For the usage of solar concentration systems, non-imaging secondary (NIS) reflectors comprised of concave and convex shapes based on differential equations are proposed in this study. Ray tracing technique is adopted in the estimation of the concentrated irradiance on the receiver. The concentrated solar irradiance on the receiver of the non-imaging reflectors shows excellent performance in terms of uniformity. This study also indicates that when the primary reflector and the receiver size are fixed, the size of the non-imaging reflectors is mainly determined by the location of the start point of its mother curves. (C) 2014 Elsevier Ltd. All rights reserved.