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

  1. Mar 24, 2016 #1
    Sunlight hits our planet, for example, and reflects light outward back into space. Hence why photos can be taken of earth from outer-space. But if we disregard technological limits to optics, etc., then in theory how much information does this reflected light contain? Is it rich enough, for instance, to contain microscopic details like bacteria? And is there a limit to the amount of detail that this reflected light contains? Further, does the amount of detail contained in this reflected light remain constant regardless of the distance that the light travels through space?
     
    Last edited: Mar 24, 2016
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  3. Mar 24, 2016 #2
    The reflected light spreads out in all directions, so energy density falls with distance. And energy density equates to information. So by using a large telescope to look at Earth, more light can be collected and more detail obtained. But we cannot see things which are smaller than the "beamwidth" given by the telescope aperture. So it will be impossible to see bacteria as they are even smaller than any telescope aperture.
     
  4. Mar 24, 2016 #3

    mfb

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    The ultimate resolution limit is proportional to the wavelength of light - you can see bacteria, as they are larger than the wavelength of visible light (a few hundred nanometers). That is just a theoretical possibility, however - there is no practical way to make a telescope that captures a large fraction (>1%) of the light reflected by Earth, and focuses it in a coherent way.
     
  5. Mar 24, 2016 #4
    A microscope can see bacteria, as I agree they are larger then the wavelength of light, but my understanding is that a telescope cannot distinguish anything smaller than its own diameter.
     
  6. Mar 24, 2016 #5

    Andy Resnick

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    This question- imaging through a turbulent layer of atmosphere- is still an active subject of research. The turbulent air degrades information, but it is possible to recover some of it through speckle imaging, adaptive optics (wavefront sensing), etc.

    Roggemann and Welsh's book is an excellent starting place:

    https://www.crcpress.com/Imaging-Through-Turbulence/Roggemann-Roggemann-Welsh-Hunt/9780849337871
     
  7. Mar 24, 2016 #6

    davenn

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    no, that isn't correct

    I can aim my scope at all sorts of things around my neighbourhood and clearly resolve objects very much smaller than the scopes' aperture
    ... insulators on power poles, a bug crawling up that same pole, leaves on trees ...... the list is endless

    EDIT: ohhh and to really go directly against your theory .......
    I can increase the aperture of the scope and have even better resolution
    This is common practice with telescopes optical and radio


    Dave
     
  8. Mar 24, 2016 #7

    anorlunda

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    Is is not so that the largest scale distributions of galactic clusters are thought to be magnifications of quantum fluctuations during inflation? Information can seem to be meaningless, but it is still information.

    2-missingdarkm.jpg
     
  9. Mar 24, 2016 #8

    mfb

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    Telescopes and microscopes are not so different. Our hypothetical oversized telescope would look more like a microscope, as the object it looks at is close to the telescope (relative to its size).
     
  10. Mar 24, 2016 #9
    I appreciate all the responses, but I think there may be too much hang-up on telescopes. Let me try a different approach and first abstract from the distance/diffusion question if that's possible.

    Google satellite images capture the human figure. But what about 250 years from now? What detail will technology be able to capture from the same distance? "But," you might say, "we don't know what kind of technology we'll have in 250 years...we might have completely different forms of light gathering."

    Which brings us precisely to my point. The reflected light itself shooting off of the earth and its objects, and how much detail is actually contained in it (i.e. regardless if the light is even "seen.")
     
  11. Mar 24, 2016 #10

    sophiecentaur

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    What else, other than a telescope, can be used to see details on the Earth from a distant point in space? If you want detail then you need a 'viewing device' (aka telescope) that has a large aperture. This is because Diffraction will impose limits on the acuity of any optics, even when fancy image processing is used over long periods of time.
    The amount of 'recoverable' detail depends entirely on the system that's used to see it with and the amount of extraneous light that is interfering with the 'wanted' image.
     
  12. Mar 24, 2016 #11
    Okay, so what if we put the system that's used to see it on a historically sliding scale, say from the beginning of telescopes to 10,000 years from now into the future (bear with me)... Doesn't that make it possible to ask the question, Well how much information is actually contained in the reflected light itself? It would be similar to asking, What is the limit of the 'system that's used to see it' beyond which it doesn't matter because there's no finer detail contained in the light itself to be communicated?
     
  13. Mar 24, 2016 #12
    Also, we can say that the above context of planets, space and the sun is perhaps arbitrary...for now.

    So that a question like the following can be asked first. If you stand 10 feet from me holding out a petri dish covered in bacteria, does the light that reflects off the petri deish and travels 186,000 mi/sec to me contain detail of that bacteria? Forget whether I can see it with my naked eye... Is the information, i.e. light describing the bacteria as distinct from its background, etc., actually making it 10 feet to me? That is, in theory, could a strong enough optical device, even if not invented yet, allow me to see the bacteria?
     
  14. Mar 24, 2016 #13

    Andy Resnick

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    As I mentioned earlier, the answer depends on what the air is doing. The movement of air affects the optical path, and if the air is not moving in a deterministic fashion then information is irretrievably lost, at length scales determined by the motion.

    Consider looking at something through thermal haze:

    http://www.the-digital-picture.com/...mm-f-5-6.3-Di-VC-USD-Lens/Railroad-Bridge.jpg

    No lens can 'undo' this type of image degradation. The best we can to is to use many images and computational approaches to guess what the undistorted image is. Looking down from space is easier than looking up from Earth, but I can't easily explain why.

    As far as the question, 'Can I resolve a bacterium at 10 feet?' The answer no. I can demonstrate this by the basic design parameters. Given a bacterium 1 x 3 microns (E. Coli) located 3 meters way, my lens needs to have an angular resolution of approximately 1.1111 × 10^-7 radians (6.366×10^-6 degrees, 0.0229 arcsec), corresponding to a lens diameter of 5.5 meters (Rayleigh criteria). So that's kind of silly. But maybe we can be smart and use aperture synthesis to reduce the mass. What about the focal length?

    The E Coli needs to span 2 x 6 pixels (since it's resolve, not detect), using 3 micron pixels (small, but not unreasonable) gives a linear magnification of 6, and since the object distance is 3 meters, the image distance is 0.5m, which gives a focal length of 0.43 meters. But maybe we can figure out how to make nm-scale detectors, which would help increase the focal length. Because right now our lens has a numerical aperture of 6.4, meaning we can't image in air. Which is what we wanted to do. So we have to turn to computational approaches, combining many 'partial' images to reconstruct the object field.

    If you want to see small things, yoo have to put your lens close to them. You can be far away (and it's often better to be further away), but the lens itself has to be close.
     
  15. Mar 24, 2016 #14
    Let's make this a non-factor. Let's say, if I understand your terminology correctly, that it's more to detect than resolve, i.e. that distortion's fine.

    What if we're talking not about lenses and the science that goes with them, but about some future and currently unfathomable means of collecting light. The point is, does the same degree of information seen under a microscope actually reach me physically (i.e. not according to perception but according to reality) in the light that travels 10 ft from the petri-dish to me?

    In older satellite images of earth, you could make out many prominent features of the landscape, but by comparison to which the human form would be regarded as a "small thing." Yet, nowadays, satellite images easily make out people. It's not that the satellites got closer. The actual information of the human form was in the light that reached the older satellites too. It was just the optical technology that lagged. Right?
     
  16. Mar 24, 2016 #15
    I didn't notice this before...it answers a large part of the question.

    What about simply a human form, as seen in today's satellite images of earth? The reflected light from earth that travels towards the optics of a satellite, insofar as it misses the satellite, keeps traveling. Is it not a matter only of technology how farther and farther away the light could be collected and the same human form still be made out? In other words, does such detail keep traveling in the light itself?
     
  17. Mar 25, 2016 #16

    mfb

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    It is "just" a matter of technology, yes. A telescope twice the size at twice the distance can (in principle) see the same as the closer and smaller telescope. Same for a microscope.
     
  18. Mar 25, 2016 #17
    Previous comments are correct that the angular resolution depends on the ratio of the aperture (diameter of telescope lens) to the distance away (and the wavelength of the light) by Rayleigh's criterion (look for "Angular Resolution" in Wikipedia). However there is also the fact that in order to obtain an image one has to divide the detection area into pixels and effectively count the number of photons landing on each pixel with sufficient statistics to be able to resolve the required intensity variations.

    If the photons arrived perfectly evenly in time then in order to resolve a 1% difference in intensity from one pixel to the next you should only need to wait for ~100 photons on each pixel. However their arrival rate is not steady but random (poissonian), and so in order to have a 1 sigma likelihood of a 1% intensity resolution, you would need to wait for ~10,000 (=100^2) photons to arrive on each pixel (I think!). If you now allow say 6x2 pixels for your bacterium, then you need to wait for 10,000 photons from each of those 12 locations on the bacteria to be scattered from its surface in just the right direction to enter the focussing aperture (which then steers them to land on the right pixel). So exposure time (or shutter speed) sets another fundamental limit to the information that you can obtain from reflected light.

    Knowing the brightness of illumination, and knowing the percentage of scattered light that will enter the aperture of your telescope, will allow you to work out how long you have to wait in order to obtain a 1% (~7 bit) brightness resolution from your (so-far) perfect photon detecting sensor array. If your sensor is imperfect and generates approximately the same rate of random thermal activations as the real photon detections, then you will need to wait 4 times longer to obtain the same intensity resolution (I think!). If your random non-photon detection rate (thermal noise in the sensor) is significantly greater than the rate of arrival of signal photons, then you may never be able to resolve an image no matter how long you wait. This is a practical (non-fundamental) limit to your information collection.

    So the diameter of a single aperture (or the distance apart of multiple apertures) together with the wavelength determines the angular resolution of your imaging device, while the illumination of the object, the total collecting area of the lens, and the efficiency of your pixel detectors determines how long you will have to wait before an acceptable image can be built up from randomly scattered and randomly arriving photons.
     
    Last edited: Mar 25, 2016
  19. Mar 25, 2016 #18

    mfb

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    Fortunately, photon statistics and angular resolution scale in the same way - at twice the distance the photon flux per area reduces by 1/4, but to keep the angular resolution your mirror area goes up by a factor of 4 as well.
    A different way to see this: for a fixed angular resolution you have to cover a fixed fraction of the solid angle, which means you capture a fixed fraction of the emitted photons. Noise is certainly a problem, illumination should not be an issue: a bacterium in sunlight emits about 10 million photons per (100nm)2 and second. Collect 1% of them and you get 1% resolution within 1/10 of a second.
     
  20. Mar 25, 2016 #19
    A good calculation. But if you allow multiple apertures - as is done with very long baseline interferometry at microwave frequencies (using the diameter of the earth as the baseline), and has been done over much lesser distances in the optical - then angular resolution is independent of photon statistics. Collecting 1% of the light scattered from a bacterium using a lens on a satellite or as the OP suggested in "outer space" would be problematic to say the least :smile:
     
  21. Mar 25, 2016 #20
    Davenn. But if the telescope is focused at infinity, then a tiny lamp at the focus produces a parallel beam the diameter of the aperture, and the converse happens when it is "receiving".
    I agree that if focussed closer then infinity it can resolve small objects. A radio telescope cannot resolve something smaller than its beamwidth (however that is defined).
     
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