Numerical approach for computing the Jacobian matrix between boundary variable vector and system variable vector for optical systems containing prisms

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The design of optical systems containing prisms is comparatively difficult since each prism may contain multiple boundary surfaces. Many geometrical optical merit functions have been proposed based on first-order derivatives of the geometrical quantities of the system with respect to the boundary variable vector Xi. However, transferring the computed quantities into the system variable vector Xsys is still highly challenging. Accordingly, this study proposes a new numerical method for determining the Jacobian matrix between Xi and Xsys directly. The proposed methodology can be easily implemented in computer code and provides a potential basis for the future development of a numerical technique for computing the second-order derivatives of the geometrical quantities of an optical system.

Original languageEnglish
Pages (from-to)747-758
Number of pages12
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Volume28
Issue number5
DOIs
Publication statusPublished - 2011

Fingerprint

Jacobian matrices
Prisms
Optical systems
prisms
Derivatives
Numerical methods
methodology
computer programs

All Science Journal Classification (ASJC) codes

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

Cite this

@article{867a2abd738349889c02d98fb843869d,
title = "Numerical approach for computing the Jacobian matrix between boundary variable vector and system variable vector for optical systems containing prisms",
abstract = "The design of optical systems containing prisms is comparatively difficult since each prism may contain multiple boundary surfaces. Many geometrical optical merit functions have been proposed based on first-order derivatives of the geometrical quantities of the system with respect to the boundary variable vector Xi. However, transferring the computed quantities into the system variable vector Xsys is still highly challenging. Accordingly, this study proposes a new numerical method for determining the Jacobian matrix between Xi and Xsys directly. The proposed methodology can be easily implemented in computer code and provides a potential basis for the future development of a numerical technique for computing the second-order derivatives of the geometrical quantities of an optical system.",
author = "Wei Wu and Psang-Dain Lin",
year = "2011",
doi = "10.1364/JOSAA.28.000747",
language = "English",
volume = "28",
pages = "747--758",
journal = "Journal of the Optical Society of America A: Optics and Image Science, and Vision",
issn = "1084-7529",
publisher = "The Optical Society",
number = "5",

}

TY - JOUR

T1 - Numerical approach for computing the Jacobian matrix between boundary variable vector and system variable vector for optical systems containing prisms

AU - Wu, Wei

AU - Lin, Psang-Dain

PY - 2011

Y1 - 2011

N2 - The design of optical systems containing prisms is comparatively difficult since each prism may contain multiple boundary surfaces. Many geometrical optical merit functions have been proposed based on first-order derivatives of the geometrical quantities of the system with respect to the boundary variable vector Xi. However, transferring the computed quantities into the system variable vector Xsys is still highly challenging. Accordingly, this study proposes a new numerical method for determining the Jacobian matrix between Xi and Xsys directly. The proposed methodology can be easily implemented in computer code and provides a potential basis for the future development of a numerical technique for computing the second-order derivatives of the geometrical quantities of an optical system.

AB - The design of optical systems containing prisms is comparatively difficult since each prism may contain multiple boundary surfaces. Many geometrical optical merit functions have been proposed based on first-order derivatives of the geometrical quantities of the system with respect to the boundary variable vector Xi. However, transferring the computed quantities into the system variable vector Xsys is still highly challenging. Accordingly, this study proposes a new numerical method for determining the Jacobian matrix between Xi and Xsys directly. The proposed methodology can be easily implemented in computer code and provides a potential basis for the future development of a numerical technique for computing the second-order derivatives of the geometrical quantities of an optical system.

UR - http://www.scopus.com/inward/record.url?scp=79958780823&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79958780823&partnerID=8YFLogxK

U2 - 10.1364/JOSAA.28.000747

DO - 10.1364/JOSAA.28.000747

M3 - Article

VL - 28

SP - 747

EP - 758

JO - Journal of the Optical Society of America A: Optics and Image Science, and Vision

JF - Journal of the Optical Society of America A: Optics and Image Science, and Vision

SN - 1084-7529

IS - 5

ER -