Cell response equalisation of the ATLAS electromagnetic calorimeter without the direct knowledge of the ionisation signals

The ATLAS LAr EM calorimeter provides multiply-sampled digitized signals with a frequency of 40~MHz. The signal amplitude is reconstructed from the samples using a digital filtering technique; the computation of the digital filter weights requires the precise knowledge of the shape of the outcoming ionization pulse. Each read-out channel can be calibrated by means of electronic pulsers, that mimic the ionization signal produced by an EM shower. However, the outcoming calibration signal differs from the ionization one, because the injected current pulses are differ in shape (exponential/triangular, respectively) and injection point (at the detector end/inside the detector). In order to perform a correct cell equalization, the ionization signal shape must have the correct normalization with respect to the calibration pulse used to compute the actual electronic gain of each channel, thus taking into account the mentioned differences. This document describes a set of algorithms developed to predict the ionization signal with the only knowledge of the information contained in the corresponding calibration pulse. The advantage of this approach is that the proper gain of each channel and the corrections for the electrical properties of each cell can be directly inferred and then embedded in the digital filtering reconstruction, without any direct knowledge of the response of the cell to the shower-induced ionization current. The performance of the algorithms has been tested on the electron test-beam data taken from an ATLAS LAr EM calorimeter production module, demonstrating the ability to predict ionization pulse shapes in agreement with the observed ones to better than 1% (0.2% at the peak). The digital filtering weights have been applied to reconstruct the energy of 245 GeV electrons with an energy resolution of 0.8% and a response uniformity of 0.4%, which fulfill the ATLAS performance requirements.