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Conventional optical systems are (at best) diffraction limited. But as I understand it, that is solely due to the instrument altering the properties of the incoming radiation -- e.g., an Airy disc only occurs because the direction of the incoming light is altered by some sort of obstacle.

What about (hypothetical) systems that observe the incoming radiation without altering any of its properties? I'm talking about the sorts of systems for which the 2012 Nobel prize was awarded (observing quantum systems non-destructively).

In this context, all I ever hear anyone talk about is quantum computers. But could these sorts of techniques be used in, say, a telescope? Would such a telescope be able to observe individual grains of sand on Mars, while it's standing on the Earth's surface and is no bigger than an ordinary SLR camera?

More generally, suppose there is a device able to determine all properties of all photons in the entire light field accessible to the instrument at some instant, up to the best limits allowed by quantum mechanics. What is the theoretical limit on resolving power for this device?

More theoretically, how much information is actually contained in any light field, and how much of this information can theoretically be extracted from it?

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"Up to the limits allowed by quantum mechanics".

If a photon passes a "lens" (or whatever other property of the device that determines its finite size - you did say "no bigger than an ordinary SLR camera") then there is a point where the position of the photon is known "to within $\Delta x$" - namely, the size of the lens. I use lens without quotation marks from here on... it is whatever determines the size of your hypothetical machine.

Now the Heisenberg Uncertainty principle tells us that we cannot know the momentum of the photon (in the plane of the lens) with infinite precision: $\Delta p \Delta x \ge \frac\hbar 2$

If you don't know the horizontal momentum with infinite precision, you cannot know the direction with infinite precision. I believe you will find that if you follow this analysis through, you will get to a very similar resolution limit as you get from "conventional diffraction". No grains of sand on Mars for you... unless you are standing awfully close.

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  • $\begingroup$ True, but Planck's constant is ridiculously tiny, especially when it needs to be applied to any macroscopic system...If you'd set $\Delta x$ to 1m (still a very reasonable camera size compared to say, a VLBI baseline), you'd have a pretty good idea of that photon's momentum...better than 1 part in ~$10^{34}$ in fact. That's still an angular resolution of $~10^{-29}$ arcsec, rather a lot better than existing telescopes...Even if this back of the envelope analysis is off by 10 orders of magnitude somehow, I'd still buy that camera :) $\endgroup$ – Rody Oldenhuis Jan 6 '17 at 17:24
  • $\begingroup$ @RodyOldenhuis you are forgetting that momentum and wavelength of photon are also related by Planck's constant... $\endgroup$ – Floris Jan 9 '17 at 20:51

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