## Abstract

The present group previously proposed a method for determining the first-order derivative matrix (i.e., the Jacobian matrix) of a skew ray by taking all the independent variables of the optical system as the system variable vector, X^{¯} _{sys}. However, many trigonometric function calls, divisions, multiplications and additions were required to determine the ray Jacobian matrix with respect to X^{¯} _{sys}. Accordingly, in the present study, the angular variables in the system variable vector, X^{¯} _{sys}, are replaced with their respective cosine and sine trigonometric functions. The boundary variable vector, X^{¯} _{i}, is similarly redefined such that it includes no angular variables. The proposed method has three main advantages over that previously reported: 1) it is valid for any pose matrix, irrespective of the order in which the rotation and translation motions of a boundary are assigned; 2) it involves only polynomial differentiation, and is thus easily implemented in computer code; and 3) the computation speed of ∂X^{¯} _{i} ^{∕} ∂X^{¯} _{sys} is improved by a factor of approximately ten times.

Original language | English |
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Pages (from-to) | 35402-35417 |

Number of pages | 16 |

Journal | Optics Express |

Volume | 27 |

Issue number | 24 |

DOIs | |

Publication status | Published - 2019 Nov 25 |

## All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics