The m-ToT technique has also been considered to process the electronic waveforms of the Optical Modules of an underwater neutrino  telescope, since that would reduce the complexity of the necessary off-shore electronics, minimizing thus power consumption and maximizing reliability. The performance of this technique was evaluated using simulated waveforms corresponding to the response of Multi-PMT type of optical modules (proposed for the KM3NeT detector) to single muon tracks and showers developed inside the active volume of the neutrino telescope. The HOU Reconstruction and Simulation (HOURS) package was used to simulate such PMT waveforms corresponding to the detected Cherenkov light, produced from secondary charge particles following an energetic (in the range of 100GeV-100PeV) neutrino interaction in the active volume of the KM3 telescope. In this study a  Multi-PMT OM comprises 31 3” small PMTs as shown in the Figure. In simulating the operation of m-ToT electronics the functional parameters were chosen in order to maximize the tracking capabilities of the telescope, i.e. the threshold values were chosen in a way that small pulses (at the level of 1 photoelectron) are crossed by the first three thresholds whilst the highest threshold is crossed by the 50% of the pulses.

It was found that there is a monotonic relation between the true charge of the waveform and the sum of the time-over-threshold intervals (henceforth stot(i), where i=1,2,…6 for the six thresholds assumed),  indicating that Stot can be used as an estimator of the waveform charge. However, each class of pulses (the nth class corresponds to pulses crossing the nth but not the n+1 threshold level) follows a different functional relation, meaning that a different calibration curve should be used for each class of pulses.

In the case of HELYCON pulses the resolution of the m-ToT charge estimation found to improve as the number of crossed thresholds increases. This is due to the fact that the signal of a HELYCON detector corresponds to photons produced in the scintillator by charged particles passing almost synchronously through the detector material and consequently the PMT pulses exhibit a more or less  standard shape. Unlike the scintillation photon in the HELYCON detectors,  the PMT pulses in the neutrino telescope correspond to photons produced by charged particles propagating through the much larger volume of the KM3NeT detector.

Moreover, some of these photons are delayed because of the optical photon scattering, while others are produced by secondary showers. The large PMT pulses in a neutrino telescope, produced by many photons with a significant fraction of them delayed, do not maintain a standard shape. Consequently, the charge estimation resolution deteriorates for larger pulses (large pulses correspond to large values of n in Stot(n)). However, in the lower amplitude domain, the estimation resolution is found to improve as the pulse amplitude increases, which is apparent in the Figure for pulses crossing up to the third threshold. This is due to the fact that when only the first three thresholds are crossed, the majority of the pulses are produced by a single photon.

In order to improve the efficiency of the m-ToT technique for higher (no standard shape) pulses, we pursued selection algorithms, based on the individual tot(i) values, in order to categorize the PMT pulses according to their shape. The most effective algorithm found utilizes the square root (henceforth called Dtot) of the difference of the squared values of tot(1) and the tot(imax), the latter corresponding to the higher crossed threshold level. Based on these studies, we defined four regions of Dtot values to classify pulses exceeding the 5th threshold and similarly four regions to classify pulses exceeding the 6th threshold level. Subsequently, we parameterized the true charge as a function of Stot for the large pulses categories described above.

The use of these new parameterizations in estimating the charge of large pulses improves substantially the resolution of the technique,  for the cases that five or six thresholds have been crossed, as shown by the asterisks in the next Figure.