The illumination system has a light source (1) with a plurality of light emitters (R, G, B). The light emitters comprise at least a first light-emitting diode of a first primary color and at least a second light-emitting diode of a second primary color, the first and the second primary colors being distinct from each other. The illumination system has a facetted light-collimator (2) for collimating light emitted by the light emitters. The facetted lightcollimator is arranged along a longitudinal axis (25) of the illumination system. Light propagation in the facetted light-collimator is based on total internal reflection or on reflection at a reflective coating provided on the facets of the facetted light-collimator. The facetted light-collimator merges into a facetted light-reflector (3) at a side facing away from the light source. The illumination system further comprises a light-shaping diffuser (17). The illumination system emits light with a uniform spatial and spatio-angular color distribution.