Modeling shot noise on Mathematica

[bluegrass12]

I've been having some trouble modeling shot noise for a photomultiplier tube on Mathematica - I know that I have to use a random number generator and the Poisson distribution to do it, but I'm having trouble synthesizing everything. (There are many things I'm going to leave just as parameters, such as the average photon incidence rate, the quantum efficiency of the PMT's photocathode, the number of dynodes in the PMT.) I'm trying to basically model the voltage sequence that is outputted from the PMT.

This article says that I should superimpose all the inflowing shots (along with an exponential decay of the shot).

Would really appreciate some direction on putting it together in Mathematica. Thanks!

 

[Valkarie]

The first step is to define the parameters of your model. You will need the average photon incidence rate, the quantum efficiency of the PMT's photocathode, the number of dynodes in the PMT, and the exponential decay of the shot. Once you have these parameters, you can use a random number generator to generate a sequence of random numbers, each of which represents a single shot. You can then use the Poisson distribution to calculate the probability that a given shot will occur. You can then use this probability to calculate the voltage output from the PMT.To superimpose all the inflowing shots, you can create a function that takes the parameters of the model and returns the voltage output for each of the shots. The sum of the voltage outputs for each of the shots should be the total voltage output from the PMT.For example, your function might look something like this:voltage[averagePhotonIncidenceRate_, photocathodeQuantumEfficiency_, dynodeNumber_, exponentialDecay_] := Module[{shotVoltage}, shotVoltage = RandomVariate[PoissonDistribution[averagePhotonIncidenceRate * photocathodeQuantumEfficiency * dynodeNumber]] Exp[-exponentialDecay * shotVoltage]; Sum[shotVoltage, {i, 1, Length[shotVoltage]}] ]This function takes the parameters of the model as arguments and returns the total voltage output from the PMT. You can then call this function with the appropriate parameters to get the total voltage output from the PMT.