An apparatus and a method for optimized calculation of 2D sub-holograms for object points of a three-dimensional scene and a pipeline for real-time calculation of holograms are provided. The invention shortens the calculation time of a hologram for representing a three-dimensional scene and/or to reduce the calculation complexity of such a hologram. This is achieved by a 2D sub-hologram of an object point, which has image elements of the spatial light modulator, comprises a half 1D sub-hologram, where the radius of each image element is determined and each image element of the 2D sub-hologram is fixedly assigned to at least one image element of the half 1D sub-hologram with identical or similar radius by way of an electronic circuit, by a method for encoding a hologram, and by a pipeline on the basis of FPGA and/or ASIC.