A directional backlight for a transmissive spatial light modulator comprises a waveguide having an input end, first and second, opposed guide surfaces for guiding light along the waveguide, and a reflective end facing the input end for reflecting light from the input light back through the waveguide. An array of light sources that output light predominantly in an emission band and in a conversion band are disposed across the input end of the waveguide and light is directed into respective optical windows in output directions distributed in the lateral direction in dependence on the input positions. To achieve crosstalk suppression, disposed between the input end and the light sources is a reflection reduction element that comprises a filter arranged to absorb light in the conversion band preferentially over light in the emission band, thereby reducing reflections of light incident on the input end after reflection from the reflective end.