In this 1987 column from the Master, he mentions that he thinks a 6 inch resolution was obtained.
Is is the best possible?
From reading about telescopes, peering at things through miles of atmosphere does not make a great viewing window. Telescopes are put up on mountains and in non-polluted areas to minimize the amount of air and contaminants in it. The best pictures we get from the Hubble, which is outside the atmosphere.
So, obviously spy satellites can’t get better and better indefinitely. They will never be able to see the paper fibers in the newspaper in the park. There has to be some kind of limit due to looking through all that non-perfect air.
One limit, of course, is f-stop. The smaller the field of view, the more light you need to get the same brightness of picture (how many photons are you capturing?). You have to gather more light. Plus, the smaller the lens relative to the magnification, the more magnified the individual flaws in the optics become.
There are several reasons this would be much MUCH harder on a space telescope imaging the ground but you asked about theoretical limit.
Even granting perfection in that adaptation system, you’ll eventually run into a Noise-exceeds-Signal limitation, though perhaps you could increase signal by reflecting a laser beam off the ground object you’re viewing.
There’s an Star Trek scene where Kirk asks for either magnification or de-magnification to a certain specification and Sulu responds something like “Already at 2 stops [above/below] that, sir.”
And the detective always spots something the expert missed.
EXPERT: Sorry, we can’t see his face in this picture.
DETECTIVE: But there’s a reflection in the window. Can’t you just zoom in on that?
EXPERT: :smack:
Of course, on CSI, it would go more like this:
EXPERT: Sorry, we can’t see his face in this picture.
DETECTIVE: But he’s holding an iPhone in front of him, which has a shiny back surface. The iPhone might be visible over his shoulder in the rearview mirror of that passing car. Just zoom in on the reflection of the phone in the mirror and we’ll be able to see his face.
EXPERT: That works, but his finger is blocking part of the image, and it’s very distorted due to the curvature of the back of the phone, the fingerprints on the phone, and the partially rolled-down car window.
DETECTIVE: Just have the software compensate for the distortion, run the visible part of the face through the face-recognition database, and when it identifies him, we can pull the full face photo from there.
EXPERT: That may take a minute or two … no, wait, I’ve got it! And I got a positive ID from the fingerprints on the phone, too.
That reminds me of a story that took place on the USS Wahoo during WW2. The sub was cruising very close to an enemy island, and the periscope officer was concerned they were too close.
“Captain, I’ve got the scope on High power and all I can see is one palm tree. I think we’re too close.”
“Dick, the scope is on Low.”
flick
“Oh, God! Now I only see one coconut! Full astern! Full astern!”
The captain never blinked, but the periscope officer needed a change of uniform.
Another limit is the Raleigh criterion. Basically, the smallest angle you can resolve is the ratio of the wavelength of light you’re using to your aperture. But of course, you can deal with this just by using a bigger scope.
