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As the muon density can vary between tens of muons per m<jats:sup>2<\/jats:sup> close to the intersection of the shower axis with the ground to much less than one per m<jats:sup>2<\/jats:sup> when far away, the necessary broad dynamic range is achieved by the simultaneous implementation of two acquisition modes in the read-out electronics: the binary mode, tuned to count single muons, and the ADC mode, suited to measure a high number of them. In this work, we present the end-to-end calibration of the muon detector modules: first, the SiPMs are calibrated by means of the binary channel, and then, the ADC channel is calibrated using atmospheric muons, detected in parallel to the shower data acquisition. The laboratory and field measurements performed to develop the implementation of the full calibration chain of both binary and ADC channels are presented and discussed. 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