We report on an extension of the previously published two-step freeform optics tailoring algorithm using a Monge-Kantorovich mass transportation framework. The algorithm's ability to design multiple freeform surfaces allows for the inclusion of multiple distinct light paths and hence the implementation of multiple lighting functions in a single optical element. We demonstrate the procedure in the context of automotive lighting, in which a fog lamp and a daytime running lamp are integrated in a single optical element illuminated by two distinct groups of LEDs.
The advent and rapid development of efficient high power LED sources with their unique emission characteristics
enables the development of illumination systems that meet very strict requirements concerning light distribution
and efficiency. Most of the algorithms used to design the necessary optical freeform surfaces rely on the point
source assumption. As long as the distance between LED and those surfaces is sufficiently large, this is a good
approximation. One further important design goal is to make the optical components as small as possible, which
makes the point source assumption less accurate. The existing design algorithms thus have to be accompanied
by methods to treat the finite-sized LED sources. We examine the limits that are set by the finite size of the light
sources and present algorithms to optimize optical freeform surfaces up to these limits. Point source results are
iteratively improved to get the desired illumination pattern employing finite sized LEDs. At each iteration step
the illumination pattern used in the point source computations is adapted so that the real illumination pattern
of an LED approximates the originally desired pattern.
Based on the Monge-Kantorovich theory of optimal mass transport, the computation of a ray mapping between source and target irradiances is used to design two-sided freeform lenses fulfilling the constraints of an automotive application: compactness and sharp bright-dark cutoff. A generic segmentation technic resulting in Fresnel-type optics is presented and the whole procedure is illustrated with the design of a fog light lens. Finally Monte Carlo simulation of the virtual model and measurements of a polycarbonate prototype are presented.
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 <i>z</i> 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 product 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 m<sup>2</sup> while mounted to the ceiling. The homogeneity is better than 80% and the optical efficiency including Fresnel losses is about 85%.