A directional backlight for a transmissive spatial light modulator, comprising: a waveguide comprising an input end; and an array of light sources at different input positions in a lateral direction across the input end, the light sources being arranged to input light into the waveguide through the input end, the light sources having light emitting areas with respective lateral extents, the waveguide further comprising first and second, opposed guide surfaces (6, 8) for guiding the input light along the waveguide, and a reflective end facing the input end for reflecting the input light guided from the input end back through the waveguide, wherein the second guide surface is arranged to deflect light reflected from the reflective end through the first guide surface as output light, the reflective end has positive optical power in the lateral direction, and the waveguide is arranged to image the light sources in the lateral direction so that the output light from the light sources is directed into respective optical windows that are distributed in the lateral direction in dependence on the input positions of the light sources, characterized in that the light sources include at least one pair of adjacent light sources (15h, 15h) arranged at input positions offset from the optical axis of the reflective end, wherein, within the pair, the light source closest to said optical axis is inclined with the normal to the lateral extent of its light emitting area inclined towards said optical axis and the light source furthest from said optical axis is inclined with the normal to the lateral extent of its light emitting area inclined away from said optical axis, and the input end of the waveguide comprises a pair of inclined input facets (500, 506) extending across the light emitting areas of the respective light sources (15h, 15g) of said pair and an intermediate facet extending between the inclined input facets (500, 506). a waveguide comprising an input end; and an array of light sources at different input positions in a lateral direction across the input end, the light sources being arranged to input light into the waveguide through the input end, the light sources having light emitting areas with respective lateral extents, the waveguide further comprising first and second, opposed guide surfaces (6, 8) for guiding the input light along the waveguide, and a reflective end facing the input end for reflecting the input light guided from the input end back through the waveguide, wherein the second guide surface is arranged to deflect light reflected from the reflective end through the first guide surface as output light, the reflective end has positive optical power in the lateral direction, and the waveguide is arranged to image the light sources in the lateral direction so that the output light from the light sources is directed into respective optical windows that are distributed in the lateral direction in dependence on the input positions of the light sources, characterized in that the light sources include at least one pair of adjacent light sources (15h, 15h) arranged at input positions offset from the optical axis of the reflective end, wherein, within the pair, the light source closest to said optical axis is inclined with the normal to the lateral extent of its light emitting area inclined towards said optical axis and the light source furthest from said optical axis is inclined with the normal to the lateral extent of its light emitting area inclined away from said optical axis, and the input end of the waveguide comprises a pair of inclined input facets (500, 506) extending across the light emitting areas of the respective light sources (15h, 15g) of said pair and an intermediate facet extending between the inclined input facets (500, 506).