A flat-panel projection display comprises a slab waveguide having a preferably embossed diffraction grating on one face, a lens for directing light into an edge of the waveguide, and in the focal plane of the lens a liquid-crystal modulator for modulating the intensity of the light as a function of lateral position and elevational direction of travel. The light is ejected from the slab waveguide by the grating at angles corresponding to the input angles, giving a virtual display. The light from the modulator can be expanded in one dimension by passing through a magnifying waveguide, followed by scattering in the plane by a screen and projection by a lens at the other end of the waveguide. Head-up and 3-D displays can be constructed using this principle.