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

The ATLAS liquid Argon electromagnetic calorimeter provides multiply-sampled digitised 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 signal emerging from the front-end electronics. Each read-out channel can be calibrated by means of electronic pulsers that mimic the ionisation signal produced by an electromagnetic shower. However, the calibration signal differs from the ionisation one, because the injected current pulses are different in shape (exponential/triangular, respectively) and injection point (at the detector end/inside the detector). In order to perform a correct cell equalisation, the ionisation signal shape must have the correct normalisation 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 ionisation signal solely from 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 ionisation current. The performance of the algorithms has been tested on the electron test-beam data taken from an ATLAS liquid Argon electromagnetic calorimeter production module, demonstrating the ability to predict ionisation 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 better than 0.4%, which fulfill the ATLAS performance requirements