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Re: Interferometry of a Monotonic Source?

Subject: Re: Interferometry of a Monotonic Source?
From: Martin Brown <|||newspam|||@nezumi.demon.co.uk>
Date: Mon, 13 Mar 2006 15:47:22 +0000
Newsgroups: sci.astro
W. Watson wrote:

Thanks, Dan. I follow the first paragraph and the paragraph on sound, but I'll have to review some of my (very) old physics texts on diffraction and fringes. I've certainly had some very past exposure to Fourier transforms and the like, so have some vague feel for what's going on.

From time to time, I open some material on interferometry and even aperture synthesis, and try to fathom what's going on w/o reviewing a week or more worth of physics. When Martin brought up the Java tool, that intrigued me. However, their documentation is sketchy and assumes more knowledge than I have. Anyway, this has prompted me to think a little more.

I happen to have a copy of "An Intro to RA" by Burke and Graham-Smith. In its favor, it actually has more words than equations. :-) After browsing through a section on this topic, I can see how the VRI software description left me with a false impression. Coverage is not geographic, it is about frequency. Not understanding the coverage idea expressed by vri doc caused me to start speculating about geographic ideas, positions of dishes, separation of dishes.

But it is all about the separation of the dishes! A very short baseline length measures low spatial frequencies in the sky brightness and progressively longer baselines measure higher spatial frequencies.

Baseline length and orientation determines where the measurement should be placed in the u-v plane. Careful placement of the dishes is essential to get a nice well behaved point spread function.

Words like support and coverage have contextual meaning. Burke and friend make it abundantly clear what u-v is about with: "It is useful to map the function W(u,v) on the u,v-plane to obtain a pictorial representation [coverage!] of the adequacy of the array in mapping the brightness distribution across sources of various angular sizes." They then go on to make it clear what is meant by support and elaborate on coverage. Unfortunately, they do not explain how some of the odd figures in the u-v plane come about (they do illustrate several patterns), but that requires some more effort on my part, at least looking for a source that addresses it.

The patterns in the u-v plane come from the set of baselines that the array provides tracked over 12 hours of the Earths rotation at least in the most simple case of classical aperture synthesis using a pure E-W baseline with multiple antennae on it. Finding a page that discusses this stuff reasonably well without mathematics is very hard.

Best I could find on u-v coverage and its effects without maths was at Leiden university:

http://www.strw.leidenuniv.nl/~pvdwerf/teaching/awt2/awt2_16k.html

Real scopes like the VLA and VLBI use baselines with N-S components as well with some additional complexity in the mathematics.

Regards,
Martin Brown

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