The present embodiments provide methods and systems to homogenize illumination on a target. Some embodiments provide rotational symmetric dual-reflector solar concentrators that include a concave primary reflector with an aim-direction directed toward the sun to receive optical radiation in a far-field angle within an angle of acceptance and redirect radiation upward and centrally generating flux concentration, a secondary reflector positioned coaxial with said primary reflector to receive said redirected radiation and redirect radiation downward and centrally generating flux concentration solar rays, and a central target zone receiving said concentrated solar rays, where cross sections of said primary and secondary reflectors both further comprise a multiplicity of segments that establish a correspondence between pairs of segments, each of said segments of said primary reflector such as to image said angle of acceptance onto said corresponding segment of said secondary reflector to image onto said target zone.