From: freeman@netcom.com (Jay Reynolds Freeman)
Date: Tue, 26 Apr 94 08:37:09 PDT
To: ravage@bga.com
Subject: Re: CU Crypto Session Sat
Message-ID: <199404261538.IAA10897@netcom.com>
MIME-Version: 1.0
Content-Type: text/plain


Phil Karn comments on spy-satellite resolution:
 
> [Technical argument with which I agree, leading to approximate one-foot
>  resolution limit, deleted.]
 
 
  Phil's argument was for a 2-meter aperture at typical slant ranges in
the visible-light band.  I once did the calculation, also for a 2-meter
aperture, with other circumstances being as optimal as I could make them;
namely, looking straight down from a rather low perigee (I picked 200 Km),
working in the near UV (where it still penetrates the atmosphere reasonably
well -- I picked 3000 Angstroms as a round number), and with perfect seeing
(which depends on luck, weather and exposure times, and perhaps on
telescope and/or image-processing technology).
 
  For a circular aperture, the nominal resolving power (in radians) --
that is, the Airy disc radius to the first minimum -- is 1.22 * wavelength
/ aperture diameter, which for this case works out to 0.183 microradian.
Multiplying by 200 Km gives 3.66 cm resolution on the ground.  If one shapes
the aperture to match the pattern under study, one can drive that factor of
1.22 down to as little as 0.5, but such shaping would likely be useful only
for specific patterns not likely in the actual observation.
 
  I am told that careful image processing can sometimes resolve things
a little below the Airy-disc limit, but not far -- the information really
goes away fast at higher angular frequencies.  So all in all, I am inclined
to think that the best ground resolution attainable with a 2-meter aperture
from orbit is about an inch.  That is in fact just about enough to read a
poker hand -- the spots on the cards are an inch or so apart -- but you
might have trouble telling the face cards apart, as well as telling hearts
from diamonds and clubs from spades.  That is, if cards were well spread
out you might see that a certain card had five black spots on it, or had
a "face".

  I should probably explain about "Airy disc":  The term crops up often
in the study of astronomical imaging.  The image of a point light source
by perfect optics is a bulls-eye, a bright central spot surrounded by
alternating light and dark rings, called the "Airy disc" after the physicist
who first described it analytically.  The 1.22 * wavelength / aperture
is the angle from the center of the bright spot to the middle of the first
dark ring.

  Of course, a possible way around this limit is to put up a larger,
segmented mirror...

                                                -- Jay Freeman


PS:  References to physics texts on request...