A directional backlight is disclosed. The directional backlight has a plurality of light sources to generate a plurality of input planar lightbeams. The plurality of input planar lightbeams illuminates a directional backplane that has a plurality of directional pixels to scatter the plurality of input planar lightbeams into a plurality of directional lightbeams. Each directional lightbeam has a direction and angular spread controlled by characteristics of a directional pixel in the plurality of directional pixels. The directional backlight can be used to generate a 3D image by specifying the characteristics of the directional pixels in the directional backplane.