In this paper, we investigate how to improve the uniformity of the spatial distribution of the illuminance at the output plane for angle-to-area-converting, light-piping systems through the introduction of cyclical surface features. A superposition approach is used for studying uniformity. Improvements in uniformity for square-to-circle and rectangle-to-circle lightpipe configurations are demonstrated for a short package length.
Angle-to-area converters are a key topic of illumination design, and much work has been done in this area over the last 30 years. However, relatively little work exists in the literature in which these converters have been designed using optimization techniques. The present work takes a fresh look at some angle-to-area conversion problems using optimized, circularly and non-circularly symmetric surfaces.
An analytical model of flux propagation in light pipes, termed the flux confinement diagram (FCD), is further developed and applied. The construction of the FCD is reviewed. Non-planar surface geometries, non-constant cross-sectional geometries, and non-rectangular cross sectional geometries are examined with the FCD. It is shown that in the limit of a circular cross section the predictions of the FCD match the theory for large core fibers. Additionally, the angular propagation space defined by the FCD is explored further to describe the redistribution of propagating flux after a sudden change in geometry, such as a bend. This analysis is used to explore total internal reflection (TIR) at light pipe output surfaces. The implications of analytical modeling with the FCD on light pipe design are discussed.
Computers are routinely used to design illumination systems. Automating the design process is enhanced through the use of optimization procedures. This paper describes some of the underlying illumination optimization fundamentals: parameterization, merit functions, and optimization algorithms. Numerous interesting examples of illumination design problems that benefit from optimization are shown. These examples illustrate illumination optimization through use of ray aiming, computing illuminance using flux tubes, and computing illuminance using Monte Carlo simulations.
An analytical model of light propagation in rectangular light pipes, termed the flux confinement diagram (FCD), is developed. Based on the edge ray concept of nonimaging optics, the FCD is a construction that describes the angular distribution of flux propagating in a light pipe depending on a light pipe's index of refraction and its geometry. With the FCD model, the angular "mode" of a ray can be defined at any plane in the system. The FCD model is developed here and used to describe flux input coupling, transport, and output coupling in light-pipe illumination systems. The practical example of a flux loss prediction due to a geometrical change (a bend) is examined using the FCD and compared to a ray-tracing analysis. We discuss how this model of flux propagation is a useful tool to aid in "first-order" design and layout of light-pipe illumination systems.
An analytical model of light propagation in rectangular light pipes is presented. Light pipe illumination systems are an efficient means of collecting, transporting, and distributing light. One area where light pipe illumination systems are successfully employed is in transportation display lighting, such as instrument panel illumination. In these applications the transportation industry takes advantage of injection molding to manufacture light pipe systems at relatively low costs. One historical drawback to using light pipe illumination systems is the design effort associated with iterative prototyping cycles and evaluation.
The model presented here is a graphical method of describing ray propagation in light pipes. The model describes ray direction vector space in spherical coordinates. With this model, the angular "mode" of a ray can be defined at any plane in the system. The angular mode propagation space describes input coupling, flux transport, and output coupling in light pipe illumination systems. The model of flux propagation described here is therefore a tool to aid in "first order" design and layout of light pipe illumination systems.
We discuss our experimental measurement and theoretical modeling of flux distributions from light sources used in waveguide illumination systems. We have constructed a computer-controlled goniometric detection system to map the intensity distributions of these light sources. As an example, we measure the intensity distribution of an incandescent light bulb. This light bulb is used in the waveguide illumination system of an automobile dashboard. The intensity distribution of this light bulb is not uniform. We present a model for this intensity distribution based on radiometric principles and the shape of the light bulb filament. This model describes the light bulb's intensity distribution as a function of the filament's projected area as seen from the detector.