  Characterization and control of the transverse phase space of high-brightness
electron beams is required at free-electron lasers or electron diffraction
experiments for emittance measurement and beam optimization as well as at
advanced acceleration experiments. Dielectric laser accelerators or plasma
accelerators with external injection indeed require beam sizes at the micron
level and below. We present a method using nano-fabricated metallic wires
oriented at different angles to obtain projections of the transverse phase
space by scanning the wires through the beam and detecting the amount of
scattered particles. Performing this measurement at several locations along the
waist allows assessing the transverse distribution at different phase advances.
By applying a novel tomographic algorithm the transverse phase space density
can be reconstructed. Measurements at the ACHIP chamber at SwissFEL confirm
that the transverse phase space of micrometer-sized electron beams can be
reliably characterized using this method.
