  Spatial modes of light provide a high-dimensional space that can be used to
encode both classical and quantum information. Current approaches for
dynamically generating and measuring these modes are slow, due to the need to
reconfigure a high-resolution phase mask such as a spatial light modulator or
digital micromirror device. The process of updating the spatial mode of light
can be greatly accelerated by multiplexing a set of static phase masks with a
fast, image-preserving optical switch, such as an acousto-optic modulator
(AOM). We experimentally realize this approach, using a double-pass AOM to
generate one of five orbital angular momentum states with a switching rate of
up to 500 kHz. We then apply this system to perform fast quantum state
tomography of spatial modes of light in a 2-dimensional Hilbert space, by
projecting the unknown state onto six spatial modes comprising three mutually
unbiased bases. We are able to reconstruct arbitrary states in under 1 ms with
an average fidelity of 96.9%.
