Method for marking a security document, comprising the steps: providing a security document blank, which comprises at least on some sections of the surface, as the outermost layer, a hologram layer with a hologram, wherein the hologram comprises a region over the entire surface of which an image of a homogeneous luminescent surface is stored, preferably an image of a homogeneous diffuse scatterer, wherein the hologram, or at least a constituent part of the hologram which represents the at least one region, is a volume hologram, providing at least one printing preparation, which comprises UV-crosslinkable monomers, which in the non-crosslinked state diffuse into the completely exposed and fixed hologram layer, providing a digital printing device, with which the at least one printing preparation can be printed, acquiring marking information, which indicates at which locations the hologram should be modified in the at least one region so as to influence a reconstruction of the hologram by means of a swelling of the hologram layer, printing of the at least one printing preparation for swelling the hologram layer onto the at least one region of the hologram layer with the digital printing device, at the locations indicated according to the marking information, such that the locations in the at least one region of the hologram at which a reconstruction of the hologram is intended to be influenced, are printed with the at least one printing preparation, fixing the crosslinkable monomers of the at least one printed printing preparation by introducing energy into the at least one region of the hologram, wherein the at least one printing preparation comprises pigments which exhibit luminescence under suitable excitation or IR-absorption or IR-remission. providing a security document blank, which comprises at least on some sections of the surface, as the outermost layer, a hologram layer with a hologram, wherein the hologram comprises a region over the entire surface of which an image of a homogeneous luminescent surface is stored, preferably an image of a homogeneous diffuse scatterer, wherein the hologram, or at least a constituent part of the hologram which represents the at least one region, is a volume hologram, providing at least one printing preparation, which comprises UV-crosslinkable monomers, which in the non-crosslinked state diffuse into the completely exposed and fixed hologram layer, providing a digital printing device, with which the at least one printing preparation can be printed, acquiring marking information, which indicates at which locations the hologram should be modified in the at least one region so as to influence a reconstruction of the hologram by means of a swelling of the hologram layer, printing of the at least one printing preparation for swelling the hologram layer onto the at least one region of the hologram layer with the digital printing device, at the locations indicated according to the marking information, such that the locations in the at least one region of the hologram at which a reconstruction of the hologram is intended to be influenced, are printed with the at least one printing preparation, fixing the crosslinkable monomers of the at least one printed printing preparation by introducing energy into the at least one region of the hologram, wherein the at least one printing preparation comprises pigments which exhibit luminescence under suitable excitation or IR-absorption or IR-remission.