estimate more accurate angular changes caused by a polarisation rotator in comparison to the state of art linear polarisation orientation (LPO) scanning systems with only a single measurement. Finally, it was demonstrated to provide an accurate estimate of Sucrose optical activity over the LPO system to a tenth of a degree.
Due to the probabilistic and Bayesian foundation of this framework, it is flexible enough to accommodate a range of system prior models for expected system behaviour. However, there can be cases where the distribution of a particular parameter in the framework is unknown or needs to be known. Future directions for this framework can be to estimate the distribution of a system component parameter for a known component. Given prior information of all the the immediate parent and dependant parameters of that system component, we can use their logical dependencies and the properties of Bayesian networks to infer their distributions. This framework has the additional benefits of being generalisable to model the behaviour of other optical processes.
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Keywords
optics, polarimetry, bayesian networks, systems design, computational