The innovative Barrel DIRC (Detection of Internally Reflected Cherenkov light) counter will provide hadronic particle identification (PID) in the central region of the PANDA experiment at the new Facility for Antiproton and Ion Research (FAIR), Darmstadt, Germany. This detector is designed to separate charged pions and kaons with at least 3 standard deviations for momenta up to 3.5 GeV/c, covering the polar angle range of 22$^{circ}$-140$^{circ}$. An array of microchannel plate photomultiplier tubes is used to detect the location and arrival time of the Cherenkov photons with a position resolution of 2 mm and time precision of about 100 ps. The time imaging reconstruction has been developed to make optimum use of the observables and to determine the performance of the detector. This reconstruction algorithm performs particle identification by directly calculating the maximum likelihoods using probability density functions based on detected photon propagation time in each pixel, determined directly from the data, or analytically, or from detailed simulations.
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