## Abstract

Our group recently showed that the Seidel primary ray aberration coefficients of an axis-symmetrical system can be accurately determined using the third-order Taylor series expansion of a skew ray R^{¯}_{m} on an image plane. This finding inspires us to determine the third-order derivative matrix of R^{¯}_{m} with respect to the vector X^{¯}_{0} of the source ray, i.e., ∂R^{¯ 3}_{m}/∂X^{¯ 3}_{0}, under reflection/refraction at a flat boundary. Finite difference methods using the second-order derivative matrix, ∂R^{¯ 2}_{m}/∂X^{¯ 2}_{0}, require multiple rays to compute ∂R^{¯ 3}_{m}/∂X^{¯ 3}_{0} and suffer from cumulative rounding and truncation errors. By contrast, the present method is based on differential geometry. Thus, it provides a greater inherent accuracy and requires the tracing of just one ray. The proposed method facilitates the analytical investigation of the primary aberrations of an axis-symmetrical system and can be easily extended to determine the higher-order derivative matrices required to explore higher-order ray aberration coefficients.

Original language | English |
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Pages (from-to) | 1435-1441 |

Number of pages | 7 |

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

Volume | 37 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2019 Sep |

## All Science Journal Classification (ASJC) codes

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