The $N$-achromat and beyond: a unified variational framework for optimal chromatic aberration correction

TL;DR

This paper introduces a unified variational framework for optimizing chromatic aberration correction in lens systems, enabling correction of multiple spectral lines and tailored optical designs with theoretical guarantees.

Contribution

It presents a novel variational approach that generalizes chromatic correction, including the pentachromat, and allows for customized, highly specialized optical system designs.

Findings

The pentachromat corrects five spectral lines effectively.

The variational formulation significantly reduces residual spectrum.

Coupling with combinatorial search optimizes glass selection and geometry.

Abstract

In this article, we present novel and effective methods for reducing chromatic aberrations in cemented lens systems. We derive an analytical solution coined the pentachromat, which corrects five distinct colors. This method can naturally be extended to accommodate an arbitrary number of lenses and to correct for a customized selection of spectral lines. Since correcting for specific rays rather than the entire residual spectrum can overconstrain the system, we introduce a variational formulation. This approach tames the residual spectrum by several orders of magnitude compared to conventional designs like the superachromat, while giving theoretical guarantees to reach the optimal solutions. Furthermore, this innovative methodology opens up previously uncharted design possibilities, such as multiple-focal-length achromatic systems. This allows for the selection of specific optical powers paired with desired bandwidths, enabling the design of highly specialized and tailored optical systems. Finally, we couple our variational framework with a combinatorial search, allowing to find the type of glasses and their geometry such that it reaches the best residual spectrum over an available catalogue.