Lightpipes are used to transfer light from the source to a desired target. The lightpipe shape typically conforms to the necessary path, thus bending of the lightpipe is required. A number of different methods of bending the lightpipe have been developed, from linear, discontinuous bends to smooth, common circular bends to bends that expand or contract the cross-sectional size of the lightpipe over the path. In this paper we develop a set of parameters to describe the overall shape of an in-plane lightpipe section. These parameters include the thickness, radius of bend, index of refraction, and ratios of sets of these parameters. The transfer efficiency from the source to target is used to quantify the utility of parameterized lightpipes. Etendue is used to highlight the results. More complex lightpipes, such as those with several bends along their path, can be developed from the combination of parameterized sections. Finally, this parameterization can be used to automate the development of lightpipe geometry within optical analysis and design software.
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