More and more lighting applications require the design of dedicated optics to achieve a given radiant intensity or irradiance distribution. Freeform optics has the advantage of providing such a functionality with a compact design. It was previously demonstrated in [Bäuerle et al., Opt. Exp. 20, 14477-14485 (2012)] that the up-front computation of the light path through the optical system (ray mapping) provides a satisfactory approximation to the problem, and allows the design of multiple freeform surfaces in transmission or in reflection. This article presents one natural extension of this work by introducing an efficient optimization procedure based on the physics of the system. The procedure allows the design of multiple freeform surfaces and can render high resolution irradiance patterns, as demonstrated by several examples, in particular by a lens made of two freeform surfaces projecting a high resolution logo (530 × 160 pixels).

The design of freeform lenses and reflectors allows to achieve non-radially symmetric irradiance distributions whilst keeping the optical system compact. In the case of a point-like source, such as an LED, it is often desired to capture a wide angle of source light in order to increase optical efficiency. This generally results in strongly curved optics, requiring both lens surfaces to contribute to the total ray refraction, and thereby minimising Fresnel losses. In this article, we report on a new design algorithm for multiple freeform optical surfaces based on the theory of optimal mass transport that adresses these requirements and give an example of its application to a problem in general lighting.

It was previously demonstrated by Bäuerle et al. [Opt. Express20, 14477 (2012)] that the computation of ray paths through the optical system (ray mapping) can be used to design multisurface freeform optical elements creating a prescribed irradiance pattern for a zero-étendue source. The procedure outlined there uses the heuristic step of reducing the ray mapping's curl to improve adherence to surface integrability criteria. This Letter formally derives a quantitative estimate for the limitations of this approach in the collimated case and shows the key factors influencing the quality of the final optics.

LEDs are a promising alternative to existing illuminants for a wide range of lighting applications. Besides efficiency and high durability, the small light source dimensions compared to conventional light sources open up new possibilities in optical design. In many lighting setups, it is desired to realize a prescribed intensity distribution, for example homogeneous irradiance on a given area on a wall or floor. This can be realized using LEDs in combination with specially designed freeform lenses and/or mirrors. For high efficiency, it is necessary to collect at least 70 - 80 degrees half-angle (measured against the z axis) of the light that the LED emits into a 90 degree half-angle. This results in a lens that resembles a hemisphere. The numerical design problem thus requires a mathematical description that can handle such strongly curved surfaces with strongly varying surface slopes. Surface parametrizations with a rectangular topography, like e.g. Cartesian tensor p roduct B-splines, have severe drawbacks when handling such surfaces. We report on the use of an alternative surface approximation scheme that uses a triangular mesh. We describe an algorithm that optimizes the two surfaces of a lens for a wall washer that generates homogeneous irradiance on a wall area of 2.8 × 2.8 m2 while mounted to the ceiling. The homogeneity is better than 80% and the optical efficiency including Fresnel losses is about 85%