Lin Psang Dain, Wu Wei
Department of Mechanical Engineering, National Cheng Kung University, Tainan 70101, Taiwan.
J Opt Soc Am A Opt Image Sci Vis. 2011 Aug 1;28(8):1600-9. doi: 10.1364/JOSAA.28.001600.
The second-order derivative of a scalar function with respect to a variable vector is known as the Hessian matrix. We present a computational scheme based on the principles of differential geometry for determining the Hessian matrix of a skew ray as it travels through a prism system. A comparison of the proposed method and the conventional finite difference (FD) method is made at last. It is shown that the proposed method has a greater inherent accuracy than FD methods based on ray-tracing data. The proposed method not only provides a convenient means of investigating the wavefront shape within complex prism systems, but it also provides a potential basis for determining the higher order derivatives of a ray by further taking higher order differentiations.
标量函数相对于变量向量的二阶导数被称为海森矩阵。我们提出了一种基于微分几何原理的计算方案，用于确定斜光线在通过棱镜系统传播时的海森矩阵。最后对所提出的方法与传统的有限差分（FD）方法进行了比较。结果表明，所提出的方法比基于光线追迹数据的FD方法具有更高的固有精度。该方法不仅为研究复杂棱镜系统内的波前形状提供了一种便捷手段，而且还为通过进一步进行高阶微分来确定光线的高阶导数提供了潜在基础。
