An illumination system for illuminating a display device includes a light-mixing chamber having a light-exit window, a rear wall situated opposite the light-exit window, and edge walls which extend between the light-exit window and the rear wall. A surface of the rear wall 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 includes a light source light out-coupling elements. The light source emits light into the light-mixing chamber in a direction substantially parallel to the light-exit window. The illumination system further includes an angularly reflective filter applied at the light-exit window. The angularly reflective filter includes substantially transparent layers, each layer having a substantially uniform thickness. Each set of two adjacent layers of the angularly reflective filter has different refractive indexes.