Proposed Methods For Measuring and Interpreting Mueller Matrices in In Vivo Retinal Polarimetry
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Mueller matrix polarimetry is the examination of how a sample transforms the polarization state of light. This requires probing the sample with input light of a variety of generated polarization states and analyzing the resulting output states, using a total of at least sixteen irradiance measurements. This allows one to calculate the Mueller matrix, which provides insight into the microstructure of the sample. In imaging applications this can yield additional contrast between different types of materials. Examination of the human retina has the potential to reveal not only ocular conditions, but also neurological disorders due to the fact that the retina is made up of neural tissue. Deposits of amyloid-beta in the brain are a standard biomarker for Alzheimer's disease. Similar deposits have been identified in the retina. By studying ex vivo human retinae, members of Campbell Labs have shown that these deposits can be imaged label-free using Mueller matrix polarimetry, and that their number correlates with the severity of Alzheimer's disease as assessed using brain pathology post-mortem. Imaging these deposits in the living eye using in vivo retinal polarimetry could provide an affordable and noninvasive biomarker for Alzheimer's disease, aiding in diagnosis. This thesis uses a "double pass model" to describe in vivo retinal polarimetry: it is assumed that light passes through the ocular tissue (i.e. the cornea, lens, and upper layers of the retina) before reflecting within the retina, and traversing polarimetrically similar tissue in the opposite direction. This model implies a particular mathematical structure for the Mueller matrix in in vivo retinal polarimetry. This thesis proposes ways in which this mathematical structure can be used advantageously when measuring and interpreting double pass Mueller matrices. While other authors have used the double pass model for in vivo retinal polarimetry, it is believed that this thesis is the first work to examine its implications without also making assumptions about the polarimetric properties of the ocular tissue. Following other authors, this thesis first describes the reciprocity theorem which relates a Mueller matrix for opposite paths through a sample, and uses it to apply the double pass model to Mueller matrices. It is shown that double pass Mueller matrices have fewer degrees of freedom than ordinary Mueller matrices. This allows double pass Mueller matrices to be calculated from as few as ten irradiance measurements. Several designs are developed for the generating and analyzing branches of a polarimeter, capable of measuring double pass Mueller matrices in ten measurements while being optimized for the best possible error performance. These are found using a novel extension of standard polarimeter optimization techniques that allows them to take into account the aforementioned restrictions on double pass Mueller matrices. These designs could be used to improve the speed of an in vivo retinal polarimeter used for Alzheimer's disease diagnosis, reducing patient discomfort and eye movement during the measurement. Next, the double pass Mueller matrix is compared to the corresponding single pass Mueller matrix for transmission once through the ocular tissue. New methods are found to calculate possible single pass polarimetric properties from the double pass Mueller matrix. This may provide additional insight into the microstructure of the sample and yield results that are more similar to the transmission properties of retinal amyloid deposits previously measured ex vivo. This thesis proposes new methods for measuring and interpreting Mueller matrices measured in in vivo retinal polarimetry assuming the double pass model. These methods could be applied in order to improve a future instrument for Alzheimer's disease diagnosis through observation of retinal amyloid deposits.
Cite this version of the work
Steven Kenneth Esau (2020). Proposed Methods For Measuring and Interpreting Mueller Matrices in In Vivo Retinal Polarimetry. UWSpace. http://hdl.handle.net/10012/16601