The Tile Calorimeter (TileCal) is the central section of the ATLAS hadronic calorimeter at the Large Hadron Collider. This detector is instrumental for the measurements of hadrons, jets, tau leptons and missing transverse energy. Scintillation light produced in the tiles is transmitted by wavelength shifting fibers to photomultiplier tubes (PMTs). The resulting electronic signals from approximately 10000 PMTs are measured and digitized before being transferred to off-detector data-acquisition systems. After an initial setting of the absolute energy scale in test beams with particles of well-defined momentum, the calibrated scale is transferred to the rest of the detector via the response to radioactive sources. The calibrated scale is valid...