A directional backlight for a transmissive spatial light modulator, comprising: 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 (15a-15n) arranged to output light predominantly in an emission band and in a conversion band, the light sources (15a-15n) each comprising a light generation element arranged to generate light in the emission band and a wavelength conversion material arranged to convert at least some of the light in the emission band generated by the light generation element into light in the conversion band, the light sources being disposed at different input positions in a lateral direction across the input end of the waveguide, the waveguide being arranged to direct input light from light sources at the different input positions across the input end after reflection from the reflective end as output light through the first guide surface for supply through a transmissive spatial light modulator into respective optical windows (26,44) in output directions distributed in the lateral direction in dependence on the input positions; and characterized in that the directional backlight further comprises: a reflection reduction element that comprises a filter, disposed between the input end and the light sources (15a-15n), and arranged to absorb light in the conversion band preferentially over light in the emission band so as to reduce reflections of light incident on the input end after reflection from the reflective end. 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 (15a-15n) arranged to output light predominantly in an emission band and in a conversion band, the light sources (15a-15n) each comprising a light generation element arranged to generate light in the emission band and a wavelength conversion material arranged to convert at least some of the light in the emission band generated by the light generation element into light in the conversion band, the light sources being disposed at different input positions in a lateral direction across the input end of the waveguide, the waveguide being arranged to direct input light from light sources at the different input positions across the input end after reflection from the reflective end as output light through the first guide surface for supply through a transmissive spatial light modulator into respective optical windows (26,44) in output directions distributed in the lateral direction in dependence on the input positions; and characterized in that the directional backlight further comprises: a reflection reduction element that comprises a filter, disposed between the input end and the light sources (15a-15n), and arranged to absorb light in the conversion band preferentially over light in the emission band so as to reduce reflections of light incident on the input end after reflection from the reflective end.