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