In order to perform imaging and spectroscopy of nano-sized emitters at a temperature of a few kelvins, we have developed a single-component reflecting objective (M. Fujiwara, et al. 2009 [1]). In this work, we report a method to find the optimum numerical aperture (NA) which balances the spherical aberration on one hand and the solid angle to collect emitted photons on the other. For the objective of a focal length of 2 mm, the optimum NA was found to be 0.50 at a wavelength of 250 nm, 0.55 at 400 nm, and 0.60 at 800 nm. (C) 2011 Published by Elsevier B. V.