### Abstract

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 Δd_{ix}, Δd_{iy}, and Δd_{iz} and the rotational errors Δ ω_{ix}, Δ ω_{iy}, 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 language | English |
---|---|

Pages (from-to) | 297-314 |

Number of pages | 18 |

Journal | Transactions of the Canadian Society for Mechanical Engineering |

Volume | 33 |

Issue number | 2 |

Publication status | Published - 2009 Dec 1 |

### Fingerprint

### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

*Transactions of the Canadian Society for Mechanical Engineering*,

*33*(2), 297-314.

**Skew ray tracing and error analysis of optical lens with cylindrical boundary surface.** / Liao, Te Tan; Chen, Shih Hung; Chen, Kuo Ying; Chen, Chun Ta.

Research output: Contribution to journal › Article

*Transactions of the Canadian Society for Mechanical Engineering*, vol. 33, no. 2, pp. 297-314.

}

TY - JOUR

T1 - Skew ray tracing and error analysis of optical lens with cylindrical boundary surface

AU - Liao, Te Tan

AU - Chen, Shih Hung

AU - Chen, Kuo Ying

AU - Chen, Chun Ta

PY - 2009/12/1

Y1 - 2009/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77955819975&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955819975&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:77955819975

VL - 33

SP - 297

EP - 314

JO - Transactions of the Canadian Society for Mechanical Engineering

JF - Transactions of the Canadian Society for Mechanical Engineering

SN - 0315-8977

IS - 2

ER -