### 摘要

The effects of variable changes on the optical path length (OPL) of optical elements such as a prism are generally evaluated by utilizing a ray tracing approach to determine the OPL before and after the variable change, respectively, and then applying a finite difference (FD) method to estimate the OPL gradient with respect to each individual variable. By contrast, this study constructs the gradient matrix of OPL of a prism which permits the effects of multiple variable changes to be determined in a single pass. The developed approach not only resolves the error inherent in the FD method as a result of the denominator being far smaller than the numerator, but also avoids the requirement for multiple ray tracing operations and therefore yields a substantial improvement in the computational efficiency. The validity of the proposed approach is demonstrated utilizing a Pechan prism for illustration purposes.

原文 | English |
---|---|

頁（從 - 到） | 471-479 |

頁數 | 9 |

期刊 | Applied Physics B: Lasers and Optics |

卷 | 98 |

發行號 | 2-3 |

DOIs | |

出版狀態 | Published - 2010 二月 1 |

### 指紋

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)

### 引用此文

}

*Applied Physics B: Lasers and Optics*, 卷 98, 編號 2-3, 頁 471-479. https://doi.org/10.1007/s00340-009-3716-4

**Gradient matrix of optical path length for evaluating the effects of design variable changes in a prism.** / Hsueh, C. C.; Lin, Psang-Dain.

研究成果: Article

TY - JOUR

T1 - Gradient matrix of optical path length for evaluating the effects of design variable changes in a prism

AU - Hsueh, C. C.

AU - Lin, Psang-Dain

PY - 2010/2/1

Y1 - 2010/2/1

N2 - The effects of variable changes on the optical path length (OPL) of optical elements such as a prism are generally evaluated by utilizing a ray tracing approach to determine the OPL before and after the variable change, respectively, and then applying a finite difference (FD) method to estimate the OPL gradient with respect to each individual variable. By contrast, this study constructs the gradient matrix of OPL of a prism which permits the effects of multiple variable changes to be determined in a single pass. The developed approach not only resolves the error inherent in the FD method as a result of the denominator being far smaller than the numerator, but also avoids the requirement for multiple ray tracing operations and therefore yields a substantial improvement in the computational efficiency. The validity of the proposed approach is demonstrated utilizing a Pechan prism for illustration purposes.

AB - The effects of variable changes on the optical path length (OPL) of optical elements such as a prism are generally evaluated by utilizing a ray tracing approach to determine the OPL before and after the variable change, respectively, and then applying a finite difference (FD) method to estimate the OPL gradient with respect to each individual variable. By contrast, this study constructs the gradient matrix of OPL of a prism which permits the effects of multiple variable changes to be determined in a single pass. The developed approach not only resolves the error inherent in the FD method as a result of the denominator being far smaller than the numerator, but also avoids the requirement for multiple ray tracing operations and therefore yields a substantial improvement in the computational efficiency. The validity of the proposed approach is demonstrated utilizing a Pechan prism for illustration purposes.

UR - http://www.scopus.com/inward/record.url?scp=73849096782&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=73849096782&partnerID=8YFLogxK

U2 - 10.1007/s00340-009-3716-4

DO - 10.1007/s00340-009-3716-4

M3 - Article

AN - SCOPUS:73849096782

VL - 98

SP - 471

EP - 479

JO - Applied Physics B: Lasers and Optics

JF - Applied Physics B: Lasers and Optics

SN - 0946-2171

IS - 2-3

ER -