  Radio frequency interference (RFI) is a significant problem for current and
future radio telescopes. We describe here a method for post-correlation
cancellation of RFI for the special case of an extended source observed with an
interferometer that spatially resolves the astronomical signal. In this
circumstance, the astronomical signal is detected through the auto-correlations
of each antenna but is not present in the cross-correlations between antennas.
We assume that the RFI is detected in both auto- and cross-correlations, which
is true for many cases. The large number of cross-correlations can provide a
very high interference to noise ratio reference signal which can be adaptively
subtracted from the autocorrelation signals. The residual signal is free of
interference to significant levels. We discuss the application of this
technique for detection of the spin-flip transition of interstellar deuterium
with the Allen Telescope Array. The technique may also be of use for epoch of
reionization experiments and with multi-beam feeds on single dish telescopes.
