Skew ray tracing and error analysis of optical lens with cylindrical boundary surface

Te Tan Liao, Shih Hung Chen, Kuo Ying Chen, Chun Ta Chen

Research output: Contribution to journalArticle


This study applies computational geometric algebra based on a 4|4 homogeneous transformation matrix and Snell's law of geometrical optics to analyze skew rays and the errors of a light ray's path as it passes through a cylindrical lens. The author addresses two important topics: (1) the determination of the direction of a reflected or refracted ray by Snell's law and (2) the expression of the combination of two principal sources of light path error using error analysis. In topic (2), one of the sources is the translational errors Δdix, Δdiy, and Δdiz and the rotational errors Δ ωix, Δ ωiy, and Dωiz that determine the deviation of the light path at each boundary surface, while the other source is the differential changes induced in the incident point position and the 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 methodology presented in this study provides a comprehensive and robust approach for evaluating the error of a light ray path as it passes through a cylindrical lens.

Original languageEnglish
Pages (from-to)297-314
Number of pages18
JournalTransactions of the Canadian Society for Mechanical Engineering
Issue number2
Publication statusPublished - 2009 Dec 1


ASJC Scopus subject areas

  • Mechanical Engineering

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