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Illumination & Displays
Simplifying the lightpipe design process
Approaches that simplify the lightpipe design process will enable the widespread use of lightpipes in displays, dashboards, lighting, and light homogenizers.
3 March 2006, SPIE Newsroom. DOI: 10.1117/2.1200602.0113
Lightpipes are simple devices that transfer light,but not images. The light travels via total internal reflection along the inner surface of a solid body made from an optical-quality highly-transmissive material. Lightpipes are used in a variety of displays such as automotive dashboards and instrument panels, in lighting applications such as pools and backlights, and as light homogenizers.1 Because of the tremendous flexibility in lightpipe geometry, illumination transfer can be tightly controlled in terms of output distribution and light channeling. So far, however, very little is known about how to ease the design of such systems. We are seeking principles that simplify calculations of flux distribution across lightpipe geometry and rules to determine layout. This will make the lightpipe design process considerably easier, enabling their widespread use in many fields.
Currently, lightpipes are designed by performing Monte Carlo ray tracing on a number of trial geometries. Although this method is excellent for designing imaging systems, it is very slow at analyzing flux across the lightpipe and selecting an adequate layout. Nor does it allow for a systematic design approach towards a desired lightpipe layout and performance in a constrained space.
To simplify the design process, we believe, there are three key analytical problems to be solved. First, we must be able to lay out the lightpipe geometry in a constrained space that takes manufacturing considerations into account. Then we need to calculate the flux-transfer efficiency across a complicated light geometry. This includes checking for the possibility of a leak-free implementation, as well as locating and quantifying any leakage. Finally, we must calculate the light distribution (spatial and angular) at the lightpipe output as a function of known input.
Solving these problems will enable us to describe lightpipe performance in terms of parameters such as the refractive index, thickness, cross-section shape and size, bend radii or a description of bend curves. This will enable a faster design process via easy access to engineering trade-off variables.
We recently demonstrated a method of parameterizing the design of a single-bend lightpipe to enable designs that avoid any undercut. Undercut means that the thickness of the lightpipe decreases along linear sections of the input and output legs and leads to, at a minimum, difficult manufacture. Relevant parameters included the lightpipe region volume, the dimensions of the input/output apertures, the bend angle and the refractive index.2 The locus of the curves along which the center of inner and outer bend of the lightpipe lay have been determined. The locus curve equations can be integrated in optical CAD software to ‘draw’ lightpipes in a given space that take care of the undercut problem. It is now possible to automate the design process via bend locus parameters to evaluate the transfer efficiencies of various bends. Figure 1shows the results.
Figure 1. Four bend geometries offer lightpipes with differing efficiencies at transfering light. The middle plot shows efficiencies with respect to the inner and outer curve radii (r1 and r2). The shaded regions are grouped into evenly spaced efficiency bands.
Earlier, we described a method to simplify the design of leakage-free multiple-bend lightpipes by showing that it is sufficient to analyze the light rays in the principal—symmetric—sections of a lightpipe3 This result was used to show that the refractive index and ratio of bend radii are the only dimensionless parameters to determine the maximum acceptance angle for a constant-cross-section right circular bend. Recently it has been shown4—by analyzing the light in the principal section of the bend—that using a spiral curve instead of a circular curve for the bend enables a 180-degree acceptance angle. Another positive development in this direction has been made by the introduction of flux confinement diagrams5 to quantify leakage across a bend. Others have recently provided theoretical insight on how to contend with the skew invariance by integrating surface features such as ripples and twisting.6
The knowledge of parametric equations that govern the flux propagation will help in quantifying lightpipe performance on the fly during the layout process, without the need for expensive ray traces. A collection of such methods to analytically determine the flux propagation through a lightpipe, and rules to determine possible layouts in a constrained space will simplify the lightpipe design, will ultimately lead to an automated design process.
Hewlett Packard Co
Anurag Gupta is a Senior Optical Engineer engaged in the design of imaging and illumination systems for displays at HP. Prior to joining HP, he designed optics for lithography and laser ablation tools at Tamarack Scientific Co. He holds a Ph.D in Optics from the University of Arizona. He is currently serving on the SPIE's co-sponsored International Optical Design Conference 2006, co-sponsored by SPIE.
R. John Koshel
Lambda Research Corporation
John Koshel is a senior staff engineer at Lambda Research Corp. Where the bulk of his time is spent working on illumination system design and algorithm development. He is also an adjunct, assistant professor at The College of Optical Sciences, University of Arizona. Prior to Lambda he worked at Spectrum Astro and Breault Research Orgnization. He obtained his PhD in optics from the University of Rochester. He has chaired two SPIE conferences. He is currently serving on the SPIE's Program, Symposia, Award, and Audit Committees. He is a co-chair for the International Optical Design Conference 2006. Finally, he is an editor for SPIE Newsroom in the area of Illumination and Displays.