The invention relates to a controllable illumination device for an autostereoscopic or holographic display, which illumination device contains an illumination matrix of primary light sources having at least one luminous element per light source and a controllable light modulator (SLM) and a reproduction matrix. A computer-generated hologram (CGH) illuminated by the primary light sources (11, . . . , 1n) is coded on the controllable light modulator (SLM) and generates, in at least one plane downstream of the SLM, a matrix—reconstructed from the computer-generated hologram (CGH)—of secondary light sources (2) having a secondary light distribution for the purpose of illuminating the reproduction matrix (4) and for the purpose of focussing in light bundles onto each eye of the viewer via an imaging matrix. The CGH is calculated and reconstructed on the basis of the number of and the positions of the viewers and the system parameters. Owing to the reconstruction of the secondary light sources in a plurality of planes, it is possible for the image information of the display to be tracked for the viewers not only in the case of lateral movements but also in the axial direction.