Radio Astronomy. Baselines and Fringes, Interferometry

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solarblast
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As I understand Interferometry, a baseline does not refer to the distance between two RA scopes. It's the distance between two line of sites for each scope. They are parallel, when directed at the same object.

Suppose we have two scopes at two stations that are some distance apart, say, Socorro, NM, and Puerto Rico. Both stations are looking at the same object. I would think what I said above holds here for the two stations. That is, the baseline is not measured along the surface of the earth.

I have seen few, if only one, article on Interferometry that gives a good insight into the topic of Interferometry in RA or optical astronomy. Scientific American magazine, 2001, March. It does a fairly reasonable job as an introduction. Typically to most descriptions, it gets into fringes, and a figure labeled on two axes as E-W baseline and N-S baseline. Of what value is the figure? Similarly, what is the importance of fringes to the description? I'm providing attachments.
 

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Perhaps a better place to ask this is in general astronomy?
 
I don't know anything about this stuff, but I can't see what the curvature of the Earth could possibly have to do with the correlation of the two views, so it certainly seems natural that the distance between two stations would be taken as the DIRECT distance between the two (direct being taken without regard to the incidental circumstance that the two happened to be sitting on a spherical body).
 
Another figure that I did not include shows the baseline as the distance between the two line of sights for a single location.
 
Technically I think what I'm asking about is what is called a very long baseline.