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

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-Ampè re (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.