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I was wondering why some apparatus seem to place a single slit right before a double slit. Then I saw this this question. The answer explained it quite well; but I still don't quite understand how a single slit produces coherent light from a partially coherent source.

For those wondering, the apparatus is in this question enter image description here the answer did not mention the effects of the single slit enter image description here

joshua mason
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  • It's more accurate to say the single slit makes the output (of the slit) much more coherent than the input. The idealized limit is a point source which has complete spatical (but not temporal) coherence. – Carl Witthoft May 03 '22 at 14:17
  • @CarlWitthoft A point source emits light in all directions .... can you clarify your comment? – PhysicsDave May 03 '22 at 19:50
  • @PhysicsDave A tiny pinhole is very close to "half" a point source, emitting into a hemisphere. However, if you start with a collimated beam & focus it onto a pinhole, the output (prior to diffraction) will be pretty well coherent with a divergence angle equal to the focus angle on the input side. – Carl Witthoft May 04 '22 at 11:57
  • @CarlWitthoft Yes the point source needs a lens to produce coherent light. We don't need a pinhole as the lens itself would serve as the aperture. So .... a point source on its own has NO coherence whatsoever !? – PhysicsDave May 05 '22 at 14:55

5 Answers5

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Single slit can have two effects:

  1. It effectively decreases the angular size of the source. Smaller source size results in better time coherence, because there is smaller spread in distances that light has to travel.
  2. If adjusted properly, the single slit can improve the source coherence in terms of wavelength spread. For demonstration let's assume that the source emits only wavelengths $\lambda_1$ and $\lambda_2$. Consider two slits as a screen for a single slit. A single slit produces diffraction pattern, which is an overlap of diffraction patterns from $\lambda_1$ and $\lambda_2$. Now you can adjust double slit in such a way that diffraction pattern minima from $\lambda_1$ coincide with maxima from $\lambda_2$. Therefore, you have filtered out $\lambda_1$.

In the end, I think that 1. is what really matters in your case.

Update: as PhysicsDave points out below, point 2. is probably wrong. Even if it's not wrong it requires very specific adjustment of the slit parameters. Point 1. is equivalent to the accepted answer in the question you cite: "That's when the first slit becomes useful as it makes light spatially coherent."

Dmytro Oliinychenko
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    #2 is not possible, if you add a 1 min to a 2 max you just see the 2 max. The problem is you are using the "high school" definition of interference .... but photons do not interfere this way (violation of conservation of energy). As Dirac, Feynman and many other famous phycists know, each photon determines its own path. If you were to selectively look at only certain portions of the pattern you could observe both 1 and 2, sometimes mixed sometimes separate. – PhysicsDave May 03 '22 at 03:03
  • Correct my understanding if it's incorrect: so are we saying having a single slit effectively makes sure that the source of light of the double slit comes exclusively from the single slit's central bright spot. And this ensures the coherence? ---

    In that case, is there a condition for the single slit's width such that it's most effective at providing this coherence?

     – joshua mason May 10 '22 at 06:49
  • @joshuamason be careful of the word coherence .... it is not binary i.e. Light is never perfectly coherent or perfectly incoherent, it is always more coherent or less coherent compared to some reference. The slit makes the light more coherent but at the cost of reducing intensity. In this modern world we could use a camera and check the pattern over a long time .... with a much smaller slit we actually start to introduce more diffraction, the beam would spread and begin to lose coherence. – PhysicsDave May 10 '22 at 11:41
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    @PhysicsDave so are the other parts of my understanding correct? In particular, "having a single slit effectively makes sure that the source of light of the double slit comes exclusively from the single slit's central bright spot" – joshua mason May 10 '22 at 12:34
  • @joshuamason see my comment below – PhysicsDave May 10 '22 at 14:44
  • @PhysicsDave "having a single slit effectively makes sure that the source of light of the double slit comes exclusively from the single slit's central bright spot". Yes, I thinks it's correct. – Dmytro Oliinychenko May 10 '22 at 23:33
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TL;DR: temporal vs. spatial coherence.

To add to other answers: there exist time coherence (or temporal coherence) and spatial coherence. While the former results from the presence/lack of correlation between the light/photons emitted at the same point at different moments of time, the latter refers to the fact that the light emitted by different parts of an extended light source might be not correlated.

A single slit or a pinhole filters out most of the light coming from the source, leaving only the light coming from a particular direction, i.e., particular place in the object. This, on the one hand, reduces the overall light intensity, but, on the other hand removes the interference due to the waves coming from from difference point sources. This does not make light coherent in time, but this is usually sufficient for the interference experiments. Note that camera obscura and pinhole camera use the same principle.

Roger V.
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Coherency of light is improved the more "hurdles" we put the light beam through. By adding slits or apertures photons that are similar in path (direction, angle, source location) will become selected and others off path will be rejected.

The most coherent light is laser light, the process of stimulated emission makes all the photons go in the same direction but in addition the laser cavity is typically small and precisely engineered which also improves coherency.

The additional single slit helps to select similar photons and makes the visible pattern sharper especially for less coherent sources like the sun. The photon has to navigate the single slit, the double slits and then finally the screen all of which affects coherency.

PhysicsDave
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  • stimulated emission does not control direction. Lasers use mirror pairs to 'reject' all photons not going in the desired direction. That's how they get significant gain in the output beam. – Carl Witthoft May 03 '22 at 14:15
  • @CarlWitthoft Stimulated emission is always in the direction of the incident photon ..... don't know why you would say "stimulated emission does not control direction" ....? – PhysicsDave May 03 '22 at 19:47
  • Yes, but there is always statistical (not stimulated) emission from the upper energy level. Those photons are emitted in random directions & the emissions they stimulate are thus in random directions. Only the photons which are along the desired axis reflect back into the laser medium to stimulate additional photons in the desired direction. – Carl Witthoft May 04 '22 at 11:59
  • @CarlWitthoft A laser would not function (produce a coherent beam) if the direction of stimulated emission was not directional ..... yet we can get a laser cavity to lase (at somewhat lower power) with no mirrors at all. The vast majority of emission in the upper energy level is stimulated at steady state. – PhysicsDave May 05 '22 at 14:56
  • @physicdave and that's because the laser cavity has a nonspherical shape . Pump up a cloud of iridium atoms and see how many directions some superradiance shows up – Carl Witthoft May 05 '22 at 17:08
  • "Coherency of light is improved the more "hurdles" we put the light beam through. By adding slits or apertures photons that are similar in path (direction, angle, source location) will become selected and others off path will be rejected." --- why? – joshua mason May 10 '22 at 07:04
  • @joshuamason the very definition of coherency is how similar the light rays are in path (spatial). – PhysicsDave May 10 '22 at 11:44
  • @PhysicsDave Sorry, I should have been more specific. "By adding slits or apertures photons that are similar in path (direction, angle, source location) will become selected" --- can you explain the mechanism behind this – joshua mason May 10 '22 at 12:33
  • @joshuamason Yes you are more correct saying the photons come from a smaller spot at the source, maybe not the brightest it depends on alignment. But a deeper understanding is from Feynman/Dirac (and others) every photon is determining its own path ... which seems impossible because they travel at c. But my interpretation and others is that the excited electron certainly already is disturbing the EM field (virtual photons) and when a path is viable the real (non virtual photon) is emitted. An electron can stay in an excited state for quite a while, all the time interacting with the EM field – PhysicsDave May 10 '22 at 14:50
  • Excited electrons are just trying to get rid of their energy ... the only way is the EM field/photon and it requires another atom/electron (at lower energy) to do this. A distant start with its massive energy emits photons .... the EM field must somehow know that lower energy states are out there. Its similar to a gravity field ... how does the apple know where to fall! – PhysicsDave May 10 '22 at 14:54
  • One of the important theories is the Feynman path integral, it states that photons consider all paths but choose probable ones. Doing the integral (which tracks/sums phase) over many paths eventually shows that photons most probable paths are multiples of their wavelength. This explains the bands in the DSE. Likely the photons are emerging from the source in a similar pattern, with the central peak most emitting. – PhysicsDave May 10 '22 at 14:58
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The set up of the first linear slit, in the diagram of the double slits above, is designed to make a line of point sources of light .

A point source with a single frequency input has to follow the inverse square law.

double slit

If far enough away from the double slits the wave from the point source can be modeled as a plane wave. (note that in the diagram there is no distance given between the point-line source and the double slits, it has to be large in order for the plane wave to be a good approximation of the wave front)

plane wave

anna v
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After reviewing the answer I cited in the question, the answers, and lectures notes on wave coherence, I have come to the following explanation.

Imagine a wave without spatial coherence, so something like:

enter image description here

What the single slit does is taking only a small section of the incoming wave, which would be approximately linear, thus introducing spatial coherence as the wavefront is now approximately parallel to the slits:

enter image description here

Feel free to point out any errors.

joshua mason
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