An inverse and analytic lens design method

TL;DR

This paper introduces an inverse and analytic lens design method called Lagrange, which formulates differential equations based on system parameters and geometry to improve lens design beyond traditional numerical approaches.

Contribution

It presents a novel analytic and inverse lens design approach using differential equations and geometric principles, addressing limitations of traditional forward numerical methods.

Findings

Derivation of equations for perfect point imaging using the Lagrange method

Application of generalized Snell's law in 3D space within the design

Use of differential geometry to formulate lens surface conditions

Abstract

Traditional lens design is a numerical and forward process based on ray tracing and aberration theory. This method has limitations because the initial configuration of the lens has to be specified and the aberrations of the lenses have to considered. This paper is an initial attempt to investigate an analytic and inverse lens design method, called Lagrange, to overcome these barriers. Lagrange method tries to build differential equations in terms of the system parameters and the system input and output (object and image). The generalized Snell's law in three dimensional space and the normal of a surface in fundamental differential geometry are applied. Based on the Lagrange method equations for a single surface system are derived which can perfectly image a point object.