Third order IMD in photomultipliers--weird behaviour

OK I mis-understood. I thought you meant quadratic when you said linear. (I've got a second problem in that when my brain sees quad it thinks 4 and not 2.)

So linear means it's there back at the source, or getting in from some sneak path around your whole signal chain. I don't see how it can be non-linearities in the pmt then. Is this a real problem in the system, or just an interesting side light? If it's a real problem, then my only trick is to try and make it worse, if I can't make it better... that will sometimes lead to the problem.

George H.

Thanks. They physics is completely different, though. Photodetection is quadratic because each photon has a fixed amount of energy, whereas the energy per electron depends on V, i.e. on the voltage dropped by all the other electrons. It's really really quadratic, over a huge range of photocurrents--in fact until you deplete the lower states or fill the higher ones. (This can be done, e.g. with femtosecond pulses, but it takes a ridiculous current density.)

Photocurrent is almost entirely independent of bias. There's often a percent or so worth of QE improvement at a volt or two, due to partially depleting the epi. That pulls carriers away from the epi/oxide interface, which is where a lot of the recombination occurs. Above there it just sits still up to the point where you start to get avalanche multiplication.

In the PMT, there may possibly be a threshold effect someplace, but it would have to be fairly late in the dynode chain, because it only seems to depend on anode current and not on the gain.

One clue is that the IM3 products are nearly but not quite in the noise in a 10-Hz bandwidth for most of the quasi-linear range. Modulating the amplitude also modulates the shot noise at the signal rate. The noise goes as the square root of the signal. So if it's some sort of quadratic effect with the noise, it could possibly come out linear. I'm not sure how to make that come out as a narrow peak, though--I'd expect it to smear out over the full bandwidth. Off to try some math.

Turning the room lights on doesn't do much except raise the noise floor.

Thanks

Phil Hobbs

Okay, I think I'm zeroing in on a candidate mechanism. The instantaneous shot noise goes as the square root of the instantaneous primary photocurrent. As you pointed out, second harmonic in the LED output would save us one order in the intermod, making it quadratic.

Thus we could have a term like

(shot noise of 2_f1) * (shot noise of f2)

which would be linear in amplitude but would be centred at 2*f1 - f2.

Normally if the two noise sources were independent, that would be smeared out to sqrt(2) the full bandwidth.. However since the fluctuation amplitude depends only on the total signal current, I think that there's a contribution that doesn't get smeared out, but arrives in a sharp spur. (The noise gets autocorrelated instead of cross-correlated, so there's a spike at zero offset.)

Regardless of where this occurs in the PMT, it will vary the same way as the signal output.

I need to do a bit more math to make sure this is sane, but it has the right sniff.

Fun--this photodetection business never ceases to amaze.

Cheers

Phil Hobbs

Errr, OK, you are starting to make my head hurt.

You've lost me there. (No worries, don't bother with more words.)

Well it seems easy enough to test (before you get lost in the math.) Drive one of the LED's harder or deeper, such that you get more at 2*f1 and see if you get a commensurate increase in the 2*f1-f2 spur.

George H.

John Larkin writ:

I know near-nothing about the subject and am barely hanging onto understanding all this. But it does fascinate me how many folks can and do contribute apparently valuable tidbits to help Dr. D. move toward a solution.

Indeed, great work, all.

Cheers, Dave

• Grey on grey. What the heck is wrong with having decent contrast? Do you do this on purpose?

Not sure about that but some guys here, many many years ago, were facing wh at you describe ... i think ... Intermodulation Distorsion.

Not sure about that but some guys here, many many years ago, were facing wh at you describe ... i think ...

This was due to magnetic and temperature influences around and near PMT loc ation. They resolved partially by mu-metal shield and peltier module near t he PMT.

OTH, Habib.

Thanks, Habib. Magnetic fields I believe--some PMTs can have their gain cut by a quarter if you orient them wrong in the Earth's field.

Cheers

Phil Hobbs

You're welcome Phil, I was a total beginner on PMT devices before i came to SERES ; some guys here are kidding me i will remain for ever !

BTW you're probably right that voltage divider (resistors ladder) through dynodes may have an influence on PMT's linearity.

Habib

to SERES ; some guys here are kidding me i will remain for ever !

h dynodes may have an influence on PMT's linearity.

That effect has been known since 1965 - H.J.Lush J.Sci.Instrum. volume 42, pages 597-602 (1965). P. Moatti published earlier ,in L'Onde electrique vol ume 43 pages 787-93 (1963), but I've never been able to find a copy of the paper.

People keep on rediscovering it, usually imperfectly.

One of the very best discussions of PMTs I've ever seen is a book chapter from "Methods of Experimental Physics" that I posted at and

Cheers

Phil Hobbs

Just noticed that the book chapter references you, Bill, on P. 53.

Cheers

Phil Hobbs

Both came up URL not found.

George H.

Whoops, quite right.

Cheers

Phil Hobbs

"Not Found". Any other URLs to try?

Thanks!

I did know about that - Google lists it, and I'd been interested enough to read the relevant chapter (which was quite interesting enough for me to hav e read anyway) . I could never quite work out why I got referenced. All I e ver did was cite papers that people - essentially US physicists - should ha ve known about and clearly didn't.

Well, I got the new bias network hooked up, and it's a win. The IM3 products are down at -55 to -60 dBc at 300 uA of anode current, vs. -40 dB with the Hamamatsu Cockroft-Walton. So we're 15 dB to the good for the effort.

The resistor string drives dynodes 1 through 5. I increased the dynode 1 bias voltage by 50% (150k vs 100k for the others).

Dynode 6 gets a 2N6517 emitter follower off the last tap of the string.

Dynode 7 through 9 get Darlington emitter followers from a 220k ohm resistor string that is adjustable from 1/4 to 1/2 of the total tube bias. The last 4 stages also have 10 nF caps directly to ground. Nothing oscillates. Total dissipation is about 0.5W, with another 200 mW or so at maximum safe anode current (~300 uA).

Interestingly, the constant -60 dBc spur is gone too. Customer should be happy.

Cheers

Phil Hobbs

o read the relevant chapter (which was quite interesting enough for me to h ave read anyway) . I could never quite work out why I got referenced. All I ever did was cite papers that people - essentially US physicists - should have known about and clearly didn't.

Rats! I looked more carefully and the citation is quite specific

Sloman, A.W. "Comment",Review of Scientific Instruments, 43, 356 (1972). (A comment on a paper on photomultiplier nonlinearity.)

which got a reply

which struck me as indicating that the author was over-reliant on his compu ter model - and hadn't noticed that the last stage of a resistive divider d ynode chain provides only the anode collection bias and no gain, despite th e fact that my comment - and Lush's paper - had both emphasised this point, as does the chapter in "Experimental Physics".

I suspect that the author of the chapter was being rude about Peter L. Land .