Is there a limit to the amount of info in reflected light?

[mfb]

@davenn: That is a description of what I said, thanks for confirming it, but what should I read why?

Interferometry is done between the Keck telescopes, with mirrors for the actual light to interfere. Interferometry is done between the VLT telescopes, same concept. There is no interferometry combining all those telescopes. You can add the images from the different sites to get more statistics, but that is something different.

 

[mrspeedybob]

From your words, one might think that satellite images of Earth in which the human form is visibe aren't practically possible. Is it merely the difference in scale between a person's head and a person's skin cell that would necessite long periods of photon collection and loss of information due to movement?

Essentially, yes. If there are a billion skin cells on top of the head, then the head as a whole will reflect a billion times more photons per unit of time. Your sensor will need a certain number of photons to resolve an image. If it's zoomed out to the scale of a head it will get them a billion times faster then if it is zoomed into the scale of a skin cell.

Again, doesn't satellite imagery containing the human form prove this to be a non-issue? Or are you saying that the decohering effect of Earth's atmosphere comes into play only regarding smaller visual details?

Atmospheric distortion is absolutely an issue. Seeing people is relatively easy, but as you zoom into smaller and smaller scales, it becomes more and more of an issue. Actually resolving skin cells from space may be technically impossible. You'd have to account for refraction through every tiny temperature and composition gradient, as well as diffraction past every dust particle. IF you could track all the billions of such obstacles and computationally compensate for them, or activate some tractor beam to move them out of the way, then you could see skin cells. This falls into the realm of what may be theoretically possible in the far future, a concept you brought up in post 9. If we move the discussion to a planet with no atmosphere and a perfectly uniform gravitational field, then get down to just the distance question, which is all jwinter and I were really addressing in our posts.

What information are you referring to when you say that, according to quantum mechanics, information cannot be destroyed?

Not just quantum mechanics. Conservation of information is pretty fundamental to every branch of physics. It's essentially a re-statement of the 2'nd law of thermodynamics, that entropy must increase. If any 2 initial states of a system evolved into the same state, then the entropy of the system would have decreased.

 

[Andy Resnick]

Are you sure it requires all that? What I meant is that it wouldn't seem to make sense to hold that, from 10 feet away, the visual information of the bacteria isn't hitting my face but is scattered too far and wide, if the "visual information of the dish's form," i.e., that info that allows my brain to form a clear, crisp, hard-edged image of the dish, has no problem making it into my small pupils.

You are right- it doesn't have to be that complicated. Usually it's a lot easier and more qualitative. The easiest method is to use the coherency matrix: if the value is exactly 1, you can perfectly reconstruct the optical field at the source. If it's less than 1, there is uncertainty in the detected field as compared to the 'truth'. When the coherency matrix is zero, the optical field has become totally randomized. There are rules that the coherency matrix obeys during the propagation of light.

The references I have posted, especially the ones by Emil Wolf, spell all this out in detail. They are worth reading.

It can be shown that when an optical field propagates through random media (i.e. clear air turbulence), the coherency matrix decreases in value. Therefore, as light propagates through the atmosphere, through the ocean, through milk, through skin, it rapidly becomes no longer possible to perfectly reconstruct the object field because the coherency matrix is less than 1.

From your words, one might think that satellite images of Earth in which the human form is visibe aren't practically possible. Is it merely the difference in scale between a person's head and a person's skin cell that would necessite long periods of photon collection and loss of information due to movement?

Well, here again it depends on what you mean- KH-11 satellites can detect objects on Earth as small as a grapefruit.

https://en.wikipedia.org/wiki/KH-11_Kennan

That doesn't mean it can image you with grapefruit-sized blurry Airy disks. But I have been careful not to state you can't see people from space. We can't see aliens on other planets. Whenever light propagates through disordered media there is a progressive loss of coherence. The rate of loss depends entirely on the specifics.

In any case, imaging people on Earth with satellites is dumb now- everyone uses drones. Humans can be well imaged with those.

Again, doesn't satellite imagery containing the human form prove this to be a non-issue? Or are you saying that the decohering effect of Earth's atmosphere comes into play only regarding smaller visual details?

That's close to what I mean. Certainly, in order to image smaller details, the aperture has to get larger- either a monolithic aperture or a synthetic aperture, like VLBI. But there's another limit on how large the aperture can be before you simply stop gaining spatial detail, and that size is set by the coherence- once the light hitting different parts of the aperture is mutually incoherent, it cannot contribute additional information to the final image. The details of the coherence: the rate of loss in time and length scales depends entirely on the specifics.

 

[Andy Resnick]

Read up on the use of the twin Keck scopes and also using them combined with the scopes in South America at the ESO's Andes site
just one small snippet
Dave

Nobody denies the existence of optical interferometers. I'm talking about the limitations on interferometry, for example: what is the maximum path difference that is achievable using a Mach-Zender interferometer? What is the maximum pinhole separation that can be achieved with a Young interferometer? Lots of variables impact these calculations: not just the spectral bandwidth or spatial bandwidth but also what happens to the coherence state as it propagates through a disordered medium like the atmosphere.

It's should not be surprising that an infinite path difference or pinhole spacing can only be achieved in artificial, idealized, conditions. The existence of maximum path length differences and pinhole spacings reflects the loss of coherence, which is how information is stored in the optical field. Emil Wolf's references that I posted earlier spell this out.