  Beam shaping - the ability to engineer the phase and the amplitude of massive
and massless particles - has long interested scientists working on
communication, imaging and the foundations of quantum mechanics. In light
optics, the shaping of electromagnetic waves (photons) can be achieved using
techniques that include, but are not limited to, direct manipulation of the
beam 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 new
possibilities for electron beam shaping. Their fabrication has been made
possible by advances in micrometric and nanometric device production using
lithography and focused ion beam patterning. This article provides a tutorial
on the generation, production and analysis of synthetic holograms for
transmission electron microscopy. It begins with an introduction to synthetic
holograms, outlining why they are useful for beam shaping to study material
properties. It then focuses on the fabrication of the required devices from
theoretical and experimental perspectives, with examples taken from both
simulations and experimental results. Applications of synthetic electron
holograms as aberration correctors, electron vortex generators and spatial mode
sorters are then presented.
