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I've been trying to find out how VLBIs work. It says in this book I've read that many radio telescopes around the world work in tandem to use the interference of waves to get a clearer picture of celestial bodies, which is how they got the black hole picture.

But what I've found only talks about the difference in the time that radio waves takes to arrive to different points on the globe and how that is calibrated. Not a single word about the interference of waves.

Wikipedia's Very Long Baseline Interferometry; Method has a short discussion, but does not really explain the basic principle of how delays and interference are used to build up an image.

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  • $\begingroup$ I thought it would be easy to point you to Wikipedia but the only article I found is not very helpful, so I've added it to your question. $\endgroup$ – uhoh Dec 14 '20 at 9:30
  • $\begingroup$ Interfering waves with different delays is taking the difference in time into account. Look up how phased arrays work, then imagine a phased array with only a few receivers. $\endgroup$ – user253751 Dec 14 '20 at 18:14
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You can think of the object being photographed as a collection of light-emitting points. The light emitted from each point is spherically symmetric, at least over the small angle that we see.

If you sample one of those point sources at two points, and the source lies exactly on the perpendicular bisector of the line segment between the sampling points, then light of the same amplitude and phase will reach both sampling points at the same time. If the source is slightly off that plane, then the matching light will reach the sampling points at slightly different times. This allows you to disentangle the light coming from different directions.

I don't know anything about real-world VLBI, but in principle the way you extract an image from the raw data is by simulating a camera. You introduce electromagnetic waves with the strengths you measured at the spacetime locations where you measured them, and simulate them reflecting off a planet-sized mirror (or refracting in a planet-sized lens) and hitting a detector. You can show that light from any point in your source object will be focused to a point on the detector by your mirror/lens, i.e. it constructively interferes there and destructively interferes elsewhere on the detector. By linearity, the sum of the light from all the source points forms an image of the source.

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