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Thread: Interference Questions

  1. #1 Interference Questions 
    Forum Senior bill alsept's Avatar
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    In either the double or single slit experiments where single photons are used could someone answer this question and or direct me to a paper/article about it.

    After going through the slits
    (1) As the photons hit the wall one at a time do any of them hit what will become a dark area of the interference pattern?
    (2) And if so are they detected as they hit?
    (3) Could they be detected as being in phase at first and then later canceled out as an out of phase photon hits the same spot?

    My thought is that photons would hit the wall everywhere based only on the probability of the bell curve of a single slit but the as the photons traveled from the slit to the wall they would oscillate between amplitudes per their color and when they hit the wall are detected by what phase of the cycle they are in. This would form a single slit interference pattern. And if you had added a second slit even if you ran the photons through it much later they too would form a single slit pattern. But as the new single slit interference pattern over layed the first pattern there would be new constructive and destructive combinations making a completely new pattern.


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    Quote Originally Posted by bill alsept View Post
    (1) As the photons hit the wall one at a time do any of them hit what will become a dark area of the interference pattern?
    Interesting question. I'm sure the answer is yes, in practice, because interference is not perfect so a small number will land in the dark areas. Equivalently, in the "classical" case the dark areas will not be completely dark.

    (2) And if so are they detected as they hit?
    They would be.

    (3) Could they be detected as being in phase at first and then later canceled out as an out of phase photon hits the same spot?
    No. Once a photon is detected, it stays detected. A photon can't cancel or destroy another photon (except in the rare case of pair production - but they both have to be present at the same time).


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    Quote Originally Posted by bill alsept View Post
    (1) As the photons hit the wall one at a time do any of them hit what will become a dark area of the interference pattern?
    Yes. The pattern is a probability distribution, and there is still a non-zero ( albeit very small ) probability of photons landing in the "destruction zone".

    (2) And if so are they detected as they hit?
    Yes. There will be a very small number of such hits, though.

    (3) Could they be detected as being in phase at first and then later canceled out as an out of phase photon hits the same spot?
    The screen does not measure "phase", only physical hits. It's much like a photographic plate - once light has discoloured a certain spot, it stays that way. Once a hit is registered, it doesn't cancel against subsequent hits.
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    Forum Senior bill alsept's Avatar
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    So is there a documented experiment that accounts for every photon? I can't find one anywhere or even anything on the subject. For example is there a recorded experiment that sends an absolute number of photons (say 10,000) and at the end of the experiment every single photon is accounted for. I would like to see the results of this experiment and how it was set up. Especialy in the single slit experiment. Thanks
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    Quote Originally Posted by bill alsept View Post
    So is there a documented experiment that accounts for every photon? I can't find one anywhere or even anything on the subject. For example is there a recorded experiment that sends an absolute number of photons (say 10,000) and at the end of the experiment every single photon is accounted for. I would like to see the results of this experiment and how it was set up. Especialy in the single slit experiment. Thanks
    I'm afraid that doesn't make any sense, because not every photon sent out will actually go through the slit; many of them will just end up on each side of the slit, and yet others might go off outside the setup altogether. Remember, we are dealing with probabilities - there is small but non-zero probability associated with every physically possible trajectory these photons could take, so you will never get a case where 100% of them go through the slit and onto the detector. That is why you couldn't find any such experiment.
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    Quote Originally Posted by Markus Hanke View Post
    I'm afraid that doesn't make any sense, because not every photon sent out will actually go through the slit; many of them will just end up on each side of the slit, and yet others might go off outside the setup altogether. Remember, we are dealing with probabilities - there is small but non-zero probability associated with every physically possible trajectory these photons could take, so you will never get a case where 100% of them go through the slit and onto the detector. That is why you couldn't find any such experiment.
    I realize they want all make it and that's why I wanted to see them accounted for at least on the single slit experiment. In a controlled experiment all the photons could be contained by just making the walls big enough. Then no matter what angle the photons trajectory is it will either be detected as a hit at the first wall or go through the only slit (in a single slit experiment) and be detected as a hit somewhere on the second wall. I can't imagine that this could not be done or that it hasn't even been tried somewhere.
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    Quote Originally Posted by bill alsept View Post
    I can't imagine that this could not be done or that it hasn't even been tried somewhere.
    It can be done quite easily by enclosing the entire setup in a closed sphere; you could then account for each photon as hits on the interior surface of the sphere. However, the interference pattern will of course be found only in places that a spherical wave-front originating from the slit can physically reach.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by bill alsept View Post
    I can't imagine that this could not be done or that it hasn't even been tried somewhere.
    It can be done quite easily by enclosing the entire setup in a closed sphere; you could then account for each photon as hits on the interior surface of the sphere. However, the interference pattern will of course be found only in places that a spherical wave-front originating from the slit can physically reach.
    Yes, well that is what I mean. So if every photon that misses the slit is accounted for by hitting the first wall then all we need to do is account for the balance of the 10,000 photons. I realize it may take a million just to get enough through the slit but 10,000 is just for discussion. Now we will know the exact number of photons that go through the slit. I would like to know first of all if everyone of them gets registered as a hit on the second wall. If not then I find that very interesting. And if every photon is detected as an actual hit then I would also like to know the pattern they make. Why hasn't this experiment been done already?
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    Quote Originally Posted by bill alsept View Post
    I would like to know first of all if everyone of them gets registered as a hit on the second wall.
    No. Some of them will end up on the enclosing sphere, but behind the "slit wall".

    If not then I find that very interesting
    Like I said, this is a matter of probabilities; there is always a non-zero probability of a photon going off at a very steep angle from the slit.

    And if every photon is detected as an actual hit then I would also like to know the pattern they make.
    You will get an interference pattern either way.

    Why hasn't this experiment been done already?
    Because it doesn't matter if every single photon hits the screen, or not - you will get an interference pattern either way, even if some photons don't make it to the screen ( for whatever reason ).
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    Forum Senior bill alsept's Avatar
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    Quote Originally Posted by Markus Hanke View Post
    No. Some of them will end up on the enclosing sphere, but behind the "slit wall".
    That's just evading because the experiment most definetly could be set up so that every photon could be accounted for. Like you said the first wall being a spherical shell will account for every photon that doesn't hit the slit. As for the second wall make it very wide and very tall. If that's not good enough then make the wall one square mile wide and at the far edges make it turn 90 degrees back toward the first wall basically closing the whole area in. If any photons manage to hit those far away sides then they too will be accounted for. I think this experiment can be done and with 100% accountability. K
    Quote Originally Posted by Markus Hanke View Post
    Like I said, this is a matter of probabilities; there is always a non-zero probability of a photon going off at a very steep angle from the slit.
    Not if the experiment is done like I described above.
    Why hasn't this experiment been done already?
    K
    Quote Originally Posted by Markus Hanke View Post
    Because it doesn't matter if every single photon hits the screen, or not - you will get an interference pattern either way, even if some photons don't make it to the screen ( for whatever reason ).
    My concern is not that they may not make it. I'm wondering if their making it and for some reason not being detected at certain locations.My point is that this experiment has not been performed and I think it could yield answers different than what is being speculated. You know me I'm all for speculating but why do it when there is an experiment than could be performed?
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    Quote Originally Posted by bill alsept View Post
    That's just evading because the experiment most definetly could be set up so that every photon could be accounted for.
    I'm not evading, and of course it can be set up so that every photon is accounted for; that doesn't mean though that every photon that goes through the slit ends up on the detector screen, which is all I was trying to say. So yes, 100% accountability is of course possible if you completely enclose the setup.

    Not if the experiment is done like I described above.
    Again, a photon can always go off at an angle, in which case it ends up on the enclosing sphere as opposed to the detector screen. In any case, it can be accounted for.

    My point is that this experiment has not been performed and I think it could yield answers different than what is being speculated.
    I very much doubt that. But in any case, this is a very straightforward experiment - all you need is a coherent light source of some kind, and two screens, one of which has a slit of the appropriate size. You can then rig up some form of enclosure, and coat it with photographic film or something on the inside.

    This should be a fun project for a couple of rainy Sunday afternoons
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    Forum Senior bill alsept's Avatar
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by bill alsept View Post
    That's just evading because the experiment most definetly could be set up so that every photon could be accounted for.
    I'm not evading, and of course it can be set up so that every photon is accounted for; that doesn't mean though that every photon that goes through the slit ends up on the detector screen, which is all I was trying to say. So yes, 100% accountability is of course possible if you completely enclose the setup.
    Not if the experiment is done like I described above.
    Again, a photon can always go off at an angle, in which case it ends up on the enclosing sphere as opposed to the detector screen. In any case, it can be accounted for.
    My point is that this experiment has not been performed and I think it could yield answers different than what is being speculated.
    I very much doubt that. But in any case, this is a very straightforward experiment - all you need is a coherent light source of some kind, and two screens, one of which has a slit of the appropriate size. You can then rig up some form of enclosure, and coat it with photographic film or something on the inside. This should be a fun project for a couple of rainy Sunday afternoons
    Now that we agree that the experiment can be performed with 100% accountability of all the photons then lets move on. I don't care about photons that hit the first wall or sphere and I don't care about the photons that go far outside the range of the normal interference pattern. I only care that their accounted for so that we will know the number of photons that actually do make up the interference pattern on the back wall. As for actually doing the experiment I agree it should be easy to perform but not by me. I don't have the right equipment to properly detect or produce single photons. Are you sure this research has not been performed somewhere?
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    Quote Originally Posted by bill alsept View Post
    I only care that their accounted for so that we will know the number of photons that actually do make up the interference pattern on the back wall.
    But no one ever doubted that in the first place...after all, photons don't just disappear in transit, for reasons of energy and momentum conservation. They can always be accounted for.

    As for actually doing the experiment I agree it should be easy to perform but not by me. I don't have the right equipment to properly detect or produce single photons.
    Why do you need to produce single photons ? The actual number of photons is irrelevant so far as the interference pattern is concerned.

    Are you sure this research has not been performed somewhere?
    Since everyone agrees that all photons can always be accounted for, no one will go through the trouble of enclosing the setup in a spherical shield. So no, I doubt very much that this has been done, simply because it isn't necessary - the interference pattern is the same with or without shield.
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  15. #14  
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    Quote Originally Posted by bill alsept View Post
    My concern is not that they may not make it. I'm wondering if their making it and for some reason not being detected at certain locations.My point is that this experiment has not been performed and I think it could yield answers different than what is being speculated. You know me I'm all for speculating but why do it when there is an experiment than could be performed?
    I'm not sure why you are concerned about photons that don't reach the detector; it is only those that do that form the interference pattern. Why would the others be relevant?

    You can see an explanation of how the pattern is built up here:
    Two-Slit Experiments
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    Forum Senior bill alsept's Avatar
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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by bill alsept View Post
    My concern is not that they may not make it. I'm wondering if their making it and for some reason not being detected at certain locations.My point is that this experiment has not been performed and I think it could yield answers different than what is being speculated. You know me I'm all for speculating but why do it when there is an experiment than could be performed?
    I'm not sure why you are concerned about photons that don't reach the detector; it is only those that do that form the interference pattern. Why would the others be relevant?You can see an explanation of how the pattern is built up here:Two-Slit Experiments
    It's just a matter of subtraction. If a finite number of photons are releases from the source and every photon that DOES NOT make it to The the interference pattern is accounted for somewhere else then we would know the number of photons that DO make up the interference pattern or approximately. Knowing this would be important if for some reason the individual and different frequencies of each single photon play a part in how it interacts with the wall where the pattern is being formed. For example it would be interesting if we knew that about 3000 photons where not accounted for anywhere else and must be part of the pattern some how. As the pattern forms and the locations of the individual photons are recorded it would be interesting to know how many individual photon hits make up the patten. If for instance only 1500 photon hits are accounted for in the pattern then where are the others. What I was speculating is that maybe those other photons do hit the pattern but because of their frequency they can only be detected when their amplitude or some other phase of their cycle is just right to interact with the atoms on the wall. So eventually dark areas would form where the angle of deflection from the slit to the wall creates a distance where the most photons are out of phase. You guys are always saying that an idea needs to be testable, well here you go. It's out of my capabilities but I,m surprised it hasn't been done already. Do you think its right to speculate that the experiment would be a waste of time because we already know everything in the world about photons and the interference pattern? It's to easy of an experiment to have never been performed it seems hard to believe.
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    Quote Originally Posted by bill alsept View Post
    Do you think its right to speculate that the experiment would be a waste of time because we already know everything in the world about photons and the interference pattern? It's to easy of an experiment to have never been performed it seems hard to believe.
    It is impossible to say it would be a waste of time because occasionally new information does come from unexpected sources. I still don't really see how "unaccounted for" photons could be relevant. IF they make it through the slits then then they will (almost certainly) strike somewhere on the screen and form the pattern.

    Knowing this would be important if for some reason the individual and different frequencies of each single photon play a part in how it interacts with the wall where the pattern is being formed. ... What I was speculating is that maybe those other photons do hit the pattern but because of their frequency they can only be detected when their amplitude or some other phase of their cycle is just right to interact with the atoms on the wall.
    As far as I know (I may be wrong) the single photons sources used are like lasers in that they generate photons of a single frequency.
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    Forum Senior bill alsept's Avatar
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    [jQUOTE=Strange;491927] I still don't really see how "unaccounted for" photons could be relevant. IF they make it through the slits then then they will (almost certainly) strike somewhere on the screen and form the pattern. [/QUOTE]

    Yes and it would be interesting know if that pattern were made of 1500 photons that were detected and 1500 that were not.

    Quote Originally Posted by Strange View Post
    As far as I know (I may be wrong) the single photons sources used are like lasers in that they generate photons of a single frequency.
    Thats good and would make the experiment even easier to keep track of.
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    I have a question about diffraction fringe patterns. On a single edge diffraction pattern the spacing appears to to get smaller and smaller the farther it gets away from the edge. This is different than the evenly spaced fringes of slit or multiple slit patterns. Is there a specific name for this dimenishing spaced fringe pattern? Is there a formula to calculate this type of pattern?
    Thanks
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    Quote Originally Posted by bill alsept View Post
    I have a question about diffraction fringe patterns. On a single edge diffraction pattern the spacing appears to to get smaller and smaller the farther it gets away from the edge. This is different than the evenly spaced fringes of slit or multiple slit patterns. Is there a specific name for this dimenishing spaced fringe pattern? Is there a formula to calculate this type of pattern?
    Thanks
    I don't know if there is a name for the specific pattern, but the phenomenon itself is called the Knife-Edge Effect. Have a look here for some introductory remarks :

    Knife-edge effect - Wikipedia, the free encyclopedia
    Diffraction
    Huygens' Principle

    This is somewhat outside my usual area of expertise, but my first guess here would have been to apply Huygen's principle and see if that explains this phenomenon - and apparently it does, as mentioned in the links above.
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    Quote Originally Posted by bill alsept View Post
    I have a question about diffraction fringe patterns. On a single edge diffraction pattern the spacing appears to to get smaller and smaller the farther it gets away from the edge. This is different than the evenly spaced fringes of slit or multiple slit patterns. Is there a specific name for this dimenishing spaced fringe pattern? Is there a formula to calculate this type of pattern?
    Thanks
    There's a nice presentation in Born and Wolf, Principles of Optics. If you don't happen to have it on your shelf, you may find the following paper of some use: http://www.propagation.gatech.edu/Ar...080708_GDD.pdf.

    ETA: Archive.org has an older edition of Born and Wolf. AFAIK, Archive.org strives to respect copyright laws, so I will assume for now that this older edition's copyright has lapsed somehow.
    Last edited by tk421; January 27th, 2014 at 03:59 AM.
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    Thanks guys, I have read both articles before as well as many others on the subject lately. I am still confused but really interested in this phenomena. There are so many papers, lectures and videos on the subject and most of them mix match the two types of patterns as if they were the same. Even these two article are more about diffraction and not so much about the diffraction pattern. I could try to fake my way through a bunch of detailed gibberish just to set up my questions but maybe it would be easier to set up an example.
    For a single SLIT its easy to calculate the spacing (y) of the dark fringes in the pattern. Not only is the formula (n times wavelength times distance to screen divided by width of slit) easy but it also calculates the distance between the other minimums (n2, n3, n4 etc) because their all equal. With a single EDGE diffraction patternthe spacing's are not all equal but continuously gets smaller and smaller the farther they get from the shadow boundary.
    Say we have a light source with a 500 nm wavelength shinning through a single slit thats 500,000 nm wide onto a screen that's 500,000,000 nm away. The simple formula would tell us that the first minimum fringe from the center of the slit would be 500,000 nm away and every other dark fringe would also be spaced at 500,000 nm's.
    Now instead of a single slit we have a single edge with the same light source and the distance from edge to screen was still 500,000,000 nm's away what would the distance to the first dark fringe be and then to the next and the next and so on? If someone could help calculate at least the first ten I would really appreciate it. Thanks
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    Forum Senior bill alsept's Avatar
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    Like I was saying its easy to calculate the equal spacing's of a diffraction pattern from a single slit or multiple slit (see below).

    SLIT DIFFRACTION PATTERN



    What I am trying to figure out is how to calculate the not so equal spacing's of the single edge or "Knife Edge" diffraction pattern (see below). Slit and edge patterns are completely different and calculating the edge diffraction pattern is much more complicated than for a slit. It seems to me there should be an easier way to accomplish this. Does anyone know of an app that would give me the distances in nm for the dark fringes starting at the edge. Like I described in post#21 above if I had 500 nm wavelength light source directed onto a knife edge and then 500,000,000 nm beyond onto a screen. What would the first ten or more dark fringe spacing's be? Is this question more for the math section?
    Thanks



    KNIFE EDGE DIFFRACTION PATTERNS
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  24. #23  
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    This is almost certainly not the right equation but it is an interestingly simple equation that gets really close.
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    Quote Originally Posted by bill alsept View Post
    What I am trying to figure out is how to calculate the not so equal spacing's of the single edge or "Knife Edge" diffraction pattern
    Have a look here : http://www.propagation.gatech.edu/Ar..._JA_090601.pdf
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    Quote Originally Posted by MagiMaster View Post
    This is almost certainly not the right equation but it is an interestingly simple equation that gets really close.
    Thanks, that does look similar to the type of pattern I'm looking for. I'll check it out
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    Quote Originally Posted by bill alsept View Post
    Quote Originally Posted by MagiMaster View Post
    This is almost certainly not the right equation but it is an interestingly simple equation that gets really close.
    Thanks, that does look similar to the type of pattern I'm looking for. I'll check it out
    If you want a more rigorous treatment, with the actual equations, see the Born and Wolf text that I referenced. Start around page 430 and read for about a half-dozen pages.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by bill alsept View Post
    What I am trying to figure out is how to calculate the not so equal spacing's of the single edge or "Knife Edge" diffraction pattern
    Have a look here : http://www.propagation.gatech.edu/Ar..._JA_090601.pdf

    I have read this paper many times trying to figure it out. The second page that is labeled 25 looks like its describing the Knife Edge Diffraction Formula and equations 4 and 5 may be what I'm looking for. I cannot tell if the equations are describing the actual geometry of the dark and light fringe pattern. If it is I can't figure it out. Can anyone?

    If I know the wavelength of the light (500 nm) and the distance from edge to screen (500,000,000 nm)How do I calculate the distances and spacing's of the dark fringes? Please help
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    Quote Originally Posted by tk421 View Post
    Quote Originally Posted by bill alsept View Post
    Quote Originally Posted by MagiMaster View Post
    This is almost certainly not the right equation but it is an interestingly simple equation that gets really close.
    Thanks, that does look similar to the type of pattern I'm looking for. I'll check it out
    If you want a more rigorous treatment, with the actual equations, see the Born and Wolf text that I referenced. Start around page 430 and read for about a half-dozen pages.
    Yes page 434 is exactly what I'm looking for but still to complicated. I will need to study it a bit before I try to input the 500 nm wavelength and 500,000,000 nm distance I set up in the other posts. I wish there was a calculator for this.
    Thanks
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    Guys, I'm not trying to be lazy here. I really can't figure the equation out YET. I had a train of thought going and needed to compare it to the actual predictions of the edge diffraction pattern. All I ever see are images like these without details of the fringe spacing's:

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    Quote Originally Posted by tk421 View Post
    Quote Originally Posted by bill alsept View Post
    Quote Originally Posted by MagiMaster View Post
    This is almost certainly not the right equation but it is an interestingly simple equation that gets really close.
    Thanks, that does look similar to the type of pattern I'm looking for. I'll check it out
    If you want a more rigorous treatment, with the actual equations, see the Born and Wolf text that I referenced. Start around page 430 and read for about a half-dozen pages.
    Yep, that equation isn't even close, or at least doesn't seem to be.
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    Quote Originally Posted by bill alsept View Post
    Guys, I'm not trying to be lazy here. I really can't figure the equation out YET. I had a train of thought going and needed to compare it to the actual predictions of the edge diffraction pattern. All I ever see are images like these without details of the fringe spacing's:

    Well, yes, you're going to have to get up to speed on the relevant maths if you want to do the calculation. As you can see from Born and Wolf, one prerequisite is the ability to evaluate Fresnel integrals. There's no closed-form, simple equation to do so, but there are simple algorithms. There are also online calculators of Fresnel integrators that will take care of the heavy lifting of those intermediate calculations. It's also straightforward to get Matlab to spit out the answers. There's a free Matlab-compatible package called Octave that I would enthusiastically recommend.

    That said, as I understand your goal, you seem to be interested mainly in what the pattern looks like in the very, very far field (e.g, a million wavelengths away). Look at the pictures above -- you should note two general trends. One is the convergence to an asymptote. The other is a decrease in the spacing between successive fringes. By the time you get to a million wavelengths away, you will be so absurdly close to the asymptote that calculating it will require a ludicrous number of significant digits, and you will similarly find that the spacing will have reduced to zero for all practical purposes. So, if I understand you correctly, there's really no need to bother learning about the mathematical details. However, if you want to understand the near- or intermediate-field behavior, then yes, you'll need to come up to speed on a bit of maths.

    ETA: I went back and reread some of your earlier posts. I see that you are most interested in the first dozen or so fringes, not ones a factor of a million out. In that case, you will have to evaluate the Fresnel integrals on the way to getting your final answer. Not hard, but a bit tedious.

    Also, I came across an online Fresnel integral evaluator, so there's always that option to help reduce the tedium a little bit.
    Last edited by tk421; January 28th, 2014 at 08:30 PM.
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  33. #32  
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    Quote Originally Posted by tk421 View Post
    Quote Originally Posted by bill alsept View Post
    Guys, I'm not trying to be lazy here. I really can't figure the equation out YET. I had a train of thought going and needed to compare it to the actual predictions of the edge diffraction pattern. All I ever see are images like these without details of the fringe spacing's:

    Well, yes, you're going to have to get up to speed on the relevant maths if you want to do the calculation. As you can see from Born and Wolf, one prerequisite is the ability to evaluate Fresnel integrals. There's no closed-form, simple equation to do so, but there are simple algorithms. There are also online calculators of Fresnel integrators that will take care of the heavy lifting of those intermediate calculations. It's also straightforward to get Matlab to spit out the answers. There's a free Matlab-compatible package called Octave that I would enthusiastically recommend.

    That said, as I understand your goal, you seem to be interested mainly in what the pattern looks like in the very, very far field (e.g, a million wavelengths away). Look at the pictures above -- you should note two general trends. One is the convergence to an asymptote. The other is a decrease in the spacing between successive fringes. By the time you get to a million wavelengths away, you will be so absurdly close to the asymptote that calculating it will require a ludicrous number of significant digits, and you will similarly find that the spacing will have reduced to zero for all practical purposes. So, if I understand you correctly, there's really no need to bother learning about the mathematical details. However, if you want to understand the near- or intermediate-field behavior, then yes, you'll need to come up to speed on a bit of maths.

    ETA: I went back and reread some of your earlier posts. I see that you are most interested in the first dozen or so fringes, not ones a factor of a million out. In that case, you will have to evaluate the Fresnel integrals on the way to getting your final answer. Not hard, but a bit tedious.

    Also, I came across an online Fresnel integral evaluator, so there's always that option to help reduce the tedium a little bit.
    Thanks tk421, I have been doing a lot of reading on this subject lately and do not mind learning the relevant math's. My first problem is establishing which equation is the correct one to calculate this pattern. I have read that section of "Born and Wolf" three times now and can't quite identify it. Could you or anyone reading this post please tell me or copy and paste the actual equation or equations that solves this (knife edge, straight edge or single edge) diffraction pattern.
    I am interested in more than the first ten fringes I only said that in hopes that I could get someone to help me on the first 10 spacing's

    Today I found this article very interesting. Diffraction effects during a lunar occultation

    Thanks again
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    Quote Originally Posted by bill alsept View Post
    Thanks tk421, I have been doing a lot of reading on this subject lately and do not mind learning the relevant math's. My first problem is establishing which equation is the correct one to calculate this pattern. I have read that section of "Born and Wolf" three times now and can't quite identify it. Could you or anyone reading this post please tell me or copy and paste the actual equation or equations that solves this (knife edge, straight edge or single edge) diffraction pattern....
    Thanks again
    Unfortunately, the "actual equation" refers to a sequence of equations, each of which refers to another...so there's a fair amount of work involved. Here's an outline of what you need to do (all equation and page numbers are from the Born and Wolf textbook cited earlier):

    1) "The" equation ultimately to be evaluated is Eqn. 28 on pg. 434. That's what you will use to generate the plot shown in Fig. 8.39, from which you can deduce the spacing between fringe nulls or peaks, or unit-crossings, or whatever feature you wish to track.

    2) Eqn. 28 in turn relies on two functions b(w) and L(w) (where b and L are written in script in the text), which are given by Eqn. 15 on pg. 431.

    3) Eqn. 15 in turn relies on P(w) and Q(w), which are given by Eqn. 16.

    So, for each value of the coordinate w, you first evaluate Eqn. 16 to find P(w) and Q(w). Then you plug those into Eqn. 15 to find b(w) and L(w). Then you plug those into Eqn. 28 to find the normalized intensity I/I^(0). Use the normalizing value I^(0) as found from Eqn. 29 if you want to denormalize the answer.

    I hope that helps.

    Enjoy calculating away!
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    I found a much easier and faster way to calculate the single edge fringe patterns and invented a simulator to show the results. The subject interests me so much I wrote a paper to explain https://www.dropbox.com/s/lu5irtlxxe...inty.docx?dl=0 I call it "Single Edge Certainty"

    My equation can calculate the fringe pattern spacings as far out as you want to go (infinitely and acurately) and does not involve the massive and complicated equations you will find everywhere else. Please proof read and let me know what you think.
    Thanks
    Last edited by bill alsept; September 3rd, 2014 at 08:09 PM.
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