  We demonstrate high-fidelity detection of the orbital angular momentum (OAM)
of light using a compact and practical OAM spectrometer that maps the OAM
spectrum to time. The spectrometer consists of a single optical delay loop to
achieve timing mapping, a vortex phase plate that iteratively decreases the OAM
value, and a single mode fibre to distinguish zero from non-zero OAM states.
Light with arbitrarily OAM compositions can be measured. For light with OAM up
to 4hbar, we measured an average crosstalk of -21.3 dB, which is mainly limited
by the purity of the input states and optical alignment.
