An optical display device, in particular for use in a head-up display or a head-mounted display, comprises an essentially planar light guide, an image-generating system, a first diffraction grating by which light that comes from the image-generating system can be coupled into the light guide, and a second diffraction grating, by which the light can be coupled out again from the light guide. At least one of the two diffraction gratings is a binary-blazed grating having a multiplicity of diffraction structures, which are composed of a multiplicity of individual substructures that ensure a blaze effect and in plan view have the shape of a closed geometrical surface.