# How are coherent astronomical objects imaged?

I am studying astronomical imaging, and am curious about how to image astronomical objects which are coherent. Stellar interferometry measures the mutual coherence function of a star, and then uses the Van Cittert-Zernike theorem to retrieve the spatial distribution of the star by a Fourier transform.

However, the Van Cittert-Zernike theorem requires the astronomical object to be incoherent. Certain astronomical objects are coherent. How are these coherent astronomical objects imaged?

• at very large distances, the source of the light will appear as a point source, so in effect you will have coherent plane waves at the point of measurement. You will not be able to image anything other than a single point. If there is decoherence, you will be able to produce a two point source for example from the interferometry measuements. – Peter R Jun 28 '16 at 16:20
• @PeterR, Thanks for the comment. If you have the time, could you clarify your comment and submit an answer? – Fred S Jun 29 '16 at 14:46

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.

I agree with Peter R.

In the case of coherent astronomical sources, The radiation arrives only from one direction. All the interferometers will measure the same visibility. You get nothing more than a point.

In 1989 K. R. Anantharamaiah, Tim Cornwell and Ramesh Narayan (NASA) wrote a paper on Imaging coherent and incoherent astronomical objects. Take a look:

https://www.researchgate.net/publication/234376818_Synthesis_Imaging_of_Spatially_Coherent_Objects

• What do you mean that "you get nothing more than a point"? If there was a binary star system, you would get two points, correct? – Fred S Jul 8 '16 at 13:44