Ray mapping approach for the efficient design of continuous freeform surfaces

Area of Science:

• Optics and Photonics
• Applied Mathematics
• Computer-Aided Design

Background:

• Designing continuous freeform optical surfaces for arbitrary light control is complex.
• Existing ray-mapping methods struggle with ensuring surface integrability and continuity.

Purpose of the Study:

• To develop an efficient and general method for designing continuous freeform surfaces for collimated light beams.
• To address the challenge of finding integrable ray mappings for arbitrary illumination patterns.

Main Methods:

• Derivation of a general condition for surface and ray mapping based on reflection/refraction laws and integrability.
• Application of optimal mass transport (OMT) for calculating ray mappings under small-angle approximation.
• Surface construction by solving a linear advection equation with specific boundary conditions.

Main Results:

• A novel condition for surface and ray mapping for collimated beams was derived.
• Optimal mass transport provides an efficient, approximately integrable mapping for freeform optics design.
• The method successfully constructs surfaces for complex illumination patterns with steep gradients.

Conclusions:

• The OMT-based approach offers an efficient solution for designing continuous freeform optical surfaces.
• This method simplifies the construction of optical surfaces by solving standard integrals.
• The approach is effective for challenging illumination designs, including those with high irradiance gradients.