Designing double freeform surfaces for collimated beam shaping with optimal mass transportation and linear assignment problems

TL;DR

This paper introduces a novel method for designing refractive optical elements for collimated beam shaping by formulating the problem as a linear assignment problem, enabling efficient and precise surface design.

Contribution

It presents a new approach combining optimal mass transportation and linear assignment problems for designing double freeform surfaces in beam shaping applications.

Findings

High efficiency of the designed optical elements confirmed by numerical simulations.

Effective reconstruction of optical surfaces from discrete ray mappings.

Versatile beam shaping from circular to variously shaped beams.

Abstract

We propose a method for designing refractive optical elements for collimated beam shaping. In this method, the problem of finding a ray mapping is formulated as a linear assignment problem, which is a discrete version of the corresponding mass transportation problem. A method for reconstructing optical surfaces from a computed discrete ray mapping is proposed. The method is suitable for designing continuous piecewise-smooth optical surfaces. The design of refractive optical elements transforming beams with circular cross-section to variously shaped (rectangular, triangular, and cross-shaped) beams with plane wavefront is discussed. The presented numerical simulation results confirm high efficiency of the designed optical elements.