Wayne,

I don't know if the others answered your question, but be careful. Your
original post says:
"...two antennas separated by a distance D would have a resolution as
the same as an antenna of size D,..."

*Resolution* is key here, not, as you state later,: "..can act as though
they are a single receiver of size D"

"Resolution" vs. "act" may be ambiguous.

I'll take a stab.

Think of water waves. Picture some very nice, regular waves. All the same
size, shape and wavelength. This is a good analogy for RF.
Now, put two *vertical* antennas in the pool (come-on in the water's fine).
From the top they just look like dots right?

First, position them so they are in the same line with the wave front -- so
each wave hits both at precisely the same time. (a broad-side array)

When like this, each antenna is receiving the same *PHASE* signal. The
voltage goes up and it goes down at the same time in both antennas.

Now, slightly rotate this array so one of the antennas gets its waves a bit
earlier. It will receive an *advanced * phase. The further apart these two
antennas are, the more sensitive it will be to a small angle of rotation.
Making your "D" bigger will make the antenna array "see" more phase shift
for the same small angle (hat it is turned, right?

Also, if the signal comes from a slightly different direction, the same
thing happens and therefore it can *RESOLVE* direction better with a larger
"D".

Help any?

73, Steve, K9DCI














"W. Watson" wrote in message
nk.net...
Richard Clark wrote:

On Sat, 25 Mar 2006 01:53:24 GMT, "W. Watson"
wrote:


Ultimately, I'm trying to comprehend, via a proof, that two receivers
separated by a distance D can act as though they are a single receiver
of
size D. Perhaps it can be done by simply considering the Young double
slit
experiment. It bothers me that the idea is passed along without ever
proving
it. Maybe the proof is trivial.


Hi Wayne,

The two receivers/antennas is called "synthetic aperture." You can
observe the same thing with one antenna that is moving, we commonly
call it "picket fencing." This effect is due to reflections and
direct signals interfering constructively and destructively as you
move through the interference field. The math for that alone is found
in "Fresnel loss."

The Young double slit IS the proof in that it contains all the math
you need. It contains two transcendental operations (sin or cos) as
many thetas as there are phases and distances, some magnitude
information, and the result pops out at you.

In fact, the math is all the same for all of these effects.

73's
Richard Clark, KB7QHC
My *old* physics book doesn't give the proof, but Hecht's Optics does.
Whoops. It's in Waves by Crawford. No mention though that is the proof of
this particular fact. Hecht mentions the experiment, and it may be proven
in
subsequent sections using Fourier methods. Waves does it the old fashioned
way. Accepting your comment then, I can read through it with a little more
attention. Thanks.


Wayne T. Watson (Watson Adventures, Prop., Nevada City, CA)
(121.015 Deg. W, 39.262 Deg. N) GMT-8 hr std. time)
Obz Site: 39° 15' 7" N, 121° 2' 32" W, 2700 feet
--
"No, Groucho is not my real name. I am only
breaking it in fora friend." -- Groucho Marx

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