# What do fringe patterns have to do with VLBI?

I think I have fundamental confusions with how VLBI works. I don't know why:

1. Resolution increases when incident rays meeting to a focal point from a farther separation along an axis perpendicular to their travel account for greater resolution of an image

2. How interferometric fringe patterns matter to us. Yes, if you vary phase difference between two telescopes a fringe pattern can be ascertained, but I don't see how this is important. To my eyes, apparently with the image below from Bob Campbell's So you want to do VLBI:

I'm assuming that the reason why the

dotted rays are lost

is because there actually is no "lens" anywhere except where the the two darkened portions are. Otherwise, that is how I would expect rays going that way would travel with a lens, which was confusing. I will assume it's because we are isolating just the darkened portions of the lens and disregarding everything else. Now, I understood this as, as the darkened portions are separated, the resolution improves (where again, I don't know why). Is this where separating telescopes far away comes in to improve resolution? If so, why can we consider antennae as the darkened portions of that figure? They're parts of a lens. Perhaps I've got it all wrong, and those two darkened portions correpond to darkened portions in one satellite/telescope. In that case, where does the other telescope come in, and how would I combine the two to form 'one effect telescope' if you will, with a diameter equal to their baseline?

1. The visibility formed by two antennae changes in the $$(u,v)$$ plane as the Earth rotates, forming curves. I had it explained to me in a talk that VLBI utilizes many different baselines to form an image (which correspond to many different values of the visibility function to get a better idea of it so we can extract the brightness from it since its Fourier Transform is brightness) in an analogy where a song can be composed by receiving and putting together many different frequencies (analogical to baselines) to form the song that's familiar to people. But here it sounds like baselines just matter in order to maximize them to improve resolution? Which one is it? More baselines, or longer baselines?
• Each dark portion is an individual telescope making a measurement. To use the two (or more) measurements to form an image, one must bring them all in to phase with each other. How to do that is left as an exercise for the reader (and figuring out why using 3 telescopes is much much much better than 2 is a strong hint). – Jon Custer Jun 26 at 16:36
• That simply involves accounting for the time difference by using some trigonometry. How can I approximate the two dark portions as an individual telescope? How can I think of them as portions of a lens for light to bounce off of and reach the focus? – sangstar Jun 26 at 16:38
• The 'siimply' does not do justice to figuring out how to actually combine data from multiple telescopes, even with modern GPS timing information. And, remember, this was all possible back in the 1960's when data was shipped by computer tape for assembly into an image. As for the lens, think of each dark area as a tiny lens with the same focal length as the lens overall. – Jon Custer Jun 26 at 16:42
• How is it justifiable to think of a separate telescope with its own lens as a tiny lens with the same focal length as the lens overall? – sangstar Jun 26 at 16:43
• Why can't each telescope have a lens with the same focal length as the others? They are just intercepting the radio waves that are incident at their spot. Look, I agree that I find the picture less than intuitive... – Jon Custer Jun 26 at 17:34