A directional backlight comprising: a waveguide comprising an input end ; and an array of light sources disposed at different input positions in a lateral direction across the input end of the waveguide, the waveguide further comprising first and second, opposed guide surfaces for guiding light along the waveguide , and a reflective end facing the input end for reflecting the input light back through the waveguide , the first guide surface being arranged to guide light by total internal reflection and the second guide surface having a stepped shape comprising: a plurality of facets oriented to reflect light from each of the light sources , after reflection from the reflective end , through the first guide surface into a respective optical window, the optical windows being in output directions distributed in a lateral direction to the normal to the first guide surface in dependence on the input positions of the light sources in the lateral direction across the input end of the waveguide, and intermediate regions between the facets that are arranged to guide light through the waveguide, characterised in that the directional backlight further comprises a rear reflector comprising a linear array of reflective facets arranged to reflect light from the light sources , that is transmitted through the plurality of facets of the waveguide , back through the waveguide to exit through the first guide surface into said respective optical windows. a waveguide comprising an input end ; and an array of light sources disposed at different input positions in a lateral direction across the input end of the waveguide, the waveguide further comprising first and second, opposed guide surfaces for guiding light along the waveguide , and a reflective end facing the input end for reflecting the input light back through the waveguide , the first guide surface being arranged to guide light by total internal reflection and the second guide surface having a stepped shape comprising: a plurality of facets oriented to reflect light from each of the light sources , after reflection from the reflective end , through the first guide surface into a respective optical window, the optical windows being in output directions distributed in a lateral direction to the normal to the first guide surface in dependence on the input positions of the light sources in the lateral direction across the input end of the waveguide, and intermediate regions between the facets that are arranged to guide light through the waveguide, a plurality of facets oriented to reflect light from each of the light sources , after reflection from the reflective end , through the first guide surface into a respective optical window, the optical windows being in output directions distributed in a lateral direction to the normal to the first guide surface in dependence on the input positions of the light sources in the lateral direction across the input end of the waveguide, and intermediate regions between the facets that are arranged to guide light through the waveguide, characterised in that the directional backlight further comprises a rear reflector comprising a linear array of reflective facets arranged to reflect light from the light sources , that is transmitted through the plurality of facets of the waveguide , back through the waveguide to exit through the first guide surface into said respective optical windows. <EOS>