On-axis diffraction-limited design of bi-parabolic singlet lenses

TL;DR

This paper presents an analytical method for designing bi-parabolic lenses that are diffraction-limited, detailing how to calculate their surfaces and conditions for optimal imaging, with practical manufacturing considerations.

Contribution

It introduces an analytical approach to design diffraction-limited bi-parabolic lenses with specific parameters, enabling cost-effective manufacturing for various applications.

Findings

Analytical formulas for parabolic surfaces are derived.

Conditions for diffraction-limited imaging are established.

A practical example validated the design method.

Abstract

A lens limited by diffraction and having two parabolic surfaces is presented. The knowledge of the following parameters: object distance, relative refractive index, lens thickness, and image distance, enables to analytically calculate the parabolic front and back surfaces. The conditions to obtain diffraction-limited images for these lenses and its maximal diameter are described. These bi-parabolic lenses can be easily manufactured at reduced costs and can be used for several commercial and industrial applications. The method to obtain such surfaces and a simple example validated by using Oslo are described here.