Gradient-index lenses: Symplectic ray tracing and optical testing
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Date
2024-02-22Author
McKeon, Ben
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Abstract
The chief objective of this thesis is to provide an introduction to symplectic numerical methods
and how they may be applied to optical problems, particularly for tracing rays within gradientindex (GRIN) optics. Specifically, we investigate how symplectic methods compare in terms
of accuracy with well-established numerical integration techniques such as Euler’s method and
the fourth-order Runge-Kutta method (RK4). As a near-term application, symplectic methods
are used to render a test image which requires nonlinear ray tracing. The accuracy of implicit
numerical methods is also considered, in addition to the derivation of algebraic iteration schemes
for lenses with separable index profiles thereby removing the need for root solvers when using
implicit methods. Finally, the pyramid wavefront sensor, a component commonly employed in
adaptive optics systems, is considered as a means of measuring aberrations present within GRIN
elements and is proposed as a tool to undertake the characterisation and optical testing of same.