The Space Interferometry Mission (SIM) will observe sources in crowded fields. 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 show that the spectral decomposition of the fringe pattern may be used to perform phase and group delay estimation for multiple field sources simultaneously. This allows disentanglement of the overlapping fringes from multiple blended sources, leading to precise astrometric measurements for each source. Effectively, this is synthesis "imaging" of point sources with just two baselines. We find that spectrally dispersed fringes enable SIM to identify and localize a limited number of field sources quite robustly, thereby reducing astrometry errors to near photon noise levels. We simulate SIM measurements of the LMC and show that (1) SIM astrometry will not be corrupted by blending and (2) 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 when spectrally dispersed fringes are measured.
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