We consider the problem of designing an ultra-high-numerical-aperture rotationally symmetric monochromatic imaging concentrator that could be used for optical detection and tracking. This problem combines requirements for both high-efficiency flux transfer and low focal-plane aberrations. A solution has been previously demonstrated using the 2D SMS technique, resulting in the RX concentrator design. We review the RX concentrator and analyze its performance. We then describe a numerical test of the RX concentrator for optimality, performed using a global optimization procedure. We present the results of this test, which produced a counter-example possessing significantly improved imaging and nonimaging performance. The solution space was then extended to a globally optimized cemented-doublet comprising three aspheric surfaces, of which two are refractive and the third reflective. Compared with the original RX concentrator, the optimized doublet provides a threefold reduction in the mean aberration level within the field of view, combined with a significant improvement in flux-transfer efficiency, without any increase in the axial lens thickness.© (2005) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.