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Even with adaptive optics you still won't get close to the diffraction limit.

> Also, the increase in CCD densities have become enormous in the past few years. So it might be possible to make a matrix that could resolve the flag in the near future.

You can't work around the diffraction limit. There's no CCD that could compensate for the lack of the 5 km aperture required. You must have at least 2 (more like 3 or 4) pieces of glass separated by 5 km or more, otherwise nothing would work.

Yes, you can break below diffraction limit. See http://en.wikipedia.org/wiki/Super-resolution

No you are still constrained by the limit, super resolution only works with the information that is captured.

The diffraction limit isn't a hard line limit rather the information disappears into noise as you go past the limit. So what SR does is use multiple images to remove the noise for details close to the limit using some neat algorithms. But noise quickly overcomes the information as you push against the limit.

Thanks for asking this, I had the same question about high density CCDs, space telescopes, and signal processing. I think it is a reasonable question to bring up.

it just isn't physically possible to resolve a flag on the surface of the moon with anything less than 3.5 mile diameter telescope. The technology used can't help much with physically impossible things!

I don't know much about this topic, but I did RTFA, so permit me to ask a stupid question:

1. if this impossibility is related to noise overwhelming the image signal (thereby causing it to be an unresolved blur)

2. and if we assume that this 3.5-mile diameter is for a naked eye looking through a telescope (i.e. we're talking about a single exposure)

3. isn't there some statistical process that could enable a reduction of the diameter of the lens, which would reconstruct a less-noisy image based on multiple exposures?

It is perfectly possible to resolve a (6-foot) flag with a telescope.

The article states "the Earth's atmosphere is never steady enough to allow resolution below about one arc second for most locations". But according to the European Southern Observatory one can do 1000x better:

"With AMBER on the Very Large Telescope Interferometer (VLTI), the astronomers were able to see details on the scale of one milli-arcsecond, corresponding to being able to distinguish, from the Earth, the headlights of a car on the Moon." -- http://amber.obs.ujf-grenoble.fr/spip.php?article154

Therefore a 6-foot-wide flag ("headlights of a car") would be visible as 1 or 2 pixels with the VLTI, which is made of four 8.2 meter reflectors.

I presume the actual flag left by the astronomers was somewhat smaller, so one would need a tad better telescope, but certainly not something with a "3.5 mile diameter".

Upvote me. HN readers need to be educated :-)

yes, but the article explicitly defines "flag being visible" as stripes of the US flag being visible. for that you would need a tad better than 6-foot resolution.

Fair enough.

On a side node, the VLTI should be able to produce a 2x2 or 3x3 pixel image of one of the russian or american lunar landers (14-foot wide). It would be a cool thing to accomplish to demonstrate the resolution of the VLTI...

Did you even read the article? Please do, so you don't look so ignorant.

The article throws numbers, it explains nothing about the Dawes number, which it explicitly describes as being discovered "A long time ago".

Asking if things discovered "a long time ago" have changed in light of modern development isn't un-called for. Especially given the vague statements.

>And, it would only be just visible as a small dot, it would not "look" like a flag at all.

Is similarly vague, and probably part of the reason for the question. We can build optical hardware with resolutions far in excess of our eyes per square unit. What we can see by looking through the scope directly has little to do with how we use more powerful modern telescopes, which appears to be how this is calculated. 20 years ago it would've been hard to predict high-density CCDs, how much more unlikely is it that something "A long time ago" took such things into account?

Lets ask another:

>The only method that could be used to (in theory) see something as small as the Flag on the Moon would be to use two optical telescopes set (for example) 1000 miles apart. This would easily provide the required resolution...

How does this help? Are they talking two Hubbles? Two 1.75 mile wide telescopes? There's zero explanation, despite such an absolute claim.

I appologize.

I didn't realize you didn't understand the article, and I thought you were just posting without reading it first.

There is an upper limit to how much detail you can see. It doesn't matter what you use to do the viewing, the eye, a ccd, anything. The information is simply not there, no matter how you magnify it.

That limit is called the diffraction limit, and it's related to the size of the lens used to collect the light. It sort of has to do with the fact that photons passing near the edge of the lens get distorted.

Dawes number is simply a calculation of the diffraction limit.

So that "small dot" that is really a flag, no matter how well you magnify it, will just look like a blur. The photons that used to show details about it have been scrambled enough that those details are lost.

Regarding the two collectors.

They are talking about two small telescopes placed far apart. They compare the image collected by both telescopes and using that they are able to synthesize information about the object that is not visible using just one telescope. But it's no longer a matter of just looking at it.

I'm sorry that I don't understand it well enough to give a simpler explanation of how that works.

I don't know if you read lord of the rings, but there is a scene where Legolas looks at riders at a great distance and can see details that the humans can't. Supposedly because of his keen eyesight. But actually it's impossible. Assuming that his eyes were about the same size as human eyes, he simply can not see those details, no matter how good of a retina he had. Here's the link: http://scienceblogs.com/principles/2009/06/the_limits_of_elv...