Direct design of aspherical lenses for extended non-Lambertian sources in three-dimensional rotational geometry

Abstract

Illumination design used to redistribute the spatial energy distribution of light source is a key technique in lighting applications. However, there is still no effective illumination design method for extended sources, especially for extended non-Lambertian sources. What we present here is to our knowledge the first direct method for extended non-Lambertian sources in three-dimensional (3D) rotational geometry. In this method, both meridional rays and skew rays of the extended source are taken into account to tailor the lens profile in the meridional plane. A set of edge rays and interior rays emitted from the extended source which will take a given direction after the refraction of the aspherical lens are found by the Snell's law, and the output intensity at this direction is then calculated to be the integral of the luminance function of the outgoing rays at this direction. This direct method is effective for both extended non-Lambertian sources and extended Lambertian sources in 3D rotational symmetry, and can directly find a solution to the prescribed design problem without cumbersome iterative illuminance compensation. Two examples are presented to demonstrate the effectiveness of the proposed method in terms of performance and capacity for tackling complex designs.

Design of compact and ultra efficient aspherical lenses for extended Lambertian sources in two-dimensional geometry

“…Since two-dimensional (2D) designs are in any case the first step towards a generalization for three-dimensional (3D) designs, we focus on the design of two refractive surfaces in 2D geometry. Compared to our previous publications [13][14][15], the contribution of this paper is threefold: we first reveal an intrinsic feature of the compact and ultra efficient two-surface design; secondly, the new methods presented in this paper overcome the limitations of one single surface design in our previous work [13][14][15], a good compactness along with high energy efficiency is easily achieved; thirdly, the second proposed method is much simpler and easier to be implemented, and has an excellent extensibility to 3D designs.…”

“…Since the entrance surface in the second method is a parabola, the second method is much simpler and easier to be implemented, and has an excellent extensibility to 3D designs. We have shown in our previous work that there are at least two ways to generalize 2D designs to 3D designs: one is illuminance feedback [13] and the other one is direct design [15]. In our future work, we will generalize the second proposed method to 3D designs for extended non-Lambertian sources.…”

“…Since the étendue of an extended source (an actual source) is nonzero, usually those zero-étendue algorithms with the assumption of ideal source will be invalid in compact designs [2][3][4][5][6][7][8]. A number of algorithms which have been developed for extended sources by taking the étendue of an extended source into account [9][10][11][12][13][14][15]. Although those algorithms for extended sources have a potential to achieve a significant reduction in size of the illumination system along with a good compactness and high energy efficiency, the illumination design for extended sources is still not well addressed and faces many unresolved challenges.…”

“…Although those algorithms for extended sources have a potential to achieve a significant reduction in size of the illumination system along with a good compactness and high energy efficiency, the illumination design for extended sources is still not well addressed and faces many unresolved challenges. Most of the existing algorithms for extended sources employ a single aspherical surface to redistribute the spatial energy of a light source [9][10][11][12][13][14][15]. Due to the limitation of a single aspherical surface, the controls on the distribution of light rays are limited, and we usually have to make a trade-off between the compactness and energy efficiency [13][14][15] (see Fig.…”

Design Ultra-Compact Aspherical Lenses for Extended Sources Using Particle Swarm Optical Optimization Algorithm

“…For zero-étendue cases, the light source is regarded as a point-like source, in which there is only one single ray passing through each point on the optical surfaces [5]. This approximation can lead to an accurate one-to-one ray mapping relationship between source and target [6], [7].…”