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Related Experiment Video

Updated: May 11, 2026

Free-form Light Actuators — Fabrication and Control of Actuation in Microscopic Scale

Free-form Light Actuators — Fabrication and Control of Actuation in Microscopic Scale

Published on: May 25, 2016

Analytical design of freeform optical elements generating an arbitrary-shape curve.

Leonid L Doskolovich¹, Anton Y Dmitriev, Evgeni A Bezus

¹Image Processing Systems Institute of the Russian Academy of Sciences, Samara, Russia. leonid@smr.ru

|May 15, 2013

Summary

This study introduces a new method for designing optical elements that precisely focus light beams into specific curve shapes. The technique uses a mathematical relationship derived from hyperboloids of revolution for accurate light focusing.

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Area of Science:

Optics and Photonics
Optical Design
Freeform Optics

Background:

Designing optical elements to focus light into arbitrary curves is challenging.
Existing methods may lack precision or flexibility for complex focusing requirements.

Purpose of the Study:

To propose a novel method for designing refractive optical elements.
To achieve precise focusing of a collimated beam into a specified curve shape.

Main Methods:

Derivation of a general relationship for freeform optical surfaces.
Utilizing a parametric family of hyperboloids of revolution.
Application of the thin optical element approximation.
Solving a first-order differential equation for hyperboloid parameters.

Main Results:

A general relationship for freeform surfaces was derived.
Optical elements were designed for line segment and circular arc foci.
Simulations confirmed the generation of high-quality curves.

Conclusions:

The proposed method enables the design of optical elements for precise curve focusing.
The technique is applicable to various specified curve shapes.
Simulation results validate the effectiveness and quality of the generated focus curves.