# Hanbury Brown and Twiss effect question

1. Aug 28, 2014

### 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:
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?

2. Aug 28, 2014

### Cthugha

Let me see what we can find out.

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.

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.

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.

3. Aug 28, 2014

### 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.

4. Aug 28, 2014

### Cthugha

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.

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?

5. Aug 28, 2014

### 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 [Broken]

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:

Last edited by a moderator: May 6, 2017
6. Aug 29, 2014

### Cthugha

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

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.

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

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.

7. Aug 29, 2014

### LmdL

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.

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?

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.

Last edited: Aug 29, 2014
8. Aug 29, 2014

### 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

9. Aug 29, 2014

### LmdL

Vanhees71,
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.

10. Aug 29, 2014

### 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.

11. Aug 29, 2014

### 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.

12. Aug 29, 2014

### Cthugha

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).

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.

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.

13. Aug 29, 2014

### 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.

14. Aug 29, 2014

### 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.

15. Aug 29, 2014

### 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.

16. Aug 29, 2014

### 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?

17. Aug 29, 2014

### 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.

Last edited: Aug 29, 2014
18. Aug 30, 2014

### Cthugha

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.

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.

Last edited: Aug 30, 2014
19. Aug 30, 2014

### LmdL

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?

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.

20. Aug 30, 2014

### Cthugha

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.