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Design of a stigmatic lens implementing a required ray mapping.

Leonid L Doskolovich, Dmitry A Bykov, Evgeni A Bezus

|October 8, 2021

Summary

This study presents a method for designing stigmatic lenses using ray mapping, simplifying lens design to solving an ordinary differential equation. The approach successfully creates lenses meeting specific optical conditions like Abbe sine and Herschel

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Area of Science:

Optics and Photonics
Lens Design
Geometric Optics

Background:

Designing optical systems requires precise control over light ray trajectories.
Stigmatic lenses, which form perfect images without aberrations, are crucial for high-resolution imaging.
Existing methods for lens design can be complex and computationally intensive.

Purpose of the Study:

To develop a novel method for designing stigmatic lenses.
To implement specific ray mappings for precise image formation.
To simplify the calculation process for lens design.

Main Methods:

Formulating lens design as a problem of implementing required ray mappings.
Reducing the lens design calculation to solving an explicit ordinary differential equation.
Applying the method to design lenses satisfying known optical conditions.

Main Results:

A straightforward method for designing stigmatic lenses based on ray mapping is established.
The calculation is simplified to solving a first-order ordinary differential equation.
Successfully designed stigmatic lenses meeting the Abbe sine condition, Herschel's condition, and constant angular magnification.

Conclusions:

The proposed method offers an efficient and explicit way to design stigmatic lenses.
This approach provides a unified framework for designing lenses with specific imaging properties.
The technique is validated by designing lenses for established optical performance criteria.