Could try intensity inteferometry? A good mental exercise
https://en.wikipedia.org/wiki/Hanbury_Brown_and_Twiss_effect
https://en.wikipedia.org/wiki/Hanbury_Brown_and_Twiss_effect
The two options are to keep those offsets under control (i.e., lock everything to a common clock) or to rapidly measure the offsets as they change and try to compensate in software (difficult).
(Another at first surprising thing is that radiation received from celestial sources is only coherent because of their very small apparent size -- the sources themselves are not coherent at all, because their physical size is very large)