Mathematical modelling of optical coherence tomography and solutions of the inverse scattering problem

Author Identifier

Anna Guan

https://orcid.org/0000-0001-8154-3944

Date of Award

2024

Document Type

Thesis

Publisher

Edith Cowan University

Degree Name

Doctor Of Philosophy

School

School of Science

First Supervisor

Dr Steven Richardson

Second Supervisor

Associate Professor Steven Hinckley

Abstract

Optical coherence tomography (OCT) is a non-invasive high-resolution imaging technology. It utilises the coherence property of light to visualise biological tissue cross-sections and produce A-scans. A-scans contain numerous peaks that are associated with layer interfaces in a given sample. Trained medical staff may be able to make a qualitative interpretation of an OCT A-scan. However, this interpretation is not always reliable in terms of identifying the key features of the sample structure. To provide an accurate prognosis and a potential treatment scheme, a more objective measure is in order. The process of inferring sample structure from an A-scan is known as the inverse scattering problem. There are two stages to mathematically solve the OCT inverse scattering problem. The first stage is to establish an OCT model as a means to simulate the A-scan of a known sample structure. This is known as the direct scattering problem. The OCT model is of significant importance in providing a quantitative measure of how well a sample structure fits the available A-scan. The second stage is to develop an efficient and reliable algorithm to infer the sample structure from the A-scan. Solving the inverse scatting problem is about establishing an algorithm to systematically search the space of feasible optical properties of the sample to best fit the available A-scan, thus inferring the tissue structure. Aligning with the two stages, the research proceeds under two main foci. The first focus is the development of the OCT models for the direct scattering problem. This includes extending the first principle OCT model to incorporate absorption, scattering and multiple reflections to create simulated A-scans. The extended OCT model will be used to study the impact of light sources, and the impact of absorption, scattering and multiple reflections on the simulated A-scans. The second focus is the solutions to the inverse scattering problem. This includes investigating and implementing a robust deterministic algorithm to efficiently and accurately solve the inverse scattering problem.

DOI

10.25958/6x26-d992

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