Spy satellites can't read your license plate

Every time I hear someone talking about imaging (spy) satellites, somebody invariably brings up those top secret high speed government spy satellites that can read the license plate on your car or the headlines of the newspaper you're reading. As far as I can tell, such claims have little basis in reality. While almost all data on satellites such as the advanced KH-12 flown by the National Reconnaissance Office (NRO) of the United States is classified, it's not all that hard to figure out what they should be capable of.

All an imaging satellite is, really, is a large, space based optical telescope/camera, not unlike the Hubble Space Telescope. The resolving power of any telescope can be calculated by the following formula:

θ = 115.8/D

where θ is angular resolution of the objective, expressed in seconds of arc, and D is the diameter of the objective in millimeters. This is commonly referred to as the Dawes limit of the objective, and is quite a good estimate of the theoretical resolution the objective is capable of. The Hubble telescope has an objective of 2.4 meters and this is probably pretty close to the maximum diameter that can be launched into space with currently available launch vehicles, so the NRO satellites can't be much bigger than this. The Dawes limit of a 2.4 meter objective works out to around .05 seconds of arc.

To figure out actual size of an object from its angular size at a given distance use the formula:

angular size(in degrees) = 57.3*actual size / distance

For a distance of about 650 kilometers, which is likely a typical operating altitude for imaging satellites, this works out to right around 10 centimeters. Unless the birds are equipped with larger, multi-segment mirrors or some other unknown capability, that is about the theoretical limit of their resolution. This does not necessarily mean that 10 centimeters is the smallest oject these cameras can distinguish, but that this is the minimum distance that must separate two objects for the satellite to tell them apart. So while they might be able to spot a golf ball on a putting green under exceptional circumstances, there is no way they could read a license plate.

Then there is the atmosphere. Long the bane of astronomers, the atmosphere also limits the performance of any telescope looking through it. Atmospheric turbulence (what astronomers refer to as 'seeing') commonly reduces the actual performance of astronomical objectives to around .5 seconds of arc, although i'm not sure this is as critical for taking pictures of terrestrial objects as it is for astronomical ones.

Now, if none of this is enough to convince you, consider this one undeniable fact: license plates are not usually mounted on the tops of cars.

First I want to say how much I enjoyed the above write up - so much so that I quickly voted it up, then fixed my hair a little bit, then sent it (in email form) to a satellite engineer I happen to know at a big scary satellite television company (ok, he's my dad).

He sent the following:

Sounds right- BUT
The author "assumes" a 650 Km orbit. Given that the resolution of the object is inversely proportional to the distance, a decrease in orbit to 320 Km increases the resolution to 5 cm. Still not enough to read the license number, but closer.

If an "agency" REALLY wanted to see detail, there is nothing to stop them (except fuel consumption) from dropping an orbit to the 200 Km range for a few orbits.

Also consider other orbits. An elliptical orbit with a 200 mile perigee and 500, 600,1000 mile apogee would provide a quick peek. If you had many of these devices orbiting at the same time, you could cover a LOT of territory "most" of the time.

With all that said, it would still be easier to call somebody and have them go outside and look at the license plate. In all the closed, restricted societies I've ever heard of the greatest danger always came from the people willing to sell information than from all the technology. The technology is best for checking up on what you have been told, and for looking for "trends".

By the way, I have no expertise in this area at all. BUT- If you'd like to look at what's available, try

http://www.terraserver.com/imagery.htm

Bear in mind that the U.S. Government restricts U.S. citizen access to some types of images available in other countries.

Sleep Well, my child

Love Dad

Sparkleface (my sister) just pointed out how easily our Dad switches from kilometers to miles! He is THAT smart!

One: While I realize that the license plate is the notional root of this thread, it should be kept in mind that only in a few circumstances would you need to know the license plate! If you're looking for the location of a vehicle, then unless the vehicle in question is in a congested area the color, make and approximate location should allow you to garner a pretty good idea as to which car you're looking at.

Two: Many spy satellite shots (I reference here the ones available publicly, for example at the Federation of American Scientists site at http://www.fas.org) are in fact taken from low angles. This is because a low-flying satellite is moving so quickly over the ground that it is only 'overhead' a brief amount of time - but has much more time as it approaches and retreats from the target point to observe. Thus, of the imagery acquired in a pass by the sat, most of the imagery will have been acquired at a low (less than 60 deg.) angle of incidence to the target. Of course, this doesn't mean the license plate is facing the right way, or that in fact the plate is readable at all given the above.

Three: Aircraft, public vehicles (buses and the like) and military vehicles often do have ID info visible from the air. Watch Speed again, or look at the wings of a large commercial aircraft. While not guaranteed, it's quite likely the latter has its aircraft number on the wings, for example.

I know this is sorta party-poopin' and off the original (license plate) topic, but it's relevant to the broader question of the limitations of satellite reconnaissance.

I'm sure this is all very true. I'm not a sciencetician, and I don't even play one on TV, but there is something I do know. The earth isn't flat. We live on a sphere. Okay, it's not a perfect sphere, but it's the only one I got and I like it, but that isn't the point. Here's the point. Just because a sattelite is in orbit, doesn't mean it's looking straight down at something. Of course increasing the angle of viewing (or decreasing?) would only complicate the very good points already mentioned. There is also the problem of terrian elevation. As the sattelite comes closer to the horizon and is in a better position to view vertical objects the possibility of an obstruction increases dramatically. And.. as the satellite gets closer to the horizon problems occur with refraction. I think this scenario is simply very unlikely and extremely impractical, but still possible.

Damn! beat to the punch by the ever more descriptive and qualified to speak Custodian.

I wildly guess that you could at maximum quadruple the number of pixels (double each axis) with this technique (requiring, say, 8 images), and maybe quadruple that using image sharpening tweaks (i.e. compensating for the effects of finer pixels you already know). So, my wild guesses say you could get 2 cm resolution from 10 cm pictures, perhaps enough to read a plate, but I think I'm overestimating this method's ability.

Anyway, the atmosphere would probably interfere in some nasty way.

Short answer: Yes.

Long answer: If we assume that the object being photographed is relatively still we can as xriso said,

'If your super spiffy spy satellite grabs 5 images, 1 second apart, ...

take multiple pictures, since the satellite is moving these pictures are separated by a distance. This effectively increases the aperture, D, that El Puerco Loco spoke about. This in turn increases the angular resolution by:

θ = 115.8/D (Loco's formula).

This is known as Synthetic Aperture. It is often used with radar. I suspect it could also be used with light.

Now xriso brought up the atmosphere. This is a problem. However, courtesy of SDI research, or Star Wars, of Ronald Reagan fame, we can mitigate this to a degree with a deformable mirror. Here is how it works. The satellite takes a picture of a known object on the ground. By finding the differences of what it sees and what it is supposed to see, deformations are put into a mirror in real time to correct for the error.