Jacobian and hessian matrices of optical path length for computing the wavefront shape, irradiance, and caustics in optical systems

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3 Citations (Scopus)

Abstract

The first- and second-order derivative matrices of the ray (i.e., ∂R̄i=∂X̄0 and ∂2R i=∂X̄20) and optical path length (i.e., ∂OPLi=∂X̄0 and ∂ 2OPLi=∂X̄20) were derived with respect to the variable vector X0 of the source ray in an optical system by our previous papers. Using the first and second fundamental forms of the wavefront, these four matrices are used to investigate the local principal curvatures of the wavefront at each boundary surface encountered by a ray traveling through the optical system. The proposed method not only yields the data needed to compute the irradiance of the wavefront but also provides the information required to determine the caustics. Importantly, the proposed methodology is applicable to both axisymmetric and nonaxisymmetric optical systems.

Original languageEnglish
Pages (from-to)2272-2280
Number of pages9
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Volume29
Issue number11
DOIs
Publication statusPublished - 2012 Jan 1

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Hessian matrices
Caustics
Wavefronts
optical paths
irradiance
Optical systems
alkalies
rays
matrices
curvature
methodology
Derivatives

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Computer Vision and Pattern Recognition

Cite this

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abstract = "The first- and second-order derivative matrices of the ray (i.e., ∂R̄i=∂X̄0 and ∂2R i=∂X̄20) and optical path length (i.e., ∂OPLi=∂X̄0 and ∂ 2OPLi=∂X̄20) were derived with respect to the variable vector X0 of the source ray in an optical system by our previous papers. Using the first and second fundamental forms of the wavefront, these four matrices are used to investigate the local principal curvatures of the wavefront at each boundary surface encountered by a ray traveling through the optical system. The proposed method not only yields the data needed to compute the irradiance of the wavefront but also provides the information required to determine the caustics. Importantly, the proposed methodology is applicable to both axisymmetric and nonaxisymmetric optical systems.",
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