On the formal analysis of Gaussian optical systems in HOL

Optics technology is being increasingly used in mainstream industrial and research domains such as terrestrial telescopes, biomedical imaging and optical communication. One of the most widely used modeling approaches for such systems is Gaussian optics, which describes light as a beam. In this paper, we propose to use higher-order-logic theorem proving for the analysis of Gaussian optical systems. In particular, we present the formalization of Gaussian beams and verify the corresponding properties such as beam transformation, beam waist radius and location. Consequently, we build formal reasoning support for the analysis of quasi-optical systems. In order to demonstrate the effectiveness of our approach, we present a case study about the receiver module of a real-world Atacama Pathfinder Experiment (APEX) telescope.