How are coherent astronomical objects imaged?

There is actually 2 questions here.

1. The van Cittert-Zernike theorem is essentially used to calculate the free space propagation of the electrical field/light. It can thus be used to reconstruct the original field at the astronomical object from our measurement on earth. However as mentioned correctly it only applies under certain incoherence conditions. So the first question might be: How do we model the propagation of partially coherent wavefields? There has been a lot of work on this in the context of the SAFARI instrument on the satellite SPICA, see e.g. this paper, in particular section 6 about propagating the correlation matrix. The gist of it is that you can write down some linear operator that describes the propagation of the full state of coherence. Finding the linear operator then depends on the system, for free space you can do a Fourier decomposition of the field and they propagate freely. This can be complicated to do, but replaces and is the more general formalism behind the van Cittert-Zernike theorem. Also note that reconstructing the field may be impossible/intrinsically has some error since the propagation operator is usually not invertible (i.e. a multiplicity of sources can produce the same distant field). This becomes more important when optical instruments are involved.
2. Then the second question is: How do we measure a partial coherence in the wavefield? There are detector that can pick up information not only about the field, but also about the state of coherence. E.g. what is used on SAFARI are waveguides in combination with transition edge sensors.