https://doi.org/10.1051/epjconf/202430903009
Differential ray tracing for an efficient computation of the Jacobian in the damped least-squares algorithm
1 Carl Zeiss AG, 73446 Oberkochen, Germany
2 Institute of Numerical Mathematics, Ulm University, 89081 Ulm, Germany
* e-mail: tobias.seger@zeiss.com
Published online: 31 October 2024
We present a framework for the optimization of optical systems based up on the damped least-squares method and differential ray tracing. First, a mathematical description for the differentiation of the ray-surface intersection is introduced. It is observed that the structure of the optimization variables and operands can be exploited such that the Jacobian for the damped least-squares algorithm can be computed in the same computational complexity as the primal ray tracing for both forward and reverse mode algorithmic differentiation. To demonstrate the advantages of the method a freeform mirror system is analyzed.
© The Authors, published by EDP Sciences, 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
