How small is the smallest hole that would still allow you to see through it?

[xpell]

TL;DR Summary

How small is the smallest hole that would still allow to see through, by natural, artificial or theoretical means?

This is not for a homework or anything, I'm just a curious person who was wondering... that: how small is the smallest hole in an opaque material that would still allow to see the "world beyond it", using your eye or any kind of existing or prospective technology?

(English is not my mother language, so please excuse any mistakes.)

 

[DaveC426913]

Depends on how bright it is on the other side. An arbitrarily small aperture will cut out a large portion of photons, resulting in the image being too dim to make much out.

 

[xpell]

Depends on how bright it is on the other side. An arbitrarily small aperture will cut out a large portion of photons, resulting in the image being too dim to make much out.

Thank you, Dave. Is there any way to calculate it? I'm curious.

 

[PeroK]

Thank you, Dave. Is there any way to calculate it? I'm curious.

How do you define a hole?

You can see through glass, even if it doesn't have holes in it.

 

[Merlin3189]

An interesting question.
I'd guess the key is diffraction.
Whether you look through the hole, point a camera at it, or allow an image to form on a screen behind it, doesn't seem to me to matter. With a small hole they'll all behave much as a pinhole camera.

With a large hole (relatively, say 1mm or so) the image is blurred due to the size of the spot produced by a single point. Reducing the hole size gives a sharper image as the spots get smaller - and dimmer, as Dave says, but perhaps we can use a photographic plate, or CCD array, as astronomers do (or did?)

The problem comes from diffraction causing spreading of light from the hole, rather than simple rectilinear spread from the source. Rayliegh showed a simple limit for the resolution of a telescope, when the diffraction patterns of adjacent dots overlap such that the peak of one coincides with the minimum of the other.
See Rayliegh criterion

The diffraction spread of a point source becomes greater as the aperture of the hole decreases. A telescope has a large aperture and resolution is very good. When you get down to the sort of size you are probably thinking of, resolution would be very poor. Maybe see Resolution calculator ( I am not familiar with this and haven't checked it out yet.

So there may not be a clear limit. Rather the image getting increasingly blurred and you decide when it is no longer useful. We can generally get over the dimness problem.

Edit:PS the shorter your wavelength, the better your resolution. So use blue light,or even UV for a suitable camera.

 

[xpell]

How do you define a hole?

You can see through glass, even if it doesn't have holes in it.

That's why I said "in an opaque material":

(...) how small is the smallest hole in an opaque material that would still allow (...)

Just imagine a small hole drilled in a wall, or a metal sheet, or a cardboard, or whatever.

 

[xpell]

An interesting question.
I'd guess the key is diffraction.
Whether you look through the hole, point a camera at it, or allow an image to form on a screen behind it, doesn't seem to me to matter. With a small hole they'll all behave much as a pinhole camera.

With a large hole (relatively, say 1mm or so) the image is blurred due to the size of the spot produced by a single point. Reducing the hole size gives a sharper image as the spots get smaller - and dimmer, as Dave says, but perhaps we can use a photographic plate, or CCD array, as astronomers do (or did?)

The problem comes from diffraction causing spreading of light from the hole, rather than simple rectilinear spread from the source. Rayliegh showed a simple limit for the resolution of a telescope, when the diffraction patterns of adjacent dots overlap such that the peak of one coincides with the minimum of the other.
See Rayliegh criterion

The diffraction spread of a point source becomes greater as the aperture of the hole decreases. A telescope has a large aperture and resolution is very good. When you get down to the sort of size you are probably thinking of, resolution would be very poor. Maybe see Resolution calculator ( I am not familiar with this and haven't checked it out yet.

So there may not be a clear limit. Rather the image getting increasingly blurred and you decide when it is no longer useful. We can generally get over the dimness problem.

Edit:PS the shorter your wavelength, the better your resolution. So use blue light,or even UV for a suitable camera.

Thank you very much, Merlin. I was reading a bit more about this and now I'm wondering if I've inadvertently described a pinhole camera?

 

[hutchphd]

The Rayleigh Criterion ( angular resolution ~ $\frac \lambda d$) is true for any aperture including cameras with lenses.
There is another entire layer of complexity when lenses are involved that does not involve diffraction at all but rather the inability to produce a truly perfect lens...the pinhole lens being perfect only in the limit of zero size. That is a separate issue involving the circles of confusion, and beyond the scope.

 

[Merlin3189]

Thanks for that comment xpell. I had a look at the reference to pinhole camera and I've already discovered something I did not know about at all - spurious resolution.

Thinking a bit more about the original question, I wonder if there is another limit, when light simply cannot pass through the hole? I'm not sure what the physics/maths of this would be, but looking at my microwave oven, the window is covered with a metal mesh which is supposed to stop the microwaves escaping, while allowing light through to see the contents. The holes are much smaller than the microwave wavelength, but much bigger than light wavelengths.
Whether we could make holes less than 1/10th the wavelength of light, I'm not sure. That would be 50 nm or less, which I think (very unsure) would be only a few hundred atoms wide. Another issue to investigate.

 

[Andy Resnick]

Summary:: How small is the smallest hole that would still allow to see through, by natural, artificial or theoretical means?

'see through' makes this question interesting to answer- subwavelength apertures allow an evanescent field to extend beyond the screen, and by placing an appropriate optical element close to the screen, one may 'see through' a subwavelength aperture (a.k.a. near-field scanning optical microscopy)

https://www.olympus-lifescience.com...e/primer/techniques/nearfield/nearfieldintro/

I don't know what the lower limit is- I expect it has to do with throughput and detector noise levels, but 50 nm (λ/10) seems 'typical'.

 

[hutchphd]

'see through' makes this question interesting to answer- subwavelength apertures allow an evanescent field to extend beyond the screen, and by placing an appropriate optical element close to the screen, one may 'see through' a subwavelength aperture (a.k.a. near-field scanning optical microscopy)

https://www.olympus-lifescience.com...e/primer/techniques/nearfield/nearfieldintro/

I don't know what the lower limit is- I expect it has to do with throughput and detector noise levels, but 50 nm (λ/10) seems 'typical'.

There is a famous paper by (one of my heroes) Hans Bethe on the subject. He shows the total transmission through a small hole in a conductor is reduced from the simple Kirchhoff result by an additional factor of kd (wavenumber X diameter). Very pretty stuff:

 

[sophiecentaur]

Thank you very much, Merlin. I was reading a bit more about this and now I'm wondering if I've inadvertently described a pinhole camera?

The title of the thread asks "see through" but the pinhole camera produces an image in a screen, which is a different thing.
Seeing through:
What you can "see through" a hole implies a field of view (in ray optics, you can't see round corners and the edge of the hole will stop you seeing anything but what the edges define. If your pupil is considered to be very small and the distance to the hole fairly large then simple geometry of a sketch diagram will show you what you could see.
If the hole is made small (not many wavelengths wide) then diffracted light from beyond the edges (which is always there) will be as bright as the small amount of light getting directly through the hole via conventional 'rays'. There is a simple experiment which shows you where diffraction starts to have an effect and that is to look at a bright object through the narrow slit that you get between the knuckles of your fingers. Focus on the object and you will also see streaky lines due to diffraction. It's up to you to decide when the quality of what you see is acceptable - can you see enough of the object, for instance.

Pinhole camera:
This has been discussed higher up the thread and, again, you have to decide between getting a bright enough image (big enough hole) and the attendant blurriness. Diffraction rings will appear when the hole is very small and, in that case, light gets through from almost all directions on the object side. A great exercise is to make a pinhole camera that can be used for projecting the best images of Sunspots on a card. (NO LOOKING DIRECTLY!)

It's like all Engineering - you need to specify the requirement before you can know how best to design your system.

 

[sysprog]

The shortest wavelength that the human eye can see is about 380 nanometers $-$ that puts a lower bound on the diameter of the 'pinhole' in your opaque material, and the light would presumably have to be bright, and subjected to post-pinhole optical apparatuses for it to be useful for visual imaging purposes $-$ some films and electronic cameras can capture much shorter wavelengths $-$ e.g. X-rays range in wavelength from .01 to 10 nanometers $-$ I think that it would be possible to make a 'pinhole camera' with an aperture that small, e.g. by using graphene micropores for the iris.

 

[sophiecentaur]

that puts a lower bound on the diameter of the 'pinhole'

Whatever the size of the hole, some light energy will get through. Think about how your car radio still works when you drive into a tunnel. The signal can still be there when the 200m radio wave gets 50m into the tunnel. Attenuation is, I agree, quite high for sub lambda sized holes. As you point out, diffraction will destroy any information about the direction the wave arrives from, though.

 

[sysprog]

Whatever the size of the hole, some light energy will get through. Think about how your car radio still works when you drive into a tunnel. The signal can still be there when the 200m radio wave gets 50m into the tunnel.

As you are no doubt aware, some of those phenomena could be due to harmonics $-$

https://punchthrough.com/wp-content/uploads/2018/12/emissions-decisions.png

 

[sophiecentaur]

As you are no doubt aware, some of those phenomena could be due to harmonics $-$

https://punchthrough.com/wp-content/uploads/2018/12/emissions-decisions.png

View attachment 272076

I'm not sure what you are getting at here. An ordinary mf AM receiver has a very narrow band reception bandwidth and good interference rejection. If it were subject to harmonic interference then it would soon find itself in the waste bin. Also, where are those harmonics generated? If you are suggesting that the transmitter could be to blame then it would fail the regs at installation. (Or are you referring to 'rusty bolts'?)

It's not clear what that fault chart refers to (it's too complex to read without any other help) but, if you put realistic figures in the boxes then, in the context of am broadcast transmitters and receivers, it's not really relevant.

In any case, second and third harmonics of an mf transmission still have huge wavelengths, compared with a typical hole in a hill.

Also, if you ever try to build yourself a Faraday Cage that actually does the job, the first thing you have to do is to eliminate all cracks and holes. There is actually no such thing as a hole that's "too small" to admit radiation. It's all a matter of how many dBs of rejection that's "enough" for the purpose.

 

[sysprog]

I was thinking of the waveguide effect of the tunnel producing higher frequency harmonics with which the receiver anntenna could symathetically resonate at its tuned frequency.

 

[sophiecentaur]

No harmonics are Generated without the presence of a nonlinearity and also high level signals. MF receivers work on only millivolts of signal level and less.
That was what I meant by the throw away term "rusty bolts".

The 'resonance' would be within the receiver and not the tunnel.

 

[sysprog]

Thanks, @sophiecentaur $-$ I'll reassess some of my suppositions . . .

 

[sophiecentaur]

Thanks, @sophiecentaur $-$ how do you account for being able to receive intelligible signal deep inside a long tunnel on a frequency the wavelength of which is more than twice as long as any non-length dimension of the tunnel?

As no one had specified how many dBs of attenuation you are implying then there is no answer to your question. But there is no actual cutoff. It drops off (iirc) exponentially.
you don’t seem to be denying the phenomenon - you are just trying to ‘explain’ it in an unlikely way. For instance, two different transmitters and two different receivers tend to give the same result. Resistive losses in rock would be relevant too, of course but harmonics? You’d need give a bit more detail, I think.

 

[sysprog]

Ooo, @sophiecentaur, I misspelled 'receive'

 

[snorkack]

For comparison, see ultramicroscope - which sees holes in a transparent medium.

You can see an arbitrarily small object, smaller than your eye/optic resolution or the wavelength limit of the latter - as a dot of light on a dark background. You cannot see any details of the shape of the dot, not even the direction from which the light is passing by the dot. You do have the ability to see the spectrum of the light.

Therefore, in an opaque sheet, you should be able to see arbitrarily small holes - as dots, with no information as to the direction of the light beyond, but full information about spectrum.
To resolve direction/images of light beyond, you need holes bigger than the light wavelength.