Flexible design method for freeform lenses with an arbitrary lens contour

Abstract

A method is presented that allows the design of freeform lenses with an arbitrary contour in a flexible and robust manner. The method is based on the generation of two equi-flux grids representing the source and target beams, with two separate curl-free mappings from an equi-spatial rectangular grid. Because the source and target grids are generated independently from one another, one can map arbitrary complex source beams with certain contours onto arbitrary complex target beams within other contours with high convergence probability. The method is illustrated by calculating a triangular freeform lens that reshapes a triangular beam from a Lambertian source into a uniform pentagonal irradiance distribution on a target plane.

Monolitic Hybrid Transmitter-Receiver Lens for Rotary On-Axis Communications

“…Thereby, they provide better results than numerical optimization methods [38], especially if the systems are complex. A great variety of design methods are known, for example ray mapping [39][40][41][42][43][44][45][46], forming surfaces using Cartesian ovals [47], the simultaneous multiple surface method in 2D [48] and 3D [38,49] or the tailored freeform design method proposed by Ries and Muschaweck [50]. Nowadays ray mapping approach, i.e., the combination of energy mapping in conjunction with geometrical surface construction, is in the focus of illumination research [39][40][41][42][43][44][45][46].…”

Design of Freeform Illumination Optics

“…The difference between the actual illuminance distribution and the target one is due to the optimal mapping of the optimal transport problem which does not satisfy the intergrability condition in the design of the freeform lens. Reproduced with permission . Copyright 2017, The Optical Society of America.…”

“…This is an inverse problem, the number of freeform surfaces which should be used depends on the design requirements. The design methods of freeform illumination optics can be broken into two groups according to the influence of the spatial or angular extent of an actual light source on the design: zero‐étendue algorithms based on ideal source assumption (point light sources or parallel light beams) and algorithms for extended light sources . When the influence of the spatial or angular extent of a light source can be ignored, the light source can be considered as an ideal source (a point source or a parallel beam) and the inverse problem can be converted into a well‐defined mathematical problem.…”

“…When the influence of the spatial or angular extent of a light source can be ignored, the light source can be considered as an ideal source (a point source or a parallel beam) and the inverse problem can be converted into a well‐defined mathematical problem. The formulization of this inverse problem can be done in the ray mapping method . A key step in the ray mapping method is to find a ray mapping such that the calculated normal field can satisfy the integrability condition, leading to a system of a first order partial differential equations .…”

“…The formulization of this inverse problem can be done in the ray mapping method. [50,51,54,55,[57][58][59][60][70][71][72][73][76][77][78][79][81][82][83][84] A key step in the ray mapping method is to find a ray mapping such that the calculated normal field can satisfy the integrability condition, leading to a system of a first order partial differential equations. [104] Finding such an integrable ray mapping may not be a simple task.…”