  A method is presented for the reconstruction of rotating monopole source
distributions using acoustic pressures measured on a sideline parallel to the
source axis. The method requires no \textit{a priori} assumptions about the
source other than that its strength at the frequency of interest vary
sinusoidally in azimuth on the source disc so that the radiated acoustic field
is composed of a single circumferential mode. When multiple azimuthal modes are
present, the acoustic field can be decomposed into azimuthal modes and the
method applied to each mode in sequence.
  The method proceeds in two stages, first finding an intermediate line source
derived from the source distribution and then inverting this line source to
find the radial variation of source strength. A far-field form of the radiation
integrals is derived, showing that the far field pressure is a band-limited
Fourier transform of the line source, establishing a limit on the quality of
source reconstruction which can be achieved using far-field measurements. The
method is applied to simulated data representing wind-tunnel testing of a
ducted rotor system (tip Mach number~0.74) and to control of noise from an
automotive cooling fan (tip Mach number~0.14), studies which have appeared in
the literature of source identification.
