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Beam shaping - the ability to engineer the phase and the amplitude of massiveand massless particles - has long interested scientists working oncommunication, imaging and the foundations of quantum mechanics. In lightoptics, the shaping of electromagnetic waves (photons) can be achieved usingtechniques that include, but are not limited to, direct manipulation of thebeam source (as in X-ray Free Electron Lasers (XFELs) and Synchrotrons),deformable mirrors, spatial light modulators, mode converters and holograms.The recent introduction of holographic masks for electrons provides newpossibilities for electron beam shaping. Their fabrication has been madepossible by advances in micrometric and nanometric device production usinglithography and focused ion beam patterning. This article provides a tutorialon the generation, production and analysis of synthetic holograms fortransmission electron microscopy. It begins with an introduction to syntheticholograms, outlining why they are useful for beam shaping to study materialproperties. It then focuses on the fabrication of the required devices fromtheoretical and experimental perspectives, with examples taken from bothsimulations and experimental results. Applications of synthetic electronholograms as aberration correctors, electron vortex generators and spatial modesorters are then presented.

Theoretical and practical aspects of the design and production of synthetic holograms for transmission electron microscopy