Hanbury Brown and Twiss effect question

[LmdL]

Hello,
I'm a student which needs to setup a HBT experiment in the lab and I have some questions. I already read this thread:
https://www.physicsforums.com/showthread.php?t=757064
and it was very useful, so I'm asking for help from Cthugha or anyone who knows.

My experimental setup is as following:

Light from the the blue LED after passing through a 0.2[mm] pinhole, travels ~1.25[m] and is divided into 2 beams, each hits either the PMT #1 or PMT #2. Two signals from the detectors are being saved in a frequency of 1.25[GHz]. I perform a cross-correlation of the two signals in MATLAB.

Problem: I did several runs - recorded the signals for 10 minutes, 40 minutes, 3 hours, 6 hours. In any of the runs the cross-correlation didn't show the peak (which corresponds to the photons correlation).
After failing again and again I decided to check again my equipment for any misfitting to the theoretical basis of the experiment.

Questions:
1. Light source.
As I know, Brown and Twiss, in their original experiment used a mercury arc lamp, which is a thermal radiation source. I'm not sure if blue LED is a thermal radiation source or a single-photon.

2. Pinhole.
I have different pinhole sizes, from 1um to 200um, but according to the theory - the more light PMTs receive, the higher the correlation, so I used the largest pinhole I have. The question is - do I have to use the lens before pinhole, in order to focus the light into it?

3. Maybe it's just a matter of time and I need far more than 6 hours of signals data?

Thanks in advance.

 

[Cthugha]

Let me see what we can find out.

1. Light source.
As I know, Brown and Twiss, in their original experiment used a mercury arc lamp, which is a thermal radiation source. I'm not sure if blue LED is a thermal radiation source or a single-photon.

I do not think it will be a single photon source, but is it really a LED (thermal light) or is it a blue laser diode? A laser diode should not show the correlation peak. Only thermal light will show it.

2. Pinhole.
I have different pinhole sizes, from 1um to 200um, but according to the theory - the more light PMTs receive, the higher the correlation, so I used the largest pinhole I have. The question is - do I have to use the lens before pinhole, in order to focus the light into it?

This is kind of a common misconception. The more single mode light you have, the higher the correlation will be. If you have more than one mode present, each will fluctuate independently and the coincidence peak will average out and not be visible. You typically try to focus down onto the pinhole to get a nice mode. A 50 micron pinhole might do the trick. Maybe also 30 micron. However, you need to worry about spectral modes, too. If the diode has different emission modes, they will also fluctuate independently and the peak will not show up. So you might want to try a spectral filter to single out one emission mode.

3. Maybe it's just a matter of time and I need far more than 6 hours of signals data?

I do not think so, but another issue might be important here. Is your light source pulsed or cw? the peak will only show up during the coherence time of the emission. This is usually incredibly short. For semiconductors, it is on the order of tens of picoseconds. The time resolution of typical photomultipliers is usually too bad to reach this time scale, so the coincidence count peak will just wash out and will be invisible if you look at cw signals or long pulses (>100 ps). One workaround might be to artificially increase the coherence time. The coherence time of the emission is related to the power spectral density of your emission. Or simply speaking: The narrower your emission spectrum is, the longer your coherence time will be. You might artificially increase it by using a REALLY narrow spectral filter. However, that will drastically reduce your signal intensity.

Could you explain a bit, what kind of diode you are using and what kind of result you expect from the measurement? That might make it a bit easier to help you.

 

[LmdL]

Hi Cthugha,
First of all, thank you so much for a fast reply!
Secondly, I'll do my best to describe my equipment as precise as possible. I'm currently not in a lab - will be there tomorrow morning in order to check out all the specifications.
For now, I know the following:

1. High-Power LED:
Max power: 5W
Wavelength: 465[nm]
Bandwidth: Δλ ≈ 50[nm]
I also have a possibility to use square-wave modulated LED (2.8W, 15kHz), but I didn't use it yet.

2. PMTs - I use 2x Photomultiplier Tube R7400U from HAMAMATSU.
Time resolution ~ 1.56[ns].

I'll try to dig out more information about the LED tomorrow. Regarding the experiment purpose - the final purpose is to put a pinhole, which will mimic a star with certain diameter, and by recording the signals and computing a correlation between them in MATLAB find out the "star"s angular diameter. Of course for this I will need to perform a common procedure - compute correlation, move one of the PMTs, compute correlation again, move PMT further and so on, but for now I don't get the correlation peak even for zero distance baseline.

 

[Cthugha]

1. High-Power LED:
Max power: 5W
Wavelength: 465[nm]
Bandwidth: Δλ ≈ 50[nm]
I also have a possibility to use square-wave modulated LED (2.8W, 15kHz), but I didn't use it yet.

2. PMTs - I use 2x Photomultiplier Tube R7400U from HAMAMATSU.
Time resolution ~ 1.56[ns].

Ok, I do not know the exact numbers, but a bandwidth of about 50 nm corresponds to a coherence time of below 100 fs. That is at least four orders of magnitude faster than your detectors. Therefore, it is not too surprising that you do not see any peak. What you measure is a convolution of your signal (decaying from peak to baseline in about 100 fs) with the response function of your detector (something like a Gaussian with 1.5 ns width), which more or less just leaves you with the baseline signal. I am afraid you need to do a LOT of spectral filtering in order to see something.

I'll try to dig out more information about the LED tomorrow. Regarding the experiment purpose - the final purpose is to put a pinhole, which will mimic a star with certain diameter, and by recording the signals and computing a correlation between them in MATLAB find out the "star"s angular diameter. Of course for this I will need to perform a common procedure - compute correlation, move one of the PMTs, compute correlation again, move PMT further and so on, but for now I don't get the correlation peak even for zero distance baseline.

So you kind of want to mimic the original HBT experiment on the light from Sirius B with a LED? That might be tough, but possible. Do you actually need a LED or do you just need some arbitrary light source with thermal statistics?

 

[LmdL]

Yeah, actually the experiment is the same as HBT, but they did it with analog correlator - linear multiplier. My final purpose is to design an FPGA board that receives 2 signals from the detectors patch by patch (2048 points each) and outputs the correlation value. That is, perform a digital version of the HBT experiment.
Regarding the sourse - I can use anything. Actually, in my previous experiment (nothing to do with HBT) I created my "star" from a halogen light bulb with 150 Watt power which I focused into pinhole with a lens:
http://images.monstermarketplace.com/optical-systems-and-microscopes/osram-64225-fhd-esa-microscope-halogen-light-bulb-6-volt-10-watt-150x150.jpg

In HBT experiment, I thought it will not be useful from two reasons:
1. Heat. In previous experiment I turned on the light only for short time to record the data. In HBT I need to record the data over long time and such a bulb becomes very hot - it starts to melt the bulb mount and other plastic mounts around.
2. Spectral range. In previous experiment it was good to have a white light star. In HBT white light corresponds to total uncorrelation (Brown and Twiss performed "dummy" runs with white light), so I need to broaden the spectra of the source as much as possible, though not to get a "laser".

So I chose a LED to use. Actually, I have another type of LED in my lab - Bi-Color red-blue LED. But, I don't know if it's possible to use it, since even if I filter the second wavelength's peak I still have a large bandwidth. So I used the one I described before, which I thought fits to the experiment better than the others. If I still have to decrease the bandwidth from 50[nm] I can use a blue narrow band filter.

From HBT experiment I understand that they used a mercury arc lamp and put a filter after it to pass only a 435.8[nm] mercury line. As I understand, they still didn't get a "laser" in that way, but a line with very narrow bandwidth. So I ask myself If I can do the same with LED + blue narrow band filter or it's worth to use a white light + blue narrow band filter instead.

By the way, regarding the pinholes - I have 1um, 2um and 15um industrial pinholes (Thor Labs), larger pinholes I produce myself with a needle and aluminum foil. Do you suggest to try to make a 50[um] pinhole by making a hole in aluminum foil with a needle (which won't be an ideal circle) or to use a 15[um] industrial one?

Regarding the correlation I get, seems like you are right. The signals from detectors I receive look like this:

X-axis point-to-point is ~1.5[ns]. Each peak is a photon.
And convolution over 10,000 patches like these:

 

[Cthugha]

Yeah, actually the experiment is the same as HBT, but they did it with analog correlator - linear multiplier. My final purpose is to design an FPGA board that receives 2 signals from the detectors patch by patch (2048 points each) and outputs the correlation value. That is, perform a digital version of the HBT experiment.

Ok, so you do not actually want to move the PMTs, right?

2. Spectral range. In previous experiment it was good to have a white light star. In HBT white light corresponds to total uncorrelation (Brown and Twiss performed "dummy" runs with white light), so I need to broaden the spectra of the source as much as possible, though not to get a "laser".

That is true. However, a spectral width of 50 nm is more or less like white light. The coincidence peak will vanish roughly after one coherence time, so you want matching temporal resolution. You can calculate the necessary spectral width quite easily: http://en.wikipedia.org/wiki/Coherence_time

I did not check it, but I guess we are talking pm linewidths or less here.

From HBT experiment I understand that they used a mercury arc lamp and put a filter after it to pass only a 435.8[nm] mercury line. As I understand, they still didn't get a "laser" in that way, but a line with very narrow bandwidth. So I ask myself If I can do the same with LED + blue narrow band filter or it's worth to use a white light + blue narrow band filter instead.

It depends a bit on how much intensity you can afford to lose.

By the way, regarding the pinholes - I have 1um, 2um and 15um industrial pinholes (Thor Labs), larger pinholes I produce myself with a needle and aluminum foil. Do you suggest to try to make a 50[um] pinhole by making a hole in aluminum foil with a needle (which won't be an ideal circle) or to use a 15[um] industrial one?

Oh, of course the industrial ones at 15 micron are fine, too.


All in all, I am not sure whether you can filter your light well enough. If that is a problem, you might want to use a pseudothermal Martienssen lamp like I mentioned in the topic you linked at the beginning. I built one once and measured the possible coherence times. I might still be able to dig up the values in case you are interested. The other possible solution is of course to use a different detection scheme, but it seems like the focus is rather on building a HBT than to characterize your light field. If you are interested in alternative experimental schemes, I can give you some references, too.

 

[LmdL]

Ok, so you do not actually want to move the PMTs, right?

I will need to, in order to get the graph of correlation vs. baseline distance, so I'll be able to find out where this graph gets first zero and from that to calculate the star's angular diameter.

That is true. However, a spectral width of 50 nm is more or less like white light. The coincidence peak will vanish roughly after one coherence time, so you want matching temporal resolution. You can calculate the necessary spectral width quite easily: http://en.wikipedia.org/wiki/Coherence_time

I did not check it, but I guess we are talking pm linewidths or less here.

I already calculated it - with current setup the result is τ=14[fs], which is 5 orders of magnitude less than time resolution of the PMTs. If I want to coherence time to be equal to time resolution of the PMTs, I need a bandwidth of ~0.5[pm], which is smaller than an atom radius. So I guess, with current setup I cannot measure any correlation. I need to lower the bandwidth as much as possible, as well as change my PMTs to faster ones.

Another question - is coherence time of 5 orders of magnitude less than time resolution of the PMTs is actually tells me that only correlation between a pair of photons from each 10,000 pairs I will detect? If so, I don't need to raise a coherence time till time resolution of the PMTs. Its enough to have a ration of ~1/100 (i.e. correlation of a pair out of each 100 pairs) and run the correlation for a long time. Am I right?

All in all, I am not sure whether you can filter your light well enough. If that is a problem, you might want to use a pseudothermal Martienssen lamp like I mentioned in the topic you linked at the beginning. I built one once and measured the possible coherence times. I might still be able to dig up the values in case you are interested. The other possible solution is of course to use a different detection scheme, but it seems like the focus is rather on building a HBT than to characterize your light field. If you are interested in alternative experimental schemes, I can give you some references, too.

So for now, my major problem is a light source. I will try to find out if I can get a mercury arc lamp, since I see that it has a bandwidth of 1[nm]. Can you explain what it is a pseudothermal Martienssen lamp? Will it have narrow bandwidth? Did you tested it as a light source in your experiments and it worked?
Sorry for so many questions, I'm new in the field of quantum optics and want to know as much as possible.
I'm interested in any additional information. Feel free to share.

 

[vanhees71]

I'm a bit puzzled. Usually, the HBT effect refers to the intensity correlation function measuring an extended far-distant incoherent-light source, e.g., the light from a star or galaxy with two detectors some distance away which is very small compared to the distance to the object. From the correlations you infer the size of the light source.

This technique is also common in heavy-ion physics. At ultrarelativistic collisions, as performed at the Relativistic Heavy Ion Collider at the Brookhaven National Lab (BNL) and at the LHC at CERN, a hot blob of dense medium is created, undergoing a transition from a partonic quark-gluon plasma state to a hot hadron gas. You can, however measure only the final state of hadrons after freeze-out of this hot and dense fireball which lasts around 10-20 fm/c (fermi over the speed of light!). One way to learn something about the extension of the source is to use pions in the same way as photons in the above described HBT setup.

In your experiment it seems that you are rather after a coherent light source, i.e., your pinhole should be small enough to let through a quite coherent beam of light. Of course, also the resolution of your photodetector must be large enough, as explained already by Cthuga in a previous posting.

A very good description about the fundamental issues concerning HBT can be found in

G. Baym, The physics of Hanbury Brown--Twiss intensity interferometry: from stars to nuclear collisions, Acta Phys. Polon. B 29:1839-1884,1998
http://arxiv.org/abs/nucl-th/9804026

Urs Achim Wiedemann, Ulrich Heinz, Particle interferometry for relativistic heavy-ion collisions, Phys. Rept. 319, 145 (1999)
http://arxiv.org/abs/nucl-th/9901094

 

[LmdL]

Vanhees71,
Thanks for reply!
Actually I'm working with this book:
"The Intensity Interferometer" (1974) by R. Hanbury Brown.
According to the book, the final step is to measure the correlation as function of baseline (distance between the detectors/PMTs). It should look like this:

From the first zero of the correlation function I can then find the angular diameter of the star θ, by:
d = 1.22λ/θ

As for now, I'm working with a baseline 0, i.e. should get maximum correlation.

 

[vanhees71]

I see. So that should be indeed the setup with a coherent light source (because the correlation function peaks at 1 not 2). So, perhaps you must make your pinhole smaller? I'm, however, not an expert in this.

 

[LmdL]

I already wrote above that I have 1um, 2um and 15um industrial pinholes (Thor Labs) I can use. The point is, if I use a very small pinhole - I decrease the intensity of my "star", i.e. detect less photons, and therefore need more time to get the correlation peak. So here, as I understand, I need to compromise between a pinhole size and a "star" intensity.
Regarding coherent source (laser) - I cannot use it, from 2 reasons.
1. As Cthugha already wrote in other thread (see link in the first message above), detections are completely uncorrelated for laser light.
2. Final purpose is to apply the system on real stars. Using the light source and filter in my system, I can setup a filter to be a part of the "telescope", i.e. part of the detection subsystem, instead of "star" subsystem, just by moving it to be before the beam splitter instead before the pinhole. But if I use laser light, coherence property will be a part of the "star" subsystem.

 

[Cthugha]

I already calculated it - with current setup the result is τ=14[fs], which is 5 orders of magnitude less than time resolution of the PMTs. If I want to coherence time to be equal to time resolution of the PMTs, I need a bandwidth of ~0.5[pm], which is smaller than an atom radius. So I guess, with current setup I cannot measure any correlation. I need to lower the bandwidth as much as possible, as well as change my PMTs to faster ones.

Another question - is coherence time of 5 orders of magnitude less than time resolution of the PMTs is actually tells me that only correlation between a pair of photons from each 10,000 pairs I will detect? If so, I don't need to raise a coherence time till time resolution of the PMTs. Its enough to have a ration of ~1/100 (i.e. correlation of a pair out of each 100 pairs) and run the correlation for a long time. Am I right?

Yes, you can have a trade-off and get a reduced peak at intermediate temporal resolution. You can find the math to calculate the expected correlation peak magnitude in Phys. Rev. Lett. 98, 043906 (2012).

So for now, my major problem is a light source. I will try to find out if I can get a mercury arc lamp, since I see that it has a bandwidth of 1[nm]. Can you explain what it is a pseudothermal Martienssen lamp? Will it have narrow bandwidth? Did you tested it as a light source in your experiments and it worked?
Sorry for so many questions, I'm new in the field of quantum optics and want to know as much as possible.
I'm interested in any additional information. Feel free to share.

A Martienssen lamp is just a ground glass scattering disk, so it scatters light. If you mount it on a motor and have it rotate, you get a changing scattering pattern. It can be shown that if you pick a small part of the scattered light, this light source also follows thermal photon number statistics, but does not have a narrow bandwidth. The coherence time depends on the rotation speed of your disk and will typically be somewhere between nanoseconds and microseconds. I built one and used it for Optics Letters 37, 2811 (2012). You can also use completely different approaches, but these can be VERY expensive. One possible way I came up with can be found in Science 325, 297 (2009). That technique gives you picosecond resolution.

I see. So that should be indeed the setup with a coherent light source (because the correlation function peaks at 1 not 2). So, perhaps you must make your pinhole smaller? I'm, however, not an expert in this.

It is still thermal light. It was just common to show g2-1 in the old days. Coherent light should not show a peak at 1, but a flat line at 1 and no peak whatsoever.

 

[LmdL]

Cthugha,
Thank you so much for your help and of course, for references. I will try your solution with Martienssen lamp, and will update with results.

 

[Cthugha]

Just as a final comment: You might want to have a look at the references inside that papers to get a grasp on the details of the pseudothermal lamp. You can kind of simulate light sources of different size by focusing on the disk in a different manner and by changing the poition on the disk (center or outside). Also, I would like to mention that this would also work using a laser as you more or less modulate your light intensity automatically in order to mimic thermal light. So it is not too difficult to realize.

 

[LmdL]

Yeah, I already read a description about Martienssen lamp. I have only one question - the "ground glass" they use, what is it? Is it just a ground glass diffuser?
Regarding the focusing on that glass, tell me if I'm right: I'm focusing the laser (for example a HeNe one) on this glass and I can change the focus size spot (by moving the focusing lens) in order to reach a large enough speckle size. Once I will perform the final part of the experiment - moving the PMT (increasing the baseline between PMTs), I should get the zero correlation exactly when baseline equals the speckle size. Am I right?
Thanks.

 

[Cthugha]

Yeah, that is just a ground glass diffuser. I got mine from ThorLAbs and used these:
http://www.thorlabs.de/newgrouppage9.cfm?objectgroup_id=1132.

I mounted them on one of these motors used for toy planes, but you could use pretty much everything. The tricky part is to drill a good hole into them, such that the hole is at the center and the glass does not break. However, these diffusers are incredibly cheap, so breaking some is not too much of a problem.

You can order them with different grit polishes. What you will want to do is focus the beam such, that you do not average over several grits.

Actually I am not sure, whether you actually need to move the PMTs. Is it possible to just record a time series for each detector seperately and correlate the detected signals at different delays afterwards? Or does your setup not allow for stuff like that?

 

[LmdL]

You mean motor like this one?

Oh, you mean that a laser beam shouldn't be focused on the center of the glass, but on the side? Like this?

I think it's not necessary, since I have a rotation mounts in my lab. Can just insert the glass inside.

My setup consists of FPGA board that takes signals from the detectors patch by patch. Each patch is 2048 points, with PMT time resolution of 1.5[ns] it should be around 3[us] each patch. Then FPGA calculates the correlation of this 2 patches. Stores the result. Takes next 2 patches, calculates the correlation, adds the result to the stored one and stores it instead. And so on. After any time, by command, I can send the stored correlation to MATLAB and see the result.
I'm not sure, but I think, there is a possibility to measure the angular diameter of my "star" without moving the PMTs and this is by changing the cable lengths coming from PMT1 and PMT2 to my FPGA, i.e. introducing the time delay.

 

[Cthugha]

You mean motor like this one?

Oh, you mean that a laser beam shouldn't be focused on the center of the glass, but on the side? Like this?

I think it's not necessary, since I have a rotation mounts in my lab. Can just insert the glass inside.

That motor should work. The coherence time of the pseudothermal light field will depend on the effective velocity of the ground glass disk passing by. If you hit it at the center, it will be pretty slow and it will be faster at the edge. Usually you want to hit at the edge to get to the nanosecond range, but that of course depends on how fine or coarse your ground glass disk is.

My setup consists of FPGA board that takes signals from the detectors patch by patch. Each patch is 2048 points, with PMT time resolution of 1.5[ns] it should be around 3[us] each patch. Then FPGA calculates the correlation of this 2 patches. Stores the result. Takes next 2 patches, calculates the correlation, adds the result to the stored one and stores it instead. And so on. After any time, by command, I can send the stored correlation to MATLAB and see the result.
I'm not sure, but I think, there is a possibility to measure the angular diameter of my "star" without moving the PMTs and this is by changing the cable lengths coming from PMT1 and PMT2 to my FPGA, i.e. introducing the time delay.

So your FPGA calculates a pointwise correlation? Like value at point 1 at PMT 1 times value at point 1 at PMT 2 and then it adds the value at point 2 at PMT 1 times the value at point 2 at PMT 2 and so on? If so, you could also check small delays by getting shifted products instead. However, I am not sure whether that will work fast enough.

 

[LmdL]

That motor should work. The coherence time of the pseudothermal light field will depend on the effective velocity of the ground glass disk passing by. If you hit it at the center, it will be pretty slow and it will be faster at the edge. Usually you want to hit at the edge to get to the nanosecond range, but that of course depends on how fine or coarse your ground glass disk is.

Rotation mounts I have can be rotated at 1 [rpm]. It should be fine, I think, as smaller the rotation, the bigger the coherence time. I'm currently reviewing the Thor Labs link you provided for ground glass diffusers. What is a "grit" number parameter? Is it responsible for a speckle size on the exit?

So your FPGA calculates a pointwise correlation? Like value at point 1 at PMT 1 times value at point 1 at PMT 2 and then it adds the value at point 2 at PMT 1 times the value at point 2 at PMT 2 and so on? If so, you could also check small delays by getting shifted products instead. However, I am not sure whether that will work fast enough.

You just described the simple multiplication of the signals point-to-point. You can see on my previous post I added 2 pictures - one of the signals and one of the correlation. Each one of the signals arrays has 2048 points and the correlation one has 4095 points (2*(signal length) -1). The correlation is done by MATLAB function xcorr(signal1,signal2) written inside FPGA, but actually does the following:

Signals: f(n), g(n), where n is a point number
Correlation:
$$h(n) = f(n)\ast g(n)=\sum_{m=0}^{2048}f(m)g(m+n)$$

So, for example, the correlation at point 0 will be just multiplication of the two signals and sum over all the values of this product. Correlation at point 1 will be multiplication of signal 1 with signal 2, which is moved by 1 point and a sum over the product. And so on.

 

[Cthugha]

Rotation mounts I have can be rotated at 1 [rpm]. It should be fine, I think, as smaller the rotation, the bigger the coherence time. I'm currently reviewing the Thor Labs link you provided for ground glass diffusers. What is a "grit" number parameter? Is it responsible for a speckle size on the exit?

Yes, that is true. Slow rotation gives you long coherence times. However, you might not want to have too long coherence times. Rotating at 1 rpm will give you something like 100 ms or so, but the time you want will of course depend on your setup.

The grit parameter is just a measure of how fine or coarse the glass is polished. Coarse grits (low numbers) give you a wider speckle pattern with bigger speckles, but you lose some more intensity.

 

[LmdL]

Yes, that is true. Slow rotation gives you long coherence times. However, you might not want to have too long coherence times. Rotating at 1 rpm will give you something like 100 ms or so, but the time you want will of course depend on your setup.

So, if my PMTs resolution time is 1.5[ns] I'll need a rotation rate which provides me with coherence time of ~5-10 [ns], right? This way I'll get coherence time not too long, but long enough to detect 2-3 points in PMTs for good correlation.

The grit parameter is just a measure of how fine or coarse the glass is polished. Coarse grits (low numbers) give you a wider speckle pattern with bigger speckles, but you lose some more intensity.

Since I'll work with the laser, intensity loss is not critical. On the other hand, big speckles is what will give me a correlation at two PMTs.
From the Thor Labs link, I don't see much difference between 120-220 grits and 600-1500 grits pairs:

I suppose, a 220 grits one should fit my experiment.

 

[Cthugha]

So, if my PMTs resolution time is 1.5[ns] I'll need a rotation rate which provides me with coherence time of ~5-10 [ns], right? This way I'll get coherence time not too long, but long enough to detect 2-3 points in PMTs for good correlation.

A slightly longer coherence time might allow you to measure the full decay with good resolution, but I guess you need to play around for a bit. There is some trade-off between fast data collection, the possible rotation speed of your disk, how stable you can keep the rotation, the focal size you can get on the disk and many other things. You might need to play around for a bit.

Since I'll work with the laser, intensity loss is not critical. On the other hand, big speckles is what will give me a correlation at two PMTs.
[...]

I suppose, a 220 grits one should fit my experiment.

I see. Yes, you might try that one.

 

[LmdL]

For now the problem is with the rotation speed. I can't find the 1 rpm rotation mounts, so for now I only have the "toy plane" motor, which, for my opinion, is too fast. Can you tell, what coherence time you got with the "toy plane" motor? Was it far below the nanosecond scale? Thanks!

 

[Cthugha]

Can you tell, what coherence time you got with the "toy plane" motor? Was it far below the nanosecond scale? Thanks!

Oh, no. Not at all. I never even got close to being below the nanosecond scale. A rotation frequency of 5 Hz gave me roughly 40 microseconds. If I remember correctly, 30 Hz corresponded to about 800 nanoseconds or something like that. To get few nanoseconds, I guess you want pretty fast rotation and hit the disk pretty far from its center.

 

[LmdL]

Oh, thanks!
Can you explain or give references to why semiconductor laser doesn't fit for the experiment? What about solid state lasers? In all articles I read authors use HeNe laser. It is interesting if other types of lasers will fit. In bottom line all we do is destructing the coherence of the light laser emits by glass diffuser. It shouldn't be matter which type of laser emits this coherent light.

 

[Cthugha]

All you do is modulating your intensity, so you can choose whatever laser you consider suitable. When I built the setup, I used a solid state laser at 638 nm.

 

[LmdL]

Hi Cthugha,
Just wanted to tell you that I had no success with getting the correlation, so any advices are highly appreciated.
First of all, there was a small problem - amplifier attached to one of the PMTs has burned out and I'm currently waiting to another one to arrive. Meanwhile I thought if it's possible to observe the HBT effect only with 1 PMT. And I think it's possible. Instead of getting correlation between 2 signals at 2 PMTs I tried to record 2 signals, while second one has a time delay, by the same PMT - and perform an auto-correlation.
I expect then to have 3 high peaks in auto-correlation graph. Peak on the center is correlation of the recorded signal with itself and 2 "side peaks" - correlation with itself shifted in time. Overall I should get something like this:

Suppose that signal is:

And same signal, delayed in time:

If PMT detects both signals (normal and delayed one), it will record:

Auto-correlation of this is:

Unfortunately, when I record the signals in my experiment, I don't get the "side" peaks, which are responsible to the HBT effect. I wonder why. Maybe you can suggest something or point to a mistake in my setup.

My experimental setup (top view):

Equipment:
L1 - Green laser (532nm, solid state). Tried HeNe (632 nm) as well.
P1 - 2um pinhole.
L2, L3, L4 - Converging lenses.
MT - Simple toy motor.
D1 -Ground glass diffuser.
BS1, BS2 - Beam Splitters (50/50).
M1, M2, M3, M4 - Mirrors.
PMT - Photo Multiplier (HAMAMATSU R7400U).
HFA - High Speed Amplifier (HAMAMATSU C5594).

How it should work:
Light from the laser is focused by L2 lens into P1 pinhole - it is done in order to "expand" the laser beam so it will be easier to focus it into diffuser later on.
Light from the pinhole is focused by L3 lens on the side of the rotating ground glass diffuser. It produces speckle pattern - I placed the diffuser on the point where it produces the largest speckles (with ~2cm square on average).
Then light is changed into plane wave by L4 lens. This is done because I need equal light spots of 2 beams when they arrive to PMT, since there is an optical path difference between 2 beams.
Light enters BS1 beam splitter and is divided into two beams: "mean" beam continues to the left and "delayed" one travels around reflected by M1, M2, M3 and M4 mirrors.
Both beams enter to BS2 beam splitter and combined back.
Combined beam is finally recorded by PMT. I put an Iris before the PMT to decrease its area to ~2mm square.

The optical path difference between 2 beams is 7 meter, which corresponds to a delay time of 23 [ns]. Resolution time of the PMT is 0.8 [nm], so the distance between center and "side" peaks in auto-correlation graph is about 29 points. I write this, because first I was wondering if "side" peaks are distinguishable from the center peak or, on the other hand, are not outside of the graph.

For the moment, the only thing I could think of is the beams inequality - the delayed beam passes larger distance and therefore has smaller intensity. In addition, because of abberations it is distorted a little (actually, a lot).
Can it be the reason?
Maybe I'm missing something in the Martienssen lamp setup?
Or am I wasting the time and should just wait for the second amplifier to arrive?

Any suggestions and advices are highly appreciated. I apologize for such a big comment, hope you'll have time to read it.
Thanks in advance!

 

[Cthugha]

Ok, a broken PMT should not be a significant problem right now.

Regarding the setup, I would like to ask how much of the light after the rotating disk you collect? You typically want only the area of a single speckle. Probably even much less. Besides that, it is possible to measure the equivalent of the HBT effect using a single detector, if both the detector time resolution and dead time are short compared to the coherence time of your light. The coherence time should be somewhere betweend hundreds of nanoseconds and microseconds, so that should work.

Can you just measure a simple time trace of your detected signal? Just the number of photon detections versus time? If so, please measure a really long time trace of several seconds (it does not have to be a consecutive measurement - more measurements of shorter intervals are fine, too) and divide it into time bins. If possible, choose the binning time such, that the photon number is moderately large, but the time bin length is still shorter than the expected coherence time. Then have a look at the statistics of the photon numbers per bin. Could you get the mean value and the variance of the number of photons per bin? The ratio of these two numbers give you the same information as the HBT peak. So if we have that, we can at least guess whether you light actually follows thermal statistics.

 

[LmdL]

Actually I cannot record something very long. My FPGA samples the signal by patches. Each patch consists of 2048 points (see signal example pictures in last message). Each point is a PMT's measurement. Each PMT's measurement, according PMT's response time, is 0.8 [ns]. So each patch consists of about 1.6 [ms] of signal. I can collect any number of such patches. Getting 1000 patches takes about 20 minutes or so.
According this paper - equation (3):
http://cpl.iphy.ac.cn/EN/Y2009/V26/I7/74205
coherence time in my setup is about 350[ns].

If I understood you right, I need to collect, let's say, 3000 patches. Divide them into groups of, let's say, 50 patches (in chronological order), such that each group consists of photons arrived in the interval of 80 [ns]. Then, create a graph with 60 points, with X-axis as group number (1,2,3,..,59,60) and Y-axis as a number of arrived photons in that group. Finally, calculate the mean value and variance of the distribution in this graph. If I got it right, I will post here the results as soon as possible.
Just to be sure, why such graph won't be constant, on average?

 

[Cthugha]

Yes, you need a number of patches corresponding to, say, 80 ns and the number of photons detected in each time window of 80 ns and then calculate the mean and variance. You could also plot a histogram of the photon numbers.

This graph should not be constant because the photon number distribution should roughly follow a Bose-Einstein distribution. That means that quite often you should get no photons at all and sometimes lots of photons. The "instantaneous" photon number present changes slowly on a timescale on the order of the coherence time of your light field. So if you choose your patches such that you time bin is shorter than the coherence time of your light, you will directly see that noise. If your time bin is chosen to be way longer than your coherence time, you average over several "instantaneous" photon numbers and will get a constant graph. So if you get a noisy graph, you are fine. If you get a constant graph, you are either not creating thermal light (in that case you probably collect too much of the scattered light field) or your time bin is way longer than your coherence time.

What you should get: For thermal light the variance is twice as large as the mean. Otherwise the variance should more or less be equal to the mean.

 

[LmdL]

Hi,
I just recorded 3000 patches.
There were patches with photons:

Patches with noise only:

And patches with some strange "noise" (296 patches out of 3000):

I supposed that pattern in last picture is a kind of noise (i.e. didn't count it for photons).
Photon number distribution over all 3000 patches:

Mean: 0.7257. Variance: 0.8027.Combined into 60 bins, 50 patches each bin:

Mean: 36.2833. Variance: 41.9692.So, I suppose, "my" Martienssen lamp doesn't work?
Somehow, I still think the problem is in the second light path. When I put out the diffuser - I see almost identical Airy discs on both light paths, but when I return it back - on the short path I see big speckles, but nothing is on the long path. Or it's just becomes too faint to see.

 

[LmdL]

By the way, before collecting the patches I slightly changed the "Martienssen lamp" part in my experimental setup. Now it looks like this:

Laser L1 produces a beam that passes through ND neutral density filter and is focused by L2 lens on the side of the D1 diffuser that is rotated by MT motor. Speckle pattern produced passes through a 2um PH pinhole and converged by L3 lens into plane wave.
Plane wave was set up without rotating diffuser and density filter mounted - for simplicity. Then I just inserted them back in.
In addition, I added a converging lens between BS2 beam splitter and a PMT in order to focus the combined beam into PMT.

 

[Cthugha]

I do not think that the second beam is the problem right now. It might be bad (it is a huge delay), but at these timescales, the effect should be visible just looking at the first beam alone.

Actually I think your lamp might be working. You assume a coherence time of 350 ns. You average the photon number over a time window of 2048 points which means your effective time resolution is somewhere around 1.6 microseconds. As your coherence time is much faster than your time resolution, you should only see a drastically reduced HBT peak and the variance should also not bee much larger than the mean. If the values are correct, I would expect a peak with a magnitude of roughly 10 to 20% of the real value seen with good temporal resolution. So can you subdivide each patch into smaller patches of, say, 160 ns and check, whether the mean and variance change? You might run into the problem of having pretty low photon numbers here, so I am not sure whether it is really necessary to use a 2 micron pinhole in the speckle pattern. It sounds like that may reduce your intensity really strongly. Do you have a larger pinhole or an iris or something like that?

 

[LmdL]

Hi,
Yeah, you are right. I somehow missed the fact that each patch is already longer than expected coherence time. I performed a new measurement - recorded 3000 patches again with the following changes:
1. Increased coherence time, by reducing rotation rate of the diffuser.
2. Replaced a 2um pinhole with a 15um one.

Results are as following. Bins graphs in increasing order of number of patches each bin contains:

Statistics:

First of all, I see no sense why variance/mean ratio is ~4 for most of bin size variations. Is it because 2 beams are actually involved and not 1?
Secondly, ratio is decreasing as bin time length increases, but it feels like it does so, because bins number decreases.

 

[Cthugha]

The ratio indeed is quite large. Can you block the second beam? It might (and should) cause some interferences and extra variance and the correct photon statistics can be identified from one beam alone.

Besides that, two possible issues come to my mind: If the disk is rotating slowly, additional noise may be introduced if the rotation does not go at exactly the same velocity all the time. And maybe more important: You need to sample the scattering disk evenly. So you want your total collection time to be orders of magnitude longer than your coherence time. Otherwise you just sample a part of the probability distributions. Usually a total collection time of at least 1000 coherence times is used.