A device for backlighting a liquid-crystal matrix array of a flat screen for viewing in day- or night-vision mode with NVIS compatibility includes a light guide GL which comprises a main cuboid plate shape PP assembled together with at least one right-angled triangular auxiliary prism PA1 which comprises at least one reflective face, and which is arranged together with the main plate to define, on the same lateral face of the plate, two distinct injection windows, one injection window I1 for a nighttime light source and one injection window I2 for a daytime light source. The nighttime light is injected into the plate, by reflection within or off the auxiliary prism in the direction of the respective injection window (I1). The lateral face of the prism that directly receives the light emitted by the nighttime source may comprise an optical filter FNVIS-c formed collectively over its surface by deposition of dielectric films.