  By suitably generalizing the Fourier constraint projection in the difference
map phasing algorithm, an object can be reconstructed from its diffraction
pattern even when the latter has been incoherently averaged over a discrete
group of symmetries. This resolves an ambiguity in the recent proposal for
aligning molecules by means of their anisotropic dielectric interaction with an
intense light field. The algorithm is demonstrated with simulated data in two
and three dimensions.
