math/engineering/physics gurus, I need your help

[paperclippy]

I'm trying to understand a section of a paper. They're talking about the signal generated by a photomultiplier tube when photons from fluorescence are coming into it. The sentence says, "Since the number of photo-electrons ultimately captured by the PMT is finite, the signal quantitation is stochastic with a variance governed by the Poisson

Comments

[bennj]

I can only answer two of those. Stochastic just means "probabalistic with known distribution". Some places even say "stochastic process" and "random process" are synonyms.

Poisson processes are defined by only one parameter, lambda, which is both the mean and the variance of the process. So, they're taking advantage of this and saying that the square root of the mean (aka expected number of captured photo electrons) is the same as the square root of the variance (the standard deviation).

[paperclippy]

Thanks! That helps a lot.

[floccinau]

I would read the second sentence ("Q is a measurement...") as defining a measure of efficiency in capturing photo-electrons--e.g. of this many photo-electrons emitted, we capture however many. They use fluorescence intensity as a proxy for the total number of photo-electrons emitted.

[paperclippy]

Thanks!

[camlost]

Photomultiplier tubes take individual photons and turn them into lots of electrons. In the first step, the photon generates an electron (photoelectric effect). Then, one electron flies across a large potential (and thereby gains a lot of energy) and crashes into another source of electron, this making making lots of electrons. This step is repeated until you have enough current to measure.

The finiteness of the photons means that you have to amplify the signal. This amplification presumably leads to a Poisson distribution. If you had an infinite/enormous source of photons, you wouldn't need this amplification and could take a (more) direct reading, which would be more or less non-distributed. Or at least that's my guess.

[paperclippy]

That's interesting, thanks for the info! I know we have settings on our PMTs for voltage and gain which affect the amplification, so there is definitely something going on there.

[zwilichkl]

It looks like people have answered a lot of your questions. I think the reason the PMT is Poisson is because it is a counting function. The Poisson distribution is a way of describing how much time there is between counts (photon detections, in this case). I think "signal quantitation" means what you said.

Are you good with your first set of questions?

Is Q still talking about the PMT? If so, I think it is just saying that if you need fewer photo-electrons to get a measurable signal (fluorescence intensity), there will be more error in the signal because the signal is triggered relatively easily (and could be triggered by stray photons hitting the tube that did not come from your source of interest).

[paperclippy]

Yay for having friends who know this stuff! Thanks, I think I get it now!