Statistical analysis and correction of the pile-up effect in MAPMT single photoelectron counting with the SPACIROC-3 ASIC: application to the Mini-EUSO experiment

TL;DR

The paper addresses pile-up caused by extended dead time ($\tau$) in SPACIROC-3 MAPMTs used for single-photon counting in Mini-EUSO. It develops a correction framework combining Monte Carlo simulations, renewal theory, and calibration experiments to map observed counts $N_{count}$ to true rates $\rho$, including uncertainty propagation via $\sigma_{\rho}$ and the Lambert $W$ function. A per-pixel dead-time estimator is built by analyzing long-term histograms with supervised ML, producing pixel-wise flux corrections. The corrected flux reconstruction improves measurements of transient UV phenomena (ELVES, meteors) and supports future JEM-EUSO missions.

Abstract

We present a comprehensive study addressing pile-up effects in single photoelectron counting with R-11265 Hamamatsu multi-anode photomultiplier tubes (MAPMTs) equipped with the SPACIROC-3 ASIC. Extended dead time in the electronics causes saturation and quenching of the counting rate, an effect we counter by inverting the pile-up plot once the double pulse resolution is determined. Our work combines extensive numerical simulations with experimental validations to quantify the statistical uncertainties associated with the corrected event rates. We apply this methodology to the Mini-EUSO experiment onboard the International Space Station where machine learning techniques are employed to extract pixel-by-pixel double pulse resolutions from long-term photon count histograms. This integrated approach enables the accurate recovery of true photon fluxes essential for studying ELVES, meteors and other transient phenomena detected by Mini-EUSO.

Figures (6)

• Figure 1: Left: pile-up plot showing the number of occurrences (color code) of a given photon count (in ordinate) as a function of the photon rate (in abscissa), for a three different values of the double pulse resolution $\tau$. The solid lines show the average $\langle N_\mathrm{count}\rangle(\rho)$, also known as the pile-up curve or saturation curve. Right: example of histograms obtained from vertical (blue) and horizontal (red) cuts of a pile-up plot corresponding to $\tau = 10$ ns and $T = 2500$ ns.
• Figure 2: Left : Fit of the experimental $\langle N_\mathrm{count}\rangle(\rho)$ with eq.(\ref{['eq:N_expected']}), multiplying $\rho$ by a quantum efficiency $\epsilon_{\mathrm{quantum}}$ (to convert electron into photoélectron), yielding $\tau = 12.3$ ns and $\epsilon_\mathrm{quantum} = 0.32$. Right : comparison of the experimental $\sigma_\mathrm{count}(\rho)$ with its expected shape from eq.(\ref{['eq:sigma_N']}) for the fit parameters yielded by the fit of the average. Both experimental data were obtained from a lightscan on a single channel of an MAPMT connected to a SPACIROC3-ASIC working at a GTU of 2500 ns.
• Figure 3: Comparison of $\sigma_\mathrm{count}(\rho)$ obtained from renewal theory (blue line), Monte Carlo simulation (black line), and a lightscan (red line). Both the simulated and theoretical curves assume the same fixed dead time $\tau = 12.3$ ns and a quantum efficiency of $\epsilon_{\mathrm{quantum}} = 0.32$, both obtained from the fit of the experimental data. All curves are drawn for a GTU of 2500ns.
• Figure 4: Left and Center : simulated count histograms showing the index of the secondary bump for two different $\tau$ and a GTU of 2500ns. Right : Fitted dead time values as a function of the secondary bump index of the simulated histograms.
• Figure 5: Prediction of the secondary bump index by the Random Forest Regressor model for two Mini-EUSO pixel's count histograms. The histograms are build from the data of sessions 20 to 44 and corresponds to the pixel (32,32) and (38,3) of the focal surface.