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This is an old revision of the document!
As of now there is only the prove-of-concept code in the repository that allows basic CPM + uSv/h measurement. This will be extended to a more powerful system, allowing audio-output (for all those nostalgic geiger nerds who want the classic tak tak counting sound.
In the future, with more time and the help of other enthusiastic developers, there will also be a ready-to-download image, with kernel, OS and counting, logging & data sharing infrastructure, which just needs to be copied to the SD card so that it works out-of-the-box.
https://github.com/apollo-ng/PiGI/tree/master/software
Components
The GM tube output is a short charge pulse with an amplitude that is independent of the energy of the detected radiation. It just tells you that the incoming radiation had enough energy to be detected, but not how much. That leads to the question of how to calculate some other values out of the measured count rate.
As discussed above, the GM tube doesn't know the energy of the detected radiation and also the count rate (R) depends on the tube specifications. Which means if you want to calculate a radiation dose per time (D) you can't calculate the correct value because you don't have all the information. All you can do is calculate a value as if you had radiation from Co-60, Cs-137, Sr-90 or some other radioactive isotope.
<x>D = R * conversion factor</x>
So to get from cps to µSv/h (only units here, not really a correct equation):
<x>µSv/h = cps * tube and energy specific conversion factor</x>
In terms of GM tubes the Dead-Time is the time after an event in which the tube will not register another count. Positive ions close to the anode reduce the intense electric field so that approaching electrons do not gain enough energy to start new avalanches. The GM tube is then inoperative (dead) for the time required for the ions to migrate outward far enough for the field gradient to recover above the avalanche threshold. The time required for recovery to a value high enough for a new pulse to be generated and counted is called the “Dead-Time” and is of the order of 100 μs (microseconds). 1) 2)
To correct for this statistical error one has to calculate the actual (corrected) rate R with the measured (observed) rate and the tube specific Dead-Time.
<x 14>R_{corrected} = R_{observed} / {1 - (R_{observed} * t_{dead})}</x>
Count rate R is 87,55 CPS (counts per second) with an SBM-20 tube.
<x 14>R_{observed} = 87.55 1/s</x>
The Dead-Time for this tube is listed as 190 uS.
<x 14>t_{dead} = 190 µs = 0.000190s</x>
<x 14>R_{corrected} = {87.55 1/s} / {1 - ((87.55 1/s) * 0.000190s)} = 87.55 / 0.98337 1/s = 89.03 1/s</x>
This means that the tube missed 1,48 counts per second. The actual (corrected) rate is 89,03 CPS.
Measurements with the LND712 showed a longer dead time than the datasheet advertised (about 120-150us). Moving up higher in the plateau also seemed to increase the dead time. For perfect operating conditions, the tube voltage should be set to a value within the advertised operating range and then fine tuned to decrease the dead time to the lowest possible value, without affecting the tubes.