Freeform lens design for a point source and far-field target

Area of Science:

• Optics
• Optical Engineering
• Nonimaging Optics

Background:

• Advancements in fabrication enable complex freeform surfaces for light control.
• Designing freeform optics to precisely redistribute light is a significant challenge.
• Existing strategies in academia and industry address freeform illumination design.

Purpose of the Study:

• To develop a mathematical approach for designing a single freeform lens.
• To convert light from an ideal point source into a specific far-field target irradiance.
• To demonstrate the algorithm's capability in generating practical optical designs.

Main Methods:

• Derivation of a generalized Monge-Ampère equation using optimal transport theory and energy conservation.
• Numerical solution of the equation using a generalized least-squares algorithm.
• Computation of the optical map followed by construction of the optical surface.

Main Results:

• Successful generation of a peanut-shaped freeform lens for roadlighting.
• Creation of a detailed freeform lens capable of projecting an image in the far field.
• Validation of the mathematical approach for freeform illumination design.

Conclusions:

• The presented mathematical framework and algorithm effectively design single freeform lenses.
• The method offers a robust solution for converting point source light into complex far-field distributions.
• This work advances the field of freeform optics with practical applications in illumination and projection.