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Single freeform surface design for prescribed input wavefront and target irradiance.

Christoph Bösel, Herbert Gross

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

|October 17, 2017

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This study presents a new method for designing single freeform optical surfaces to precisely control light beams. The approach simplifies optical systems, reducing cost and size for various beam shaping applications.

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Area of Science:

Optics and Photonics
Optical Engineering
Computational Optics

Background:

Minimizing optical elements enhances system compactness and reduces cost in beam shaping.
Designing single freeform surfaces is crucial for non-planar and non-spherical input wavefronts.

Purpose of the Study:

Investigate the design of single freeform surfaces for zero-étendue sources with complex target irradiances.
Develop a method applicable to general input conditions beyond collimated beams or point sources.

Main Methods:

Derived a partial differential equation (PDE) system of Monge-Ampère type from energy conservation and ray-tracing equations.
Formulated the PDE for general zero-étendue sources in Cartesian coordinates.
Discretized the PDE system using finite differences and solved using a root-finding algorithm with an optimal mass transport-based initial iterate.

Main Results:

Successfully designed single freeform surfaces for complex irradiance redistribution.
Demonstrated the method's efficiency with examples including collimated beams, point sources, and astigmatic wavefronts.
The numerical algorithm efficiently solves the nonlinear equation system.

Conclusions:

The developed PDE-based method enables efficient design of single freeform surfaces for advanced beam shaping.
This approach offers a significant advancement for compact and cost-effective optical system design.
The method is versatile, handling diverse input wavefronts and target irradiance distributions.