Correct particle count for PMT linearity

[153957]

PMT response curves are not always linear.

This has an effect on both the pulse height and integral. Moreover the HiSPARC electronics have ADCs which only go to -2 V. Larger signals are saturated. We need to account for these effects.

Old power supplies:

New power supplies:

As can be seen the old power supply barely reaches 2 V, this differs from PMT to PMT, and may be influenced by the high voltage on the PMT. This means the signals are unlikely to reach the saturation threshold of the HiSPARC ADCs, this can easily be checked for detectors in the pulse height histograms. Saturated signals may require more effort to reconstruct.

Todo:

• Account for ADC saturation
• Account for non-linearity
  • Check pulse height versus pulse integral (if linear -> new pmt)
  • Check maximum pulse height

[153957]

A fit formula found in arXiv:1002.2442, eq 4. Seems to work well for fitting the pulseheight saturation. Not yet tested on pulse integral.

[davidfokkema]

Nice!

[153957]

Also works for pulseintegrals.

Note that here, and in previous example, the p₁ parameter was fixed (also to prevent possible division by 0). Varying it does not greatly affect the goodness of fit, mostly the magnitude of the p₀ parameter..

[153957]

A fit based on two linear lines connected by a circle segment (on log log axes) has replaced the fit shown in the previous comments. It has 3 degrees of freedom; intercept and slope of the second line and the radius of the circle. The first line intersects with (0, 0) and has a slope of 1 (i.e. x = y).