  The Space Interferometry Mission (SIM) will observe sources in crowded
fields. Recent work has shown that source crowding can induce significant
positional errors in SIM's astrometric measurements, even for targets many
magnitudes brighter than all other crowding sources. Here we investigate
whether the spectral decomposition of the fringe pattern may be used to
disentangle the overlapping fringes from multiple blended sources, effectively
by performing synthesis imaging with two baselines. We find that spectrally
dispersed fringes enable SIM to identify and localize a limited number of field
sources quite robustly, thereby removing their effect from SIM astrometry and
reducing astrometry errors to near photon noise levels. We simulate SIM
measurements of the LMC, and show that (a) SIM astrometry will not be corrupted
by blending and (b) extremely precise imaging of mildly crowded fields may be
performed using only two orthogonal baseline orientations, allowing
microarcsecond positional measurements. We lastly illustrate the method's
potential with the example of astrometric microlensing, showing that SIM's mass
and distance measurements of lenses will be untainted by crowding.
