In order to see interference fringes in double slit one needs the two slits to be very close (1-2 wavelengths) even using highly coherent laser. But in Holography this condition apparently does not play role. There is interference when the object is very far from the reference beam. Why is this?
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4 Answers
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Unfortunately, the condition you mention is not true. The simple truth is that interference is observed when highly coherent waves interact which each other. the source of the waves (be it slits, mirrors, or any other object) does not matter, as long as the interaction happens within the coherence length because only then the waves are correlated enough to each other to produce the interference.
A typical red laser has a coherence length of ~20cm. This means that if you illuminate a Michealson interferometer with a red laser (let's say HeNe laser), the optical path difference between the two mirrors (which act like duplicate laser sources) can be as large as ~20cm, and you will still see interference patterns.
In holography, you also combine laser light from two sources: a reference beam and light scattered from the object you wish to image. Like the above example, in the optical path difference is within the coherence length (which it must be to achieve holography:), you will see interference.
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$\begingroup$ Do you mean that interference can be seen with He-Ne when the slits are 20 cm away after the beam is b.e. split by a beam splitter to be headed in the slits? Or when the planar wave is converted to a spherical by a pinhole? If true why can I see such experiment made somewhere? Secondly I don't think you are talking about two lasers in the last part of the answer, do you? $\endgroup$– MercuryJun 28, 2017 at 20:07
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$\begingroup$ 1. When I say the coherence length is 20cm, I don't mean that the slits can be 20cm apart. What I meant was that the path DIFFERENCE between the two beams of laser can be as far as 20cm, and still you will see interference. 2. In the last section I was definitely talking about two lasers: the general technique of holography is that you take a laser source, split it into two beams, illuminate a reference mirror with one beam, illuminate your object with the second beam, and then recombine the beams to get the interferogram, which is actualy the hologam. $\endgroup$ Jun 29, 2017 at 6:35
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$\begingroup$ 1. I dont really understand!!! If the slits are 20 cm apart, so would be the difference in the paths (even less expecially for 0,1,2,3 maximums), the difference can get close to 20 in infinity left or right on the screen (maximmum N 100 if not more). So can you be conclusive - will there be itfr when the slits are 20 cm apart. 2. So not two lasers - but one slit with BS. I have seen a paper of Mandel who insisted for interference from two lasers, but the condition were so that you can not be sure if it is not selfinterference. Thank you anyway! $\endgroup$– MercuryJun 29, 2017 at 13:33
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You are wrong about that condition. For example, in his original experiment, using just Sunlight, Young divided a light ray with a card about one thirtieth of an inch thick. In a setup with two slits, that would be equivalent to a distance between the slits three orders of magnitude larger than the wavelength. I think you confuse with the width of each slit which has to be of the order of the wavelength for diffraction to happen.
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$\begingroup$ Ok maybe more -2-3 mm in fact what I wanted to write. But in holography the object can be many meters away. So that does not answer but just corrects the question a bit. $\endgroup$– MercuryJun 26, 2017 at 13:38
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$\begingroup$ The first half of the answer is that the spacing between dark bands in Young experiment is $\Delta=\lambda l/d$ where $\lambda$ is the wavelength, $l$ is the distance from the slits to the screen where the fringes are observed, and $d$ is the separation of the slits. So if you plug in $\lambda\approx500\text{ nm}$ and $l$ of the order of the meter, to get $\Delta$ of the order of the millimeter, so that the fringers can be observed with the naked eye, we need $d$ of the order of 1/2 millimeter. $\endgroup$– user154997Jun 26, 2017 at 16:24
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$\begingroup$ For the holography "side" of the answer, you would need to describe what kind of setup you have in mind. $\endgroup$– user154997Jun 26, 2017 at 16:40
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First, you can't directly compare both experiments. In holography, interference patterns are created by overlaying a reference beam with the object beam. In off-axis holography, overlaying the beams is done with beam splitters and mirrors; in in-line holography, objects are small and often transparent, and since reference beam and object beam stem from the same light source, they will interfere.
In Young's double slit experiment, parallel light is shone through two slits, creating two (theoretically) identical beams that interfere with each other. They are parallel though, so all interference is caused by the parts diffracted to the left or right side when passing the slit. In terms of intensity, the diffracted part is only a small part of each beam, and the further you place the slits apart, the less the two beams can overlap and interfere with each other. In theory, interference will happen no matter how far the slits are apart, but not in practice because the light is not perfectly parallel or perfectly monochrome, the slits aren't cut perfectly straight, light is absorbed and scattered in the atmosphere etc, and you'd need a perfect detector to see the interference pattern.
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The spacing of the slits and the wavelength of the light, together, determine the fringe spacing in Young's experiment. The farther apart the slits, the closer together the fringe spacing (assuming that the fringes are viewed/recorded a fixed distance from the slits). This is because the angle between the light coming from the two slits at any point on the recording plane is larger when the slits are farther apart, and the fringe spacing depends inversely on that angle.
In Young's double slit experiment, there will be interference regardless of the distance between the slits if the path from the light source to a slit, then to a point on the recording plane, is the same for both slits. If the light has a relatively long coherence length (such as is provided by a laser), there will still be interference whenever the difference between those two distances is less than the coherence length of the light.
The reason the two slits are close together in Young's original experiment is that the coherence length of this light was very short, and his optical setup was very simple. However, it's entirely possible to repeat Young's experiment by scaling everything up larger: put the point source a long distance away so the light spreads over a wide area that can cover two slits separated by a wide distance. Far downstream, light that makes its way through the slits will spread enough to overlap, and will interfere to form widely spaced fringes.
It is also possible to modify Young's experiment to obtain very closely spaced fringes: spread the slits relatively far apart and use a pair of prisms or mirrors to tilt the beams toward each other so they overlap sooner and at a wider angle.
Bottom line: Young's experiment is actually a very, very simple holography setup. Just substitute a laser for the light source and add a few optical elements so the beam geometry can be controlled, and Young's experiment morphs into a modern holography setup. If Young had realized (and pointed out) that a recording of the fringe pattern could be used to reconstruct one of the beams from the other, he might have been given credit instead of Gabor, for inventing holography.
answered May 15, 2018 at 17:39