| Author | Message | ||
     Eric LALOUM |
Dear all, I have seen that there is a new process NIR FT spectrometer in a post-dispersive configuration (Bruker Matrix). This system comprises a remote module with four lamps illuminating the sample and one collecting fiber sending diffused light back to the interferometer and detection. I'm quite dubious with this configuration because as far as I remember, to work properly, the interferometer needs as an input light that is in time coherence so that "beam-splitted" rays can interefer. It also the reason why interferometer need an aperture stop to limit angular dispersion and assure coherence in time. With this post-dispersive configuration, it seems to me that all the different photons that will be collected will all have different pathway inside material (a powder) and that it will be harder to get interference from them. Since the system is marketed it should work, so I might have missed something... The only thing that could maybe explain this "paradox" is that with four intense lamp (20 W), the number of photons is multiplied and so the probability to have many photons that go the same pathway in material. Any comments ? Eric LALOUM | ||
| Tony Davies (Td) |
Dear Eric, I can remember being very dubious when I first heard that people were using FT systems for measuring diffuse radiation. However, I think the explanation is that at the instant the radiation is split into two beams each beam will be more-or-less equivalent so that the path difference applied to one of them is "seen" as the major difference and interference is produced. One thing that I have never been able to get any figure for is the number of photons in a typical measurement. If this was small then you would expect the beams to be significantly different before any path difference had been applied [I assume that we can ignore quantum effects so that any single photon can only be present in one of the split beams]but they wouldn't give rise to interference if they were recombined without any path difference because they would not be coherent. This seems like a circular argument(!!) so I guess that we are normally measuring a large number of photons. Perhaps someone has a figure? I have heard very good reports of the Matrix system. Best wishes, Tony | ||
| Dr. Heinrich Pr�fer (H_Pruefer) |
Dear Eric and Tony, Please accept my interference. When you speak about photons and interference both at the same time it is impossible to ignore quantum effects, because you are talking wave-particle dualism. And there we have to consider the strange behaviour that even a single photon can "interfere" in the sense that the probability to find it at a certain place is distributed according to the interference pattern. When more single photons are added, the interference pattern becomes more and more complete. At the end of the single photon experiment the result is the same as if all photons would be transmitted at once. (I have no idea how they can manage this in detail, but there is experimental evidence...) So I also can not provide a figure, but I don´t think you need it for explanation. Best regards, Heinrich | ||
| Tony Davies (Td) |
Heinrich, Many thanks for your correction. I guess photon behaviour is not common sense! Best wishes, Tony | ||
| hlmark |
Heinrich, Tony - You've got to remember that photons behave exactly the way they're supposed to: they behave like photons! The descriptions of them in terms of "waves" or "particles" are conventions that we mere humans have to impose on them in order for our limited understanding to be able to make sense of the physical reality that photons impose on us. That being said, thinking of them in terms of "waves" is the only way we can reasonably describe interference phenomena (and certain other behaviors), and thinking of them as "particles" is the only way we can reasonably describe their behavior in certain other circumstances, despite the fact that in both cases the photons are simply exhibiting "photonny" behavior. So in describing the way an interferometer works, for example, it makes no sense to try to figure the behavior out in terms of particle behavior despite the fact that, as Heinrich said, the macroscopic effects of the particle aspect describe the probabilistic behavior of the photon's particle aspect that gives rise to the oberved intensities of different part of the interference pattern. But if you want to calculate interference patterns, the only sensible approach is to do it in terms of the wave aspect. To do it the other way is not impossible, but it might as well be, for practical purposes. Regarding Tony's question about the number of photons involved in a measurement, I don't know the answer either, but it can be estimated relatively straightforwardly. First let me make a couple of comments: In terms of the practical value of knowing that, the only application I can see is in determining the contribution of the photons to the noise level of a measurement. We know from other branches of spectroscopy (X-ray, for example) that photon statistics follow a Poisson distribution, and also that the standard deviation of a Poisson distribution equals the square root of the mean value of the number of photons. In X-ray and UV-Vis spectroscopy, for example, we know that the Poisson distribution causes the S/N ratio to vary also with the square root of the number of photons. My off-the-cuff estimate of the number of photons involved in standard NIR is that it is somewhere between 10^15 and 10^20 per second (instructions for more precise figures follow). Therefore the S/N is somewhere between 10^7 and 10^10 and the contribution to total noise correspondingly small. I think we can ignore that source of noise in our measurements, at least until the signal gets weak enough for this effect to become appreciable, as it is in UV-Vis spectroscopy with photon counting, for example. Now for the method of estimating the number of photons: it can be done on the basis of simple energy considerations. From the laws of blackbody radiation we know how much energy will be emitted in any given area from a blackbody raidator, withing a specified wavelength range. We know from quantum mechanics the energy of a photon: h*nu. Divide one by the other and you've got your estimate. When you've figure it out, let us know, I think we're all curious about that by now. Howard \o/ /_\ | ||
| hlmark |
Eric - the operation of an interfereometer does not depend on the light being coherent except within the interferometer itself. If it were otherwise, we would need to use lasers as the source. Therefore the use of a non-coherent sample introduces no problems except those that instruments based on all technologies are subject to, e.g., being able to collect enough energy to measure. There are no unique aspects to it. Howard \o/ /_\ | ||
| Eric |
Dear Howard, Thank you for your comment but I'm not sure being totally satisfied with it. Of course you can bring whatever light you want inside an interferometer, you will always get some output. And it is the system by itself (i.e. the beamsplitter) that generate two rays prone to interfere with each other after mechanically varying phase shift between them. But once again, if we stick with photons, (the reasoning would be the same with waves), the beamsplitter separate incoming photons. And at the minimum, I would expect to have at least 2 photons in coherence in order to have them interfering. So for post dispersive configuration, my guess is that you add variability in phase coherence between photons, and that at the end the performance should decrease... Regarding coherence, I'm sorry to say that my definition would be as "circular" as Tony's one ! "Coherence is a property of waves that measures the ability of the waves to interfere with each other" Two waves that are coherent can be combined to produce an interferogram. Waves that are incoherent, when combined, produce rapidly moving areas of constructive and destructive interference and therefore do not produce a visible interference pattern. Laser waves are of course always coherent, but waves do not have to be monochromatic in order to be coherent with each other. Two non-monochromatic waves are fully coherent with each other if they both have exactly the same range of wavelengths and the same phase difference at each constituent wavelength. For waves to be coherent with each other, they generally must either both come from, or be phase-locked to, the same source (e.g. the sunlight passing through the two slits of Young's double-slit experiment), or be monochromatic with precisely the same frequency. For instance, I'm not in trouble with post dispersive FT spectrometer analyzing light from stars because, since the distance is very long, phase shift can be negligted. | ||
| hlmark |
Eric - I'm afraid that you've fallen into one of the traps that await when you start to think about these things in the wrong way. That's why it's much safer to stick with one picture at a time, and to not try to use the wrong aspect to try to explain a phenomenon that should be described by the other aspect. For example, when you said: " ... And at the minimum, I would expect to have at least 2 photons in coherence in order to have them interfering.", I'm afraid that statement is incorrect, and you misunderstand the nature of the interference process. If you insist on using the photon description of the light, then what you have to say happens in an interferometer is that each photon interferes with itself. Your natural question to this answer is "How can that happen? What does it mean to say for a photon to interfere with itself?" And the answer to THAT question is: nobody knows. Truly comprehending the nature of photons, that allows it to do these sorts of things is beyond our current state of comprehension. In our ordinary macroscopic existence we are not used to dealing with things that behave in such ways. But the fact remains that the only explanation that is consistent with all the experimental evidence concerning the behavior of light and photons involves those sorts of counterintuitive phenomena. That's why quantum mechanics causes us such problems when we try to understand what's "really" happening: most of them fly in the face of our ordinary experience. But then you don't need two photons, and it becomes easier to understand why incoherent light can be used at all with an interferometer, and also why it doesn't have to be coherent outside the interferomter. And I structured my statement the way I did ("a question to the answer"): as an analogy to the fact that in the microscopic world where Q.M. applies, things are very much topsy-turvy compared to the macroscopic world of our ordinary experience. That's why we have such a hard time understanding it. So in these terms, an interferometer operates by having each photon be split at the beamsplitter; that makes the two parts of each photon be coherent with the other part, and then they can recombine at the beamsplitter with phase properties intact. What are the parts of the photon during this process? Here again, we don't know. The wave/particle duality is a very tenuous thing. All experiments performed that involve it show that you cannot make a photon exibit both aspects simultaneously. Heinrich mentioned the single-photon experiments that were performed about a century ago, now. You should read up on them. The results are unbelievable, and nobody would believe them if they hadn't been repeated and repeated over and over again, with all conceivable variations, and care to avoid errors. In a nutshell, if you shine light through an interferometer, you'll get an interference pattern, no matter how weak the light is, and even if it becomes so weak that only one photon at a time is going through the interferometer. In this case the wave properties of the photon are being measured. If you now do something to the interferometer to measure the particle properties, such as put in some sort of a photon detector, you will indeed measure the particle properties. You can put the particle detector in either beam, or in both beams, and you will detect a photon in one beam or the other, but never both simultaneously - just as you would expect for a single particle. Under these conditions, however, you will not obtain an interference pattern. This summary will raise numerous questions in your mind, of course ("What happens to the energy of the photon while it's split?" for example), but those questions were also raised in the minds of the physicists doing the work and were adressed. No matter how clever the scheme used to try to measure wave and particle properties simultaneously, it was never achieved. That's one consequence of Heisenberg's uncertainty principle: that wave properties and particle properties can never be observed simultaneously. It's almost as though the photons "knew" how they were supposed to behave in a given experiment, and would never break the rules. If you really want to understand these phenomena, you really have to read up on those old experiments, they are classics. And the results will amaze you. Remember that Quantum mechanics wasn't invented just because physicists wanted a more complicated way to describe the universe, it was created because it was necessary to have something that would give a description, however abstruse, that could describe these otherwise unbelieveable results. Howard \o/ /_\ | ||
| Eric |
Howard, I could not imaging that we would have to tackle such "magic" things when asking the question ! I'm totally aware of all the paradoxes associated with quantum world, like the EPR one where two photons going opposite emerging from one single event do some kind of "telepathy" !!! My request was more practical, I've well understood from your clear explanations that even if light flux is very low, FT will still work properly, even if input beam has lost some coherence (because of divergence for instance). Maybe we could then just conclude that quantitatively, for NIR diffuse reflectance, "post-sample" FT might be less efficient than "pre-sample" FT ? One good thing would be to do the experiment, for instance with 2 Bruker Matrix, in the 2 configurations, on the same sample. Has anyone the possibility to test for this ? I would be ready to bet that (all other parameters being controlled, and esp. stray light issue) it's better to put the interferometer before the sample. Besides, I would also expect the resolution limit of "post-sample" configuration larger than for "pre-sample" because the aperture stop would necesseraly be greater in order to collect more diffused light. Here is an extract regarding aperture stop (Jacquinot stop) and resolution from the site : http://www.ijvs.com/volume5/edition5/section1.html "As resolution is improved and hence the mirror travel increases it becomes essential to restrict the beams that lie off the optical axis of the interferometer. To achieve this, the size of the Jacquinot Stop is reduced as the resolution is improved. Typical values are ~8mm diameter at 4cm-1 resolution and perhaps 3mm at 1cm-1 or less. The effect is that less energy passes through the interferometer when operated at high resolution than at low". Thank you again for your comments. Eric | ||
| djdahm |
A couple of points. Howard�s statement above: �That's one consequence of Heisenberg's uncertainty principle: that wave properties and particle properties can never be observed simultaneously.� That is usually referred to as Bohr�s Principle of Complementarity. There is a bit of controversy , which happens to be centered at my university (Rowan) at the moment, on whether or not Bohr�s principle has been violated by recent experiments {See: http://users.rowan.edu/~afshar/ }. But I am sure that Howard�s statement that it is a consequence of the uncertainty principle would be vigorously challenged if he made it at one of our lunch table discussions. I use mathematics based on geometric optics in my work all the time. However, they hold only at certain limits: particles large compared to the wavelength, etc. I use them because they are easier for me to understand than wave equations. Similarly, we use the concept of photons because it makes it easier to understand certain things (like the photoelectric effect). However, the concept of photons as reality is overemphasized in my opinion. Most of the properties of light are far better understood if we assume they act as waves. Light acts as waves that apparently don�t need a medium, and which exhibit quantized energies when they interact with matter, but that doesn�t mean that light is corpuscular. When we create a model (like the concept of a photon), we frequently start believing that we have described reality, when we have actually abstracted it. But that shouldn�t keep us from struggling to understand the answer to important questions. And an important question has been put on the table. Would we expect that there will be the important differences in interpreting the results from a post-dispersive configuration? It�s not unlike asking what the important differences in interpreting the results from a remission experiment (as opposed to transmission). Heaven knows that one kept folks busy arguing for years. | ||
| Tony Davies (Td) |
Don, I never expected that this discussion group would get involved with high level physics!! You would be very disappointed with me if you ever came to one of our training courses at Chambersburg. I explain diffuse reflection (for novices) in terms of photons!! It is a photon of a particluar energy that gets absorbed, so I think it is much easier for people to think of a stream of photons passing into the sample and just a few of them being absorbed. There is always some bright spark who asks "How many?" and I have to admit I do not know, hence my question. It would be nice to have an answer ready next time. Best wishes, Tony | ||
| hlmark |
Well, I was out all morning for personal reasons, and just got back to find the messages from Eric, Don and Tony, all of which cued some comments in my head: Eric - Note in your extract that the need for the aperture stop is only to maintain the resolution of the interferometer. This is done by limiting the degree of non-collimation (an effect purely of geometric optics) of the light passing through the interferometer. You could, in fact, keep the aperture stopped down for low resolution measurements as well as high, but that would degrade the S/N below the potential S/N achievable. On the other hand, opening the stop and trying to measure high-resolution spectra would be futile. This is because rays at wider angles would be able to pass through the interferometer. What happens is that for a ray going through the interferometer at an angle, the retardation of that ray equals D / cos (theta), where D is the retardation of a collimated ray, and theta is the angle to the direction of collimation. At some point, this quantity equals or exeeds a half-wavelength of the light, and then the angular ray is 180 degrees out of phase with the straight-through ray, and the two cancel. At that wavelength (and shorter ones, too, of course) you will not get any interference with the ray going through the other arm of the interferometer. Peter Griffiths describes this, and all other aspects of interferometer operation in his book. The key point here is that that has nothing to do with the sample, nor the relation of the sample to the interferometer. There is an advantage in having the sample after the interferometer, if you're doing diffuse reflection or diffuse transmission, in that it is usually easier to collect the light from the source and collimate to pass through the interferometer than it is to collect the light that was diffusely reflected from a sample, and still get as much energy. For that reason having the interferometer pre-sample is usually better. For clear transmission or specular reflection, there is essentially no difference. In practice you're usually limited to how your instrument is set up; most people do not have the capabilites to make such major modifications to their instrument. Don - yeah, it's been a long time since I've looked at some of this stuff, so I guess I got my terminology mixed up. If you look at my first posting to this thread, I started out: "You've got to remember that photons behave exactly the way they're supposed to: they behave like photons! The descriptions of them in terms of "waves" or "particles" are conventions that we mere humans have to impose on them in order for our limited understanding to be able to make sense of the physical reality that photons impose on us.", which I think is pretty much the same thing you said in your last paragraph. So I'd say we're in agreement, for a change. I'd also say that on account of that, keep your eyes open: the Messiah must be right around the corner!! Tony - I see no problem with your explanation in terms of the particulate nature of photons. As both Don and I said (in our own ways) the whole concept of wave/particle duality is mainly a convention that we use to simplify the behavior of the photons to the point where we can think we understand it. The photons themselves have no difficulties whatosever. So if better understanding is gained through use of the particulate aspect, so much the better. \o/ /_\ | ||
| djdahm |
Howard: You don�t need to back off too far on terminology. Heisenberg, both personally and through the Uncertainty Principle, was very much in the loop. And thanks for the discussion just above. Tony: Not to worry. None of us needs to apologize for using abstractions as a road to understanding. The problem comes if we forget the limitations of our tools. I think the basic laws and theories of absorption are best explained by �photons�. For example, the Bouguer-Lambert Law is relatively easy to understand as the fraction of the incident photons that are absorbed by some small thickness of material, just like you described. It�s the scatter part that has led to much of the insanity we have had to suffer through. Refraction and reflection by a planar surface works well when explained by geometric optics (read �rays� or �photons�), but after that we get lost in a hurry. The Mie Theory uses wave equations, but it is rather complex and applies only to spheres. The problem with wave equations is that you have to be able to describe the sample in mathematical terms (kind of like describing a three-dimensional wave field). Thorsten Burger�s model uses wave equations, but they can�t work with a complex sample except by averaging its properties on a scale small compared to the wavelength of the light. (Then too, I think they made some fallacious claims about the relationship of their coefficients to those in the Mie theory, but that�s a different argument.) My approach is based on geometric optics and can treat rather complex samples. However, it is a one way theory. We can deduce what the observed intensity should be if we have a well characterized sample, but we can�t go the other way. Ten years ago, I started work on a general wave based theory of diffuse reflectance. I�m going to describe it at EAS this fall, but I�ve not made much progress on it. | ||
| hlmark |
No problem, Don. I am curious to know if Tony is making any progress on estimating the number of photons involved. Have any progress reports yet, Tony? \o/ /_\ | ||
| Chen |
Eric - Your analyze is really sensible but keep in mind that the illuminated surface of the Bruker Matrix-E system (non contact FT-NIR "post dispersive" instrument) is higher than for diffuse reflectance probe laboratory instrument and the distance to sample is also higher: this can also explain the 80W source... Anyway, I agree with your argument regarding the performances of the system according to the position of the interferometer before of after the sample compartment. Regards, Chen |