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Thick Pinhole and Spot size

  1. Jun 25, 2014 #1
    Didn't seem to have much luck on the actual reasoning with this elsewhere.

    A regular pinhole projects an image, and has a diffraction limit for the image, that is the size of the airy disk.

    What if we take a thick pinhole, no a pinhole in metal foil for example, but a long solid cylinder, several cm (or longer if need be) thick, with a fine pinhole drilled through it.

    Can this project a non-image very fine spot that is smaller than the diffraction limit of a thin pinhole of the same diameter?

    Oblique rays are essentially cut out, and you're left with on-axis.


    I know someone will bring up ripple simulations / diffraction waves, like water down a long hallway (or sewer), it'll bounce off the walls, interfere with itself and propagate forward, and spread out at the exit.



    But there are some obvious differences that are usually more or less neglible in thin aperture ripple simulations.

    What if the material absorbed the wave as it hits the material of the aperture. This only portion of the wave to make it out, would be the center portion propagating on a narrow enough angle to avoid hitting the material.


    Any idea on this?
     
  2. jcsd
  3. Jun 25, 2014 #2

    UltrafastPED

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    As the tube becomes longer and longer the cone of rays which can pass becomes smaller and smaller; thus the field of view is reduced, and the image becomes fainter and fainter due to loss of light.

    As the hole becomes smaller and smaller the diffraction effects would increase, thus causing more light to be lost in the tube, diffracted onto the side (and absorbed, hopefully - this is why microscope tubes have special dark coatings on the inside, to get rid of the extraneous light).

    Ultimately, as the hole size is reduced, all that you will see is a somewhat dim spot of light, with no distinguishable content beyond its intensity and spectrum.

    As the hole becomes smaller yet, the longer wavelengths will not be able to propagate through the hole, and the spectrum will accordingly be shifted towards the shorter wavelengths.

    If the walls of the tube are conductive, the incident light at the top, which is hitting the area around the hole, may induce quantum mechanical effects - in this case, plasmons, which are quantized waves of charge (= neutral plasma waves). These have can propagate along the interior edges of the tube due to their shorter wavelengths, and yet carry the frequencies of the incident waves along with them. This is possible because their speed of travel is much slower than light, hence the wavelengths fit.

    At the opposite end of the tube the plasmons re-radiate a portion of their energy as light, and an image may be formed - if everything is just so - and thus it is possible to form an image smaller than the diffraction limit, and even focus it with specially engineered holes.



    See, for example, "Imaging nanoscale features with plasmon-coupled leakage radiation from far-field radiation":

    http://www.opticsinfobase.org/view_...20827.pdf?da=1&id=241011&seq=0&mobile=no&org=


    There has been a lot of work on this in the past few years; also see
    https://en.wikipedia.org/wiki/Superlens
     
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