Symplectic numerical methods in optics and imaging: ray tracing in spherical gradient-index lenses and computer-generated image rendering
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Published:2023-11-03
Issue:32
Volume:62
Page:8621
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ISSN:1559-128X
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Container-title:Applied Optics
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language:en
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Short-container-title:Appl. Opt.
Author:
McKeon BenORCID,
Goncharov Alexander V.
Abstract
This paper provides an introduction to symplectic numerical integration techniques and examines various optical applications. We first outline the fundamentals of Hamiltonian optics and detail the construction of a symplectic method via the splitting technique. Numerical experiments involving a selection of spherically symmetric gradient-index lenses compare the accuracy of various first-, second-, and fourth-order symplectic methods with equivalent nonsymplectic methods. The best-performing methods are then further tested as part of an image rendering task involving nonlinear ray tracing, comparing the trace time required by each method. Future improvements, recommendations, and uses for symplectic ray tracing are also considered.
Funder
University of Galway
Irish Research eLibrary
Publisher
Optica Publishing Group
Subject
Atomic and Molecular Physics, and Optics,Engineering (miscellaneous),Electrical and Electronic Engineering