The invention relates to an illumination system (10, 20, 30) for illuminating a display device (40) and to a display device (40). The illumination system comprises a light-mixing chamber (50) which comprises a light-exit window (52), a rear wall (54) which is situated opposite the light-exit window (52), and edge walls (56, 58) which extend between the light-exit window (52) and the rear wall (54). A surface (55) of the rear wall (54) is substantially specularly reflective for specularly reflecting light impinging on the surface of the rear wall and having a relatively large angle of incidence with respect to an axis perpendicular to the rear wall. The illumination system further comprises a light source (60, 62) and a plurality of light out-coupling elements (70). The light source emits light into the light-mixing chamber in a direction substantially parallel to the light-exit window. The illumination system further comprises an angularly reflective filter (80) applied at the light-exit window. The angularly reflective filter is constituted of a plurality of substantially transparent layers (81, 82, 83, 84), each layer having a substantially uniform thickness. Each set of two adjacent layers (81, 82, 83, 84) of the angularly reflective filter has different refractive indexes.