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

[mfb]

But we can specify the initial state, if we like. In theory only, of course.

The microwaves from every pixel area in space is just as "incoherent" as the light from every pixel area on a bacterium.

If the physics arguments don't convince you, what about the actual astronomy done? If VLBI would work with sources of visible light, how stupid would astronomers have to be to not use it? Using the Earth as baseline would increase the baseline by 6 orders of magnitude compared to current telescopes, and 4.5 orders of magnitude compared to VLT interferometry.

 

[my2cts]

The limiting resolution is something like λ/NA where the numerical aperture is lens diameter divided by distance.
The NA drops to astronomically small values for telescopes. In principle, with a very large telescope or interference telescopy NA could be increased, but requirements on phase coherence will impose a technical limit.
The light source does not have to be coherent, but the different parts of the telescope must have a well defined phase relation.

 

[jwinter]

If the physics arguments don't convince you, what about the actual astronomy done? If VLBI would work with sources of visible light, how stupid would astronomers have to be to not use it? Using the Earth as baseline would increase the baseline by 6 orders of magnitude compared to current telescopes, and 4.5 orders of magnitude compared to VLT interferometry.

The phyics arguments are unconvincing because there are none (at least none that I have seen or thought of). But the technology problems should be obvious. Optical frequency combs with sub-Hertz stability have only become possible in the last few years, and even if the stability reached is sufficient (I don't know if it is), the challenges are horrific. Think how many microwave (ie gigahertz) bandwidths there are in a 500 terahertz light signal! And all of the bands have to be split out and processed separately with individual optical detection and VLBI type electronics all operating in parallel. Astronomers are not stupid - they propose things that can be built, not things that are still out of reach.

 

[mrspeedybob]

Seems to me like jwinter mostly answered this question in post 17. The original question wasn't about what information was resolvable (which is what most posts are addressing) but what information is actually there. The only thing I would add to jwinter's answer is that while you may just be able to wait long periods of time to collect enough photons to have enough information to extract any arbitrarily small detail (limited by the wavelength of light), you would, at the same time, loose time resolution. If the bacteria was moving, you would not ever be able to get a clear picture of it.

 

[Andy Resnick]

But we can specify the initial state, if we like. In theory only, of course.

This is exactly how *blind* deconvolution works, which I mentioned very early in this thread as a non-optical method of reconstructing information from a blurry image. Furthermore, you keep ignoring the fact that propagation of light through the Earth's atmosphere irreversibly decoheres the light. And it is indeed irreversible. If you keep claiming otherwise, then Google 'seeing', and try to explain why astronomers have spent so much time and effort on this problem. Hint: why is VLBI easy in radio but hard in visible?

 

[Andy Resnick]

Seems to me like jwinter mostly answered this question in post 17. The original question wasn't about what information was resolvable (which is what most posts are addressing) but what information is actually there.

I have tried to clearly answer how information degrades as light propagates through a turbulent atmosphere (posts 5, 13, 26). This loss of information is irreversible.

Performing calculations is difficult, but measurements of the information loss can be done- this is an excellent reference:
https://www.repository.cam.ac.uk/handle/1810/251667

 

[mfb]

If you keep claiming otherwise, then Google 'seeing', and try to explain why astronomers have spent so much time and effort on this problem.

It is impossible in practice, but not in theory. If astronomers could know the precise state of the atmosphere, seeing could be corrected perfectly. They do not, so it can only be corrected approximately (which is done already). You keep ignoring the difference between theory and actual applications, and as long as you do that I don't see how this discussion could make progress. Go get your Nobel Prize if you can prove time evolution is not fundamentally symmetric. Probably my last post on that subtopic here.

 

[DrClaude]

What @mfb is alluding to is that according to quantum mechanics, information cannot be destroyed. The evolution of quantum systems being unitary, and considering that everything is a quantum system, means that information is never lost. This is the core issue in the black hole information paradox, since black holes appear to destroy information. There have been a few threads on the subject, especially following Hawking's recent proposal to solve the paradox.

That said, from a practical point of view, as @Andy Resnick has been saying, information can be so hard to recover that it is lost FAPP. But that is, in a sense, a technical limit, not a fundamental one. It appears when, for instance, we trace away the environment the light has interacted with, because we simply can't completely describe the state of the environment, due to the number of particles involved. But if we could know the full quantum state, we would find that the information is still there.

 

[DavidReishi]

Please carefully define what "the visual information of the dish's form" means. I'll start you off- "the dish's form is represented by a 3-D optical field, created when incident light illuminates and scatters off of the dish. The 3-D field can be modeled with Kirchhoff's diffraction formula, considering the dish as the illuminated aperture". Now you go from there to "the visual information of the dish's form".

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.

Seems to me like jwinter mostly answered this question in post 17. The original question wasn't about what information was resolvable (which is what most posts are addressing) but what information is actually there. The only thing I would add to jwinter's answer is that while you may just be able to wait long periods of time to collect enough photons to have enough information to extract any arbitrarily small detail (limited by the wavelength of light), you would, at the same time, loose time resolution. If the bacteria was moving, you would not ever be able to get a clear picture of it.

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?

...[P]ropagation of light through the Earth's atmosphere irreversibly decoheres the light. And it is indeed irreversible.

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?

What @mfb is alluding to is that according to quantum mechanics, information cannot be destroyed. The evolution of quantum systems being unitary, and considering that everything is a quantum system, means that information is never lost.

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

 

[davenn]

If VLBI would work with sources of visible light, how stupid would astronomers have to be to not use it?

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

Another approach to increasing angular resolution is to interferometrically combine the light from two or more telescopes. In the field of large telescopes, this is being done with the twin Keck telescopes 4,5 and the four 8m telescopes of the European Southern Observatory. The 85m Keck baseline provides an angular resolution of 5 milliarcseconds at a 2μm wavelength. The AO-corrected light from each telescope is relayed through a series of mirrors to the basement between the two, where the optical paths are matched before the light is interfered. The available science mode consists of fringe-visibility measurements on a near-IR camera. The contrast of the interference fringes is used to determine the size, or other characteristics, of the object being studied.

http://spie.org/newsroom/technical-...esolution-at-keck-observatory?highlight=x2418Dave

 

[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.