Re: Technically, can images with a one inch resolution be taken from space?

Hello Alan!

You present an interesting question. I'll start with a little history of
high resolution images that I found.  In June 1978, President Carter issued
a Presidential Directive (37) that limited the spatial resolution within US
Landsat images to 10 meters.  In 1994, Clinton further decreased this
maximum allowable resolution to 1 meter for commercial satellites.  In
fact, I saw an image with about 1 meter resolution at the American
Astronomical Society meeting in Rochester, NY this past June.  The detail
was incredible--you could even make out lines painted in roads and
helicopter blades, though they were not perfectly clear.  These are legal
limits imposed by the government on commercial satellites.  They do not
represent technological limits.  Commercial satellites cannot therefore use
images to identify individual people, for example.  I found tantalizing
hints that the highest resolution images obtained by American satellites
were a few inches across, but of course those images are not publicly
available.  I did not find any indication that satellites with 1 inch
resolution capability are currently in use or planned (though this
information may be classified).

The resolution of an image depends on the wavelength of light used in
making the observation and the diameter of the telescope.  This gives an
angle.  The actual physical measurement, in terms of inches or meters,
depends on the distance between the observer and whatever is being imaged. 
So for imaging very small scales you would want a combination of a large
telescope and a low orbit.  A typical low earth orbit is 300-1000 miles. 
Lets take the lower limit of 300 miles for this demonstration.  (Keep in
mind that the lower the orbit of a satellite, the faster its orbit degrades
so that these satellites have a lower lifetime than satellites in higher
orbits.)  To be able to image an object of 1 inch from this height, the
telescope must have an angular resolution of 0.011 arc seconds (where an
arc second is 1/3600 of a degree).  The theoretical angular resolution of a
telescope is given by theta(in arc seconds) =
1.22*206265*wavelength/(mirror diameter).  If we take the wavelength to be
500 nm (visible light) then the mirror would have to be 11.4 meters in
diameter (much too big to launch right now).  On the other hand, to image a
1-meter object, the mirror would only have to be 0.3 meters--much more
reasonable in terms of technology and cost.  For a 1-meter telescope to
resolve a 1 inch object, it would have to be a mere 26 miles away.

Keep in mind these numbers are a theoretical minimum and do not take into
account conditions which degrade the performance of an instrument. 
Interference due to the atmosphere itself--the bane of any ground based
astronomer--will act to decrease resolution and image quality.  Remarkable
methods of improving image quality and resolution have been developed over
the last few years.  A method called adaptive optics
(http://www.us-gemini.noao.edu/public/adaptive.html) is used by the Gemini
telescopes to compensate for atmospheric degradation.  Clever data
reduction techniques also help to improve image quality.  So while there is
no technological reason why a 1 inch resolution cannot be obtained, it
would be very difficult and expensive to do so.

As for moving the aperture--the closer a satellite is to Earth, the faster
it moves relative to the ground.  While a satellite can track a stationary
object, this fast motion means that (for low earth orbit satellites) the
object is only visible for a couple minutes while the satellite is above
the horizon.  It is possible to point a satellite to image an area of
interest using gyroscopes.  To move the satellite itself is more of a
problem and would not be done unless absolutely necessary.

Erika