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Microfabrication of Implantable Optics Integrated in a Microstructured Imaging Window for Advanced In Vivo Imaging

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Generating-function approach for double freeform lens design.

L B Romijn, M J H Anthonissen, J H M Ten Thije Boonkkamp

Journal of the Optical Society of America. A, Optics, Image Science, and Vision

|March 10, 2021

Summary

This summary is machine-generated.

This study presents a new method for designing LED lenses with multiple optical surfaces. The technique uses generalized Monge-Ampère equations to control light distribution, enabling complex optical designs.

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Area of Science:

Optics and Photonics
Computational Physics
Applied Mathematics

Background:

Designing LED lighting often requires complex optical surfaces, such as lenses with two refractive surfaces.
Existing methods may not efficiently handle the intricate light distribution requirements for advanced LED applications.

Purpose of the Study:

To develop a novel computational method for designing optical surfaces in LED lighting.
To enable precise control over light intensity distribution using a generalized optimal transport approach.

Main Methods:

The problem is framed using Hamilton's characteristic functions, leading to two generalized Monge-Ampère equations.
A generating function, generalizing optimal transport cost functions, is derived for each surface.
An iterative least-squares algorithm is employed to solve these equations.

Main Results:

The method successfully designs optical surfaces by solving generalized Monge-Ampère equations.
An intermediate target intensity serves as a control parameter to distribute refractive power between surfaces.
The algorithm demonstrated capability in producing complex target intensity distributions in example cases.

Conclusions:

The presented method offers a robust framework for designing multi-surface optics for LEDs.
The use of generalized Monge-Ampère equations provides a powerful tool for optical design.
The developed "knob" allows for flexible distribution of optical power, enhancing design versatility.