title: Determination of second-order derivatives of a skew ray with respect to the variables of its source ray in optical prism systems.
abstract: 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.
authors.affiliation: Department of Mechanical Engineering, National Cheng Kung University, Tainan 70101, Taiwan. pdlin@mail.ncku.edu.tw
authors.forename: Psang Dain
authors.initials: PD
authors.lastname: Lin
authors.forename: Wei
authors.initials: W
authors.lastname: Wu