[Gate-users] correction of randoms

[Ashok Tiwari]

Hi phy phy and other GATE users,

The rate of random coincidences is proportional to the square of the activity in the FOV of the scanner, and is proportional to the coincidence timing window (2 tau). The randoms correction is implemented during the image reconstruction but not in the simulation itself. 

I also want to make this correction, so I am planning to use the following well-known equation:
Randoms rate (randoms per second) = 2 tau*N_1*N_2
Where, tau is time that we set in the GATE simulation, N1 and N2 are the individual photons detection rates in a pair of two opposite detector crystals. So for this correction, we basically need N1 and N2.

To understand this, I’ve simulated the benchPET.mac (found in GATE toolkit- without changing any parameter), the output root data contains the prompt coincidences, singles and delays.
- From the prompts coincidence tree, total number of randoms rates = 24029
- From the delayed coincidence tree (using offset of 500 ns) the total number of entries = 27277 (I think it is the total number of randoms rates using the delayed window, please someone correct me if I am wrong!)
- So, there is a difference of (27277-24029) = 3248 random rates using two different windows, and this accounts for the delayed coincidences? And how could we get N1 and N2 from the delays tree?

Hope someone will look at this and make a reply. Thank you for you help in advance.

Regards, 
Ashok Tiwari
PhD Student 
University of Iowa



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