Wu Wei, Lin Psang Dain
Department of Mechanical Engineering, National Cheng Kung University, Tainan 70101, Taiwan.
J Opt Soc Am A Opt Image Sci Vis. 2011 May 1;28(5):747-58. doi: 10.1364/JOSAA.28.000747.
The design of optical systems containing prisms is comparatively difficult since each prism may contain multiple boundary surfaces. Many geometrical optical merit functions have been proposed based on first-order derivatives of the geometrical quantities of the system with respect to the boundary variable vector X(i). However, transferring the computed quantities into the system variable vector X(sys) is still highly challenging. Accordingly, this study proposes a new numerical method for determining the Jacobian matrix between X(i) and X(sys) directly. The proposed methodology can be easily implemented in computer code and provides a potential basis for the future development of a numerical technique for computing the second-order derivatives of the geometrical quantities of an optical system.
包含棱镜的光学系统设计相对困难，因为每个棱镜可能包含多个边界表面。基于系统几何量相对于边界变量向量X(i)的一阶导数，已经提出了许多几何光学品质因数函数。然而，将计算量转换为系统变量向量X(sys)仍然极具挑战性。因此，本研究提出了一种直接确定X(i)和X(sys)之间雅可比矩阵的新数值方法。所提出的方法可以很容易地在计算机代码中实现，并为未来开发用于计算光学系统几何量二阶导数的数值技术提供了潜在基础。
