We present a detailed investigation of an optical system which couples the light of a Lambertian Source (for example, a high power LED array) to an equal etendue target. Such a system can be applied for gobo illumination or for illuminating a lightguide. Though the efficiency of such a system may by ideal in theory, real-world constraints make it imperfect. The actual light collection angle by the target may play a role, and requirements such as the clearance between the optics and source or target and the maximum system diameter will have an influence on imaging and non-imaging designs. As for some applications an uniform illumination of the target may be required, we finally analyze the ability of various designs to deliver homogeneity.
H. Rehn, H. Rehn,
"Practical optical design of an LED collimator", Proc. SPIE 9629, Optical Systems Design 2015: Illumination Optics IV, 962907 (23 September 2015); doi: 10.1117/12.2191217; https://doi.org/10.1117/12.2191217