Freeform geometrical optics I: Principles

TL;DR

This paper introduces a novel geometrical optics framework that replaces classical ray tracing with a vector analytical approach, enabling more efficient and comprehensive lens system design including various optical elements.

Contribution

It presents a new theoretical foundation for lens design that accounts for all optical elements using a reduced vector equation set, improving control over aberrations and computational efficiency.

Findings

Allows for comprehensive optical element modeling

Reduces computation time significantly

Enables better aberration control in lens design

Abstract

Lens design uses a calculation of the lens' surfaces that permit to obtain an image from a given object. A set of general rules and laws permits to calculate the essential points of the optical system such as distances, thickness, pupils, and focal distance among others. Now, the theory on which the classical lens design is based changes radically as our theoretical foundations do not rely on the classical ray tracing rules. We show that with the rules expressed in a reduced vector analytical solution set of equations, we can take into account all optical elements, i.e. refractive, reflective, catadioptric. These foundations permit to keep under control the system aberration budget in every surface. It reduces the computation time dramatically. The examples presented here were possible because of the versatility of this theoretical approach.