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The invention of holography by D. Gabor, followed by the works of E. Leith and Upatnieks, made possible to perform nearly arbitrarily wavefront transformations with the aid of optical microstructures fabricated by interference (Gabor, 1948; Leith & Upatnieks, 1962; Denisyuk, 1962; Benton, 1969). The realization by A. Lohmann and co-workers in the mid1960’s that optical holograms can be simulated by digitally generated binary transparencies was another significant step forward in the path towards widespread application of diffraction in optics (Lohmann, 1956; Brown & Lohmann 1966; Lohmann & Paris, 1967). This new approach was called digital holography, or equivalently computer-generated holography. The computer-generated hologram (CGH) is distinguished primarily from its optical cousin by the fact that the computer is able to design a hologram of a non-existent, synthetic or virtual object, and the operation of the diffractive optical element (DOE) can be optimized mathematically rather than experimentally (Turunen & Wyrowski, 1997). This is clear from the words of Professor Lohmann himself, commenting on the shift from classic holography to digital holography (Lohmann, 2008): “we considered images as information, and we applied notions about carriers from communications and information theory [...]. In other words, our approach represented a paradigm shift from physical optics to optical information processing. “ Since the operation of CGH is based on the diffraction of light, this field is also called diffractive optics. Its essence is the control of optical fields by microstructured media (Turunen & Wyrowski, 1997). The DOE is an optical device whose superficial microrelief has a height comparable to the light wavelength used. The DOE may be implemented in the form of a transparency or a reflecting mirror. Throughout this text the terms computer-generated holograms (CGH), diffractive optical element (DOE), or simply hologram are employed with no distinction among each other.

Digital Holography: Computer-Generated Holograms and Diffractive Optics in Scalar Diffraction Domain