The invention relates to a lithograph for producing digital holograms in a storage medium (4), having a light source (6, 10) for producing a write beam (12) with a predefined beam cross section, having a writing lens (14) for focusing the write beam (12) onto the storage medium (4) to be written, the writing lens (14) being arranged in a lens holder (16), and having drive means for the two-dimensional movement of the write beam relative to the storage medium. The technical problem of writing computer-generated holograms as quickly as possible and with little effort by means of optical lithography is solved in that a first drive device (18) is provided for moving the lens holder (16) substantially at right angles to the write beam (12) and in that the aperture of the writing lens (14) is smaller than the beam cross section of the write beam (12).The inventon also relates to a method for the lithographic production of a hologram in a storage medium.