Computationally efficient gradient matrix of optical path length in axisymmetric optical systems

Chun Che Hsueh, Psang Dain Lin

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We develop a mathematical method for determining the optical path length (OPL) gradient matrix relative to all the system variables such that the effects of variable changes can be evaluated in a single pass. The approach developed avoids the requirement for multiple ray-tracing operations and is, there-fore, more computationally efficient. By contrast, the effects of variable changes on the OPL of an optical system are generally evaluated by utilizing a ray-tracing approach to determine the OPL before and after the variable change and then applying a finite-difference (FD) approximation method to estimate the OPL gradient with respect to each individual variable. Utilizing a Petzval lens system for verification purposes, it is shown that the approach developed reduces the computational time by around 90% compared to that of the FD method.

Original languageEnglish
Pages (from-to)893-902
Number of pages10
JournalApplied optics
Issue number5
Publication statusPublished - 2009 Feb 10

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics
  • Engineering (miscellaneous)
  • Electrical and Electronic Engineering

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