3 October 1997 Consequences of etendue and skewness conservation for nonimaging devices with inhomogeneous sources and targets
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Abstract
We generalize a previous derivation of theoretical upper limits on measures of flux-transfer performance of nonimaging optical systems to include the case of sources and targets having inhomogeneous distributions of radiance and importance weighting. This generalization is of practical importance in understanding the limitations of optimally designed projectors which collect light from complex 3D sources such as filament or HID sources. The performance limits are derived from the conservation of etendue and--for the case of rotationally symmetric optics-- from skewness conservation. The limits on performance are calculated for examples involving the use of rotationally symmetric optics to transfer flux from homogeneous and inhomogeneous spherical sources to a homogeneous disk shaped target having a phase-space volume equal to that of the source. It is shown that an optical system which is optimal for the case of a homogeneous source and target will not necessarily provide the best achievable performance when used in conjunction with an inhomogeneous source and/or target occupying the same regions of phase space as the homogeneous source and target. The theoretical upper limits are shown to be consistent with the performance of three numerically optimized reflector designs.
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John C. Bortz, Narkis E. Shatz, Harald Ries, R. Winston, "Consequences of etendue and skewness conservation for nonimaging devices with inhomogeneous sources and targets", Proc. SPIE 3139, Nonimaging Optics: Maximum Efficiency Light Transfer IV, (3 October 1997); doi: 10.1117/12.290222; https://doi.org/10.1117/12.290222
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