  Orbital angular momentum (OAM) of light is an attractive degree of freedom
for funda- mentals studies in quantum mechanics. In addition, the discrete
unbounded state-space of OAM has been used to enhance classical and quantum
communications. Unambiguous mea- surement of OAM is a key part of all such
experiments. However, state-of-the-art methods for separating single photons
carrying a large number of different OAM values are limited to a theoretical
separation efficiency of about 77 percent. Here we demonstrate a method which
uses a series of unitary optical transformations to enable the measurement of
lights OAM with an experimental separation efficiency of more than 92 percent.
Further, we demonstrate the separation of modes in the angular position basis,
which is mutually unbiased with respect to the OAM basis. The high degree of
certainty achieved by our method makes it particu- larly attractive for
enhancing the information capacity of multi-level quantum cryptography systems.
