Phase space aberrations in freeform and gradient index imaging systems

Babington, James

doi:10.1117/1.oe.57.10.105106

Cited by 3 publications

(2 citation statements)

References 20 publications

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“…Often, notation tends to vary between authors, making the assimilation of results from disparate papers difficult. Moreover, these papers are usually mathematically dense, demanding some familiarity with group theory and differential geometry of the reader in order to be fully understood [1,2]. This publication, by comparison, seeks to minimise the use of mathematics that may be unfamiliar to optical engineers by focusing on the tangible benefits of symplectic integration schemes rather than placing any undue emphasis on their more abstract characteristics.…”

Section: Introductionmentioning

confidence: 99%

Performance Considerations for Ray Tracing in Gradient-index Optics with Symplectic Numerical Methods

McKeon,

Goncharov

2023

lim

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The primary objective of this paper is to demonstrate the utility of symplectic numerical techniques for ray tracing within gradient-index media. The relevant mathematics are explained in brief, deriving the optical Hamiltonian independently of the Lagrangian optical formalism before constructing a symplectic ray tracing algorithm. Numerical experiments with the Lüneburg and Maxwell fish-eye lenses compare the effectiveness of symplectic methods with standard numerical integration techniques, challenging the idea that the increased accuracy of higher-order numerical methods justifies their elevated computational cost. Further uses for symplectic ray tracing are also discussed.

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Section: Introductionmentioning

confidence: 99%

Performance Considerations for Ray Tracing in Gradient-index Optics with Symplectic Numerical Methods

McKeon,

Goncharov

2023

lim

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“…Furthermore, most papers examining the application of symplectic numerical techniques to optical problems make for rather dense reading, working on the assumption that the reader is already somewhat familiar with differential geometry [16]. Additional publications demand a decent knowledge of group theory in order to fully appreciate a proposed Hamiltonian alternative to Seidel aberrations for the creation of freeform optical systems [17,18]. This paper instead aims to provide an antidote to the confusion, seeking to minimise the use of mathematics that may be unfamiliar to optical engineers by focusing on the tangible benefits of symplectic integration schemes rather than placing any undue emphasis on their more abstract characteristics.…”

Section: Introductionmentioning

confidence: 99%

Symplectic numerical methods in optics and imaging: ray tracing in spherical gradient-index lenses and computer-generated image rendering

McKeon,

Goncharov

2023

Appl. Opt.

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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.

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Spatial Three-Mirror Off-Axis Freeform Optical System without Any Symmetry

Tan

Zhu

2022

Photonics

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In this manuscript, we have launched a study on the completely nonsymmetric freeform optical system with neither rotational symmetry nor planar symmetry. An off-axis three-mirror freeform optical system with nonsymmetric geometry is proposed and a direct design method is developed for the nonsymmetric freeform optical system. The design field points are sampled across the full FOV to control the imaging quality and object–image relationship. In this system, the center of the image plane is greatly away from the plane determined by the centers of the three mirrors. This nonsymmetric system with F/1.3, a focal length of 50 mm, and an 8° × 6° field of view can achieve imaging quality close to the diffraction limit. This work provides a feasible nonsymmetric system design idea for the optical community.

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Phase space aberrations in freeform and gradient index imaging systems

Cited by 3 publications

References 20 publications

Performance Considerations for Ray Tracing in Gradient-index Optics with Symplectic Numerical Methods

Performance Considerations for Ray Tracing in Gradient-index Optics with Symplectic Numerical Methods

Symplectic numerical methods in optics and imaging: ray tracing in spherical gradient-index lenses and computer-generated image rendering

Spatial Three-Mirror Off-Axis Freeform Optical System without Any Symmetry

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