Freeform beam-shaping system design with Monge-Ampère equation method

Haotian Sun; Linyue Fang; Rengmao Wu

doi:10.1117/12.3022826

17 June 2024 Freeform beam-shaping system design with Monge-Ampère equation method

Haotian Sun, Linyue Fang, Rengmao Wu

Proceedings Volume 13022, Illumination Optics VII; 130220B (2024) https://doi.org/10.1117/12.3022826
Event: SPIE Optical Systems Design, 2024, Strasbourg, France

Abstract

Freeform surfaces are optical surfaces without linear or rotational symmetry. Their flexible surface geometry offers high degrees of freedom, which can be employed to avoid restrictions on surface geometry and create compact yet efficient designs with better performance. Therefore, freeform surfaces can endow beam shaping with more new functions and satisfy the ever-growing demand for advanced beam-shaping systems. The Monge-Ampère (MA) equation method converts the design of freeform beam-shaping optics into an elliptic MA equation with a nonlinear boundary condition. The MA method can automatically satisfy the integrability condition and be implemented efficiently. In this talk, we will introduce the principles behind the MA method and reveal the mathematical essence of illumination design based on ideal source assumptions. Also, several interesting beam-shaping systems will be provided to show the effectiveness of the MA method in a wide variety of applications.

Conference Presentation

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Haotian Sun, Linyue Fang, and Rengmao Wu "Freeform beam-shaping system design with Monge-Ampère equation method", Proc. SPIE 13022, Illumination Optics VII, 130220B (17 June 2024); https://doi.org/10.1117/12.3022826

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