title: Computationally efficient gradient matrix of optical path length in axisymmetric optical systems.
abstract: We develop a mathematical method for determining the optical path length (OPL) gradient matrix relative to all the system variables such that the effects of variable changes can be evaluated in a single pass. The approach developed avoids the requirement for multiple ray-tracing operations and is, therefore, more computationally efficient. By contrast, the effects of variable changes on the OPL of an optical system are generally evaluated by utilizing a ray-tracing approach to determine the OPL before and after the variable change and then applying a finite-difference (FD) approximation method to estimate the OPL gradient with respect to each individual variable. Utilizing a Petzval lens system for verification purposes, it is shown that the approach developed reduces the computational time by around 90% compared to that of the FD method.
authors.affiliation: National Cheng Kung University Department of Mechanical Engineering Tainan, Taiwan 70101.
authors.forename: Chun-Che
authors.initials: CC
authors.lastname: Hsueh
authors.forename: Psang-Dain
authors.initials: PD
authors.lastname: Lin