Differential equation of an aspherical lens and its solution

TL;DR

This paper introduces a direct method to compute the meridian profile of aspherical lenses by solving a derived differential equation, avoiding series coefficient calculations, and simplifies the process for long-focus lenses.

Contribution

It presents a novel approach to determine aspherical lens profiles through direct differential equation solving, bypassing traditional series coefficient methods.

Findings

Derived the differential equation for aspherical lens profiles.

Numerically solved the differential equation to obtain lens profiles.

Simplified the equation for long-focus lens conditions.

Abstract

A method for calculating the meridian profile of the aspherical surface of a plane-convex lens excluding spherical aberration, without calculating the coefficients of the series, by direct solving the compiled differential equation is proposed. The differential equation of an aspherical lens was compiled, found its numerical solution, and got the meridian profile of an aspherical lens. For long-focus lenses found conditions to simplify the differential equation.