Can a thick pinhole create a spot smaller than the diffraction limit?

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In summary, the conversation discusses the possibility of using a thick pinhole, such as a long solid cylinder with a fine pinhole drilled through it, to project a non-image spot smaller than the diffraction limit of a thin pinhole. The use of oblique rays and the absorption of waves by the material of the aperture are also considered. The conversation concludes by mentioning the potential of using conductive walls and plasmons to form an image smaller than the diffraction limit. This concept has been studied and is known as superlensing.
  • #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?
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  • #2
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": has been a lot of work on this in the past few years; also see

Related to Can a thick pinhole create a spot smaller than the diffraction limit?

1. What is thick pinhole and spot size?

Thick pinhole and spot size refer to the size of a spot or hole used in optical experiments to control the amount of light passing through a system. A thick pinhole or spot has a larger diameter compared to a thin pinhole or spot.

2. How does the thickness of a pinhole or spot affect the results of an experiment?

The thickness of a pinhole or spot can affect the resolution and brightness of an image. A thicker pinhole or spot allows more light to pass through, resulting in a brighter image but potentially sacrificing some resolution. On the other hand, a thinner pinhole or spot may provide a sharper image but with less brightness.

3. What factors determine the optimal thickness of a pinhole or spot for an experiment?

The optimal thickness of a pinhole or spot depends on the specific experiment and the desired outcome. Factors that may influence the optimal thickness include the type of light source, the sensitivity of the detector, and the distance between the pinhole or spot and the detector.

4. How can the thickness of a pinhole or spot be measured?

The thickness of a pinhole or spot is typically measured using a microscope or a laser beam profiler. These tools can provide precise measurements of the diameter and shape of the pinhole or spot.

5. What are the benefits of using a thick pinhole or spot?

Thick pinholes and spots can provide a brighter and more evenly illuminated image, making them useful in low-light situations or for detecting faint signals. Additionally, a thicker pinhole or spot can reduce the effects of diffraction, resulting in sharper images.

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