A three-dimensional, 3D, electronic display comprising: a grating-based backlight comprising: a light guide (110,210,310) configured to guide a light beam (104,204,306) between a first surface and a second surface (110") of the light guide at a non-zero propagation angle relative to one of the first surface and second surface (110") of the light guide; and a plurality of reflective grating islands (120,220,320) spaced apart from one another and optically coupled to the light guide, a reflective grating island of the plurality comprising a multibeam reflection mode diffraction grating configured to diffractively couple out a portion of the guided light beam as a plurality of coupled-out light beams, wherein each coupled-out light beam is directed away from a side of the multibeam reflection mode diffraction grating that is the same as the side that the light beam is incident on the multibeam reflection mode diffraction grating, the coupled-out light beams of the plurality of coupled-out light beams having different principal angular directions from one another, such that each coupled-out light beam of the coupled-out light beam plurality is directed away from the first surface of the light guide at a predetermined principal angular direction; and a light valve array configured to modulate the coupled-out light beams of the coupled-out light beam plurality, the light valve array being adjacent to the first surface of the light guide, wherein the principal angular directions of the coupled-out light beams correspond to view directions of the 3D electronic display, each modulated light beam representing a pixel of the 3D electronic display in that view direction. a grating-based backlight comprising: a light guide (110,210,310) configured to guide a light beam (104,204,306) between a first surface and a second surface (110") of the light guide at a non-zero propagation angle relative to one of the first surface and second surface (110") of the light guide; and a plurality of reflective grating islands (120,220,320) spaced apart from one another and optically coupled to the light guide, a reflective grating island of the plurality comprising a multibeam reflection mode diffraction grating configured to diffractively couple out a portion of the guided light beam as a plurality of coupled-out light beams, wherein each coupled-out light beam is directed away from a side of the multibeam reflection mode diffraction grating that is the same as the side that the light beam is incident on the multibeam reflection mode diffraction grating, the coupled-out light beams of the plurality of coupled-out light beams having different principal angular directions from one another, such that each coupled-out light beam of the coupled-out light beam plurality is directed away from the first surface of the light guide at a predetermined principal angular direction; and a light guide (110,210,310) configured to guide a light beam (104,204,306) between a first surface and a second surface (110") of the light guide at a non-zero propagation angle relative to one of the first surface and second surface (110") of the light guide; and a plurality of reflective grating islands (120,220,320) spaced apart from one another and optically coupled to the light guide, a reflective grating island of the plurality comprising a multibeam reflection mode diffraction grating configured to diffractively couple out a portion of the guided light beam as a plurality of coupled-out light beams, wherein each coupled-out light beam is directed away from a side of the multibeam reflection mode diffraction grating that is the same as the side that the light beam is incident on the multibeam reflection mode diffraction grating, the coupled-out light beams of the plurality of coupled-out light beams having different principal angular directions from one another, such that each coupled-out light beam of the coupled-out light beam plurality is directed away from the first surface of the light guide at a predetermined principal angular direction; and a light valve array configured to modulate the coupled-out light beams of the coupled-out light beam plurality, the light valve array being adjacent to the first surface of the light guide, wherein the principal angular directions of the coupled-out light beams correspond to view directions of the 3D electronic display, each modulated light beam representing a pixel of the 3D electronic display in that view direction.