LEDs are considered to be the next-generation light source because they offer good color control, dimming capability, short switching response times, compactness, long lifetimes, and they are environmentally friendly. They are already being widely used in liquid crystal displays (LCDs), signal lamps, and decorative lighting. Currently one of the biggest limitations to using LEDs for general lighting is their high cost per lumen. Improving the efficiency of the systems is important for the future of LED lighting applications.

Traditionally, most lenses are spherical and most reflectors aspherical because these shapes are relatively easy to produce. Such simple shapes, however, lack the design freedom engineers need to solve complex energy distribution problems in lighting systems.^{1} On the other hand, with the development of modern manufacturing technology, more and more free-form surfaces are being adopted in lighting systems. Compared to traditional shapes, these surfaces can provide many more variables for the designer to use.

With free-form surfaces, the light can be precisely controlled so complex and irregular energy distribution can be achieved, and the efficiency of the whole system can be made quite high. Free form representation and optimization algorithms can be used to design optical components for LED lighting systems. One kind of widely-used free-form surface is called a B-spline. It has many properties that make the design process easier. For example, the order of the spline function is independent of the number of control points. Also, local changes to the surface shape are possible because individual control points have only local influences.^{2}

The traditional design process for lighting systems is labor intensive. To realize automated design, the light system needs to be parameterized and a merit function constructed, then a proper optimization algorithm can be chosen. A B-spline surface combined with the differential evolution (DE) algorithm enables us to perform automated free-form lens design. As shown in Figure 1, a free-form lens is required to generate a uniform illuminance distribution. The LED chip in this example measures 1×1mm and emits light from its front surface with a Lambertian angular distribution. A receiver is set 100mm away from the lens. The first surface of the plastic lens is spherical, while the second surface is obtained from a B-spline curve symmetrical around the axis. The coordinates of the nine control points of the B-spline curve are treated as variables, and a proper merit function is constructed. We use a commercial package to perform non-sequential ray tracing , then use the illuminance mesh data on the receiver to calculate the merit function value. After about 50 iterations, the software gave a solution as shown in Figure 1(a). With the lens, about 78% of the total energy from the LED is distributed within the required area and the illuminance uniformity is better than 73%.

**Figure 1.** (a) A free-form lens for an LED that generates a uniform illuminance distribution within a 120° range. (b) The illuminance distribution generated by an LED chip without the free-form lens on a receiver 100mm away. (c) The illuminance distribution generated by the LED chip and the lens, on the same receiver.

**Figure 2.** (a) The lighting system with a free-form segmented reflector and an LED source. (b) The illuminance distribution generated by the free-form reflector on a receiver 500mm away.

The optimization algorithms using derivatives can be found if the system merit function can be differentiated. For most of these systems, the performance can be evaluated through sequential raytracing. For example, a geometrical ray fan is sufficient to evaluate the performance of a rotationally symmetric collimator. Usually the structure of such a system is simple and symmetric.

It's hard to directly use such an approach for systems with a complex energy distribution requirement, but the problem can be simplified by dividing the system into subsystems. One of the classic examples of such a system is the vehicle headlamp reflector: the energy distribution near the light is complex and non-symmetric. It is difficult to obtain such a distribution with one simple reflector, so the reflector is segmented and each segment only reflects light to a small region on the receiver.

The concept of characteristic rays can be introduced in the optimization process for such segmented reflector designs.^{3} First, the designer determines the XY segment map. Each segment is a B-spline surface and the Z coordinates of the control points of each segment are treated as variables. Sampling points are uniformly selected on each segment. Rays traveling from the source to the surface sampling points are traced. These sampling point rays are called the characteristic rays. Next, the designer sets up a merit function. The coordinates of the intersection points of each characteristic ray with the receiver are used to calculate the merit function value. The DLS (dumped least squares) algorithm is adopted for optimization in this case. Each segment is then optimized separately. Boundary limits can be added to keep the segments connected with each other during optimization. As shown in Figure 2, the illuminance pattern of the three letters ‘VTT’ can be generated with an LED and a reflector with 20 segments. Light is limited to distribution only in the ‘VTT’ pattern region. No other optical component is needed to generate the pattern. The efficiency is high because it is affected only by the the LED's emitting angle and the reflector's efficiency.

As we have shown, free-form optical components can provide complex light distribution and high efficiencies. We have proposed an approach that uses free-form surfaces and an optimization algorithm to perform automated optical design of LED lighting systems.

Bo Yang

GE (China) Research and Development Center Co., Ltd

Shanghai, China

Bo Yang is currently working for the GE (China) Research and Development Center. His research interest is imaging technology and optical system design. Bo Yang acquired his doctoral degree from the Beijing Institute of Technology in 2005, and finished his post-doctoral research at Tsinghua University in 2007. He was also a visiting scholar at the VTT Technical Research Centre of Finland in 2006.