A skew ray tracing approach for the error analysis of optical elements with spherical boundary surfaces

Te Tan Liao, Chun Ta Chen

Research output: Contribution to journalArticle

3 Citations (Scopus)


This study applies a skew ray tracing approach based on a 44 homogeneous coordinate transformation matrix and Snell's law to analyze the errors of a ray's light path as it passes through a series of optical elements with spherical boundary surfaces. The proposed error analysis methodology considers two principal sources of light path error, namely: (1) the translational errors Xi, Yi and Zi and the rotational errors [image omitted], [image omitted] and [image omitted], which determine the deviation of the light path at each boundary surface, and (2) the differential changes induced in the incident point position and unit directional vector of the refracted/reflected ray as a result of differential changes in the position and unit directional vector of the light source. The validity of the proposed methodology is verified by analyzing the effects of optical errors in a solid glass cat's eye.

Original languageEnglish
Pages (from-to)1981-2002
Number of pages22
JournalJournal of Modern Optics
Issue number12
Publication statusPublished - 2008 Jul 1



  • Cat's eye
  • Error analysis
  • Skew ray tracing

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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