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Illumination & Displays
Optimizing LED illumination systems
Sergey Kudaev and Peter Schreiber
Getting the best applicationspecific illumination systems involves direct optimization of nonimaging optical elements.
8 October 2006, SPIE Newsroom. DOI: 10.1117/2.1200609.0353
From imager illumination and special inspection systems to general internal and even external lighting, LEDs are promising light sources for a variety of applications because of their compactness, good color control, dimming capability, short switching response, and long lifetime. Already, modern highpower LEDs are comparable to incandescent lamps in their electrooptical conversion efficiency. However, to be competitive with incandescent lamps, illumination systems need to operate with maximal performance in such areas as transmittance, homogeneity, and size. This is because of the current but temporarily high lumen cost of LED light.
Modular approaches are most common in the design of optical systems, so we separate our design into primary optics (for collimation of Lambertianlike light sources with small residual divergence, typically ±3…±20° ) and secondary optics (for further beam shaping and transformations). Classical design of nonimaging collimators includes externally generating a mathematical description of the element and then converting it to CAD formats.^{1} Then, the CAD model is imported into raytracing software for performance evaluation. This approach has several drawbacks as typically the designer needs different design tools for different collimator types. This approach also provides insufficient freedom to explore the parameter space, with possible loss of precision due to multiple dataformat conversions. Thus, we use direct optimization of the collimator shape according to different criteria.^{2}
The general tradeoff in nonimaging optics is between conservation of etendue (in optical systems the product of emitting area times the solid angle of emitted light cannot decrease without losses) and both mechanical and technological constraints. Optimization makes it possible to find the best compromise solution to fulfill the requirements and to limit the constraints. For instance, it is almost impossible to analytically design a system with limited sizes producing maximal light flux, or a system that is insensitive to misalignments of LEDs relative to optical elements. Design with optimization makes these possible if the designer has the required tools: parametrical description of the object, a definition of the merit function, and the appropriate optimization algorithms. All these tools differ from classical optical design because only nonsequential raytracing can adequately simulate nonimaging optics. Our design methods consist of addons for commercially available optical design software, ensuring the necessary flexibility and robustness.
For parametrical modelling of optical elements we use rational Bezier splines to ensure sufficient flexibility in representing standard conic curves and even piecewise Cartesian ovals.^{3} Highorder Bezier splines are numerically stable (we are using curves to the 20^{th} order) even with highly nonuniform sampling.^{4} A very important feature of rational Bezier splines is that the curve order (i.e. the number of degrees of freedom for optimization) can be increased without changing the already optimized shape. After searching for a global optimum with a small number of variables, we perform local optimization with sequentially increasing orders of the curve (after some iterations).
The choice of optimization algorithm and merit function depends strongly on the problem definition. If it is possible to find a simple abstraction, that is, to describe the properties of the system in a geometrical manner, then we can use optimization algorithms with derivatives (for example, dumped least squares or DLS). An example of such an abstraction is the edgeray principle: rays from the edge point of the extended light source should propagate under the angle of residual divergence of the output beam after leaving the collimator.^{1} Thus, we are optimizing the system in such a way that each ray in two ray fans from edges of the source propagates collinear and under the maximum target angle. Rotationally symmetrical collimators (see Figure 1), designed according to this principle operate almost at the etendueconservation limit.^{3}
Figure 1. Because of the two light paths (refraction through a central lens or total internal reflection on the front surface, and reflection on the metallized back surface and refraction through front surface), this parametrical model of the collimator with folded, multiple reflections is very compact with a lengthtodiameter ratio of 1/3. Each ray fan propagates collinear after leaving the collimator.
A couple of applications require additional, special (typically, homogeneous) light distributions. For these applications it is impossible to find the geometrical abstraction for the merit function. Instead, we optimize them by estimating overall flux and its distribution within residual divergence (see Figure 2). The flux is determined by tracing a limited number of rays (MonteCarlo raytracing). In essence, we apply methods of nonlinear optimization without derivatives for such a design, which is stable even in the tasks of statistical estimation of merit functions. Note that DLS algorithms fail to optimize such a system.^{2}
Figure 2. Rectangular crosssection and optimized profile ensure homogeneous nearfield light distribution (optimization with MonteCarlo raytracing) in this collimator with residual divergence ±10°.
In summary, we use direct optimization of nonimaging collimators for design of applicationspecific illumination systems. Compared with ‘off the shelf’ optical components, our approach ensures size reduction, the increase of useful transmission, and irradiance homogenization without the use of secondary optics.
Figure 3. On the left, the collimator has residual divergence±5° (transmission more than 80%, 34mm, length 12mm). On the right, the collimator has residual divergence ±15°(transmission ∼90%, 14mm, length 15mm). Both are made of polymethyl methacrylate for OSRAM OSTAR® LED modules.
Authors
Sergey Kudaev, Peter Schreiber
Microoptical Systems Dept, Fraunhofer IOF
Jena, Germany
Sergey Kudaev received his firstclass diploma in electronic engineering in 1996 and PhD in 2000 from Vladimir State University in Russia. Currently, he works at the Fraunhofer Institute of Applied Optics and Precision Engineering in Jena, Germany. His research interests include developing new methods of nonimaging optical design.


