A new method for the synthesis of holograms, based on a Fourier transformation, has been theoretically derived and experimentally verified. The method extends the familiar two-dimensional optical Fouriertransform analysis to include objects located in a volume centered about the focal point of the transform lens, and is specifically developed to provide an easily synthesized binary hologram for the reconstruction of three-dimensional objects. The synthetic holograms produced display, in addition to three-dimensionality of the reconstructed image, all other properties associated with photographic holograms. This technique for synthesizing holograms has the potential advantage of computational simplicity and increased image resolution over the Fresnel-transform technique, and permits the synthesis of a variety of objects composed of discrete points, continuous lines, and continuous surfaces.
JAMES P. WATERS, "Three-Dimensional Fourier-Transform Method for Synthesizing Binary Holograms," J. Opt. Soc. Am. 58, 1284-1287 (1968)