Illumination system (10, 20, 30) for illuminating a display device, the illumination system (10, 20, 30) comprising, - a light-mixing chamber comprising a light-exit window, a rear wall situated opposite the light-exit window, and edge walls (56, 58) extending between the light-exit window and the rear wall, a surface of the rear wall being 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 relatively large angle of incidence being larger than 60 degrees, - a light source (60, 62) for emitting light into the light-mixing chamber, the light being emitted into the light-mixing chamber in a direction substantially parallel to the light-exit window, the emitted light being substantially polarized light having a polarization direction parallel to the light-exit window, - a plurality of light out-coupling elements (70, 72) for coupling out the light from the light-mixing chamber, and characterized by - an angularly reflective filter arranged at the light-exit window, the angularly reflective filter being constituted of a plurality of substantially transparent layers (81, 82, 83, 84), each layer (81, 82, 83, 84) having a substantially uniform layer-thickness and having a refractive index (n1, n2), each set of two adjacent layers (81, 82, 83, 84) having different refractive indexes (n1, n2), the angularly reflective filter acting as an angularly selective reflective filter for reflecting light impinging on the light-exit window having the relatively large angle of incidence with respect to a normal-axis to the light-exit window and for transmitting light impinging on the light-exit window having a relatively small angle of incidence with respect to the normal-axis. - a light-mixing chamber comprising a light-exit window, a rear wall situated opposite the light-exit window, and edge walls (56, 58) extending between the light-exit window and the rear wall, a surface of the rear wall being 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 relatively large angle of incidence being larger than 60 degrees, - a light source (60, 62) for emitting light into the light-mixing chamber, the light being emitted into the light-mixing chamber in a direction substantially parallel to the light-exit window, the emitted light being substantially polarized light having a polarization direction parallel to the light-exit window, - a plurality of light out-coupling elements (70, 72) for coupling out the light from the light-mixing chamber, and characterized by - an angularly reflective filter arranged at the light-exit window, the angularly reflective filter being constituted of a plurality of substantially transparent layers (81, 82, 83, 84), each layer (81, 82, 83, 84) having a substantially uniform layer-thickness and having a refractive index (n1, n2), each set of two adjacent layers (81, 82, 83, 84) having different refractive indexes (n1, n2), the angularly reflective filter acting as an angularly selective reflective filter for reflecting light impinging on the light-exit window having the relatively large angle of incidence with respect to a normal-axis to the light-exit window and for transmitting light impinging on the light-exit window having a relatively small angle of incidence with respect to the normal-axis.