What are GVD calibrations?

When the GVD trigger system registers an event, it sends the digitized PMT waveform slices to the shore station. The slices are then split into individual pulses. Each pulse has a time, amplitude and charge provided in FADC codes. To reconstruct an event we need to transform these values from FADC codes to physical dimensions.

Specifically, we need to

  • Transform impulse time from FADC time codes into nanoseconds, then individual channel delays should be subtracted.
  • Transform the amplitude/charge of an impulse from FADC codes to the number of photoelectrons corresponding to this amplitude/charge.

Transforming a GVD response from FADC codes into a tangible physical data is called calibrating the response. Or, specifically, time calibration, charge calibration and amplitude calibration.

Time calibration

An FADC time code corresponds to 5 nanoseconds, so obtaining a nanosecond time mark for an impulse is as easy, as multiplying it's time code by 5.

However, a waveform for each channel has an individual delay that should be compensated to ensure that all PMT waveforms in the event start at the same time. This delay is due to the variation in the length of the OM cables and individual PMT and electronics delays.

Furthermore, each section has an individual time offset that should be applied to all channels in it. This is done to ensure that the trigger window for each section is roughly in the center of the waveforms of its channels.

So, finally, to acquire a photon arrival time $t_i$ to channel $i$:

$t_i = 5t_{FADC} - T_i - O_i$

Here:

  • $t_i$ - calibratied impulse time, nanoseconds
  • $t_{FADC}$ - impulse time, in FADC codes
  • $T_i$ - individual time delay for channel $i$, nanoseconds
  • $O_i$ - section offset for channel $i$, nanoseconds.

Amplitude and charge calibration

Amplitude and charge values of an impulse in FADC codes are assumed to be linear with respect to the number of photoelectrons

$ N_{p.e.} = \alpha_{Q}Q_{FADC}$

$ N_{p.e.} = \alpha_{A}A_{FADC}$

However, due to the "amplitude effect" (impulse deformation at large amplitudes), amplitude is only linear up to ~30 p.e. It is therefore advised to rely on impulse charge, rather then its amplitude.

The values of $\alpha_{Q}$ and $\alpha_{A}$ are unique for each channel. So, calculating the charge $Q^i_{p.e.}$ and amplitude $A^i_{p.e.}$ for an impulse on channel $i$ is done as follows

$Q^i_{p.e.} = \alpha^i_{Q}Q_{FADC}$

$A^i_{p.e.} = \alpha^i_{A}A_{FADC}$