In this article, a new method is discussed for the calibration and monitoring of photomultiplier tubes (PMTs). This method is based on a Discrete Fourier Transform (DFT) and it is fast and general so that it can be used in cases where an analytical model of the PMT response is not available. The DFT approach is employed for the absolute calibration of the Hamamatsu R1408 photomultiplier tube. It should be noted that the R1408 PMTs do not show a sharp peak at the single photoelectron distribution and gain determination via conventional methods is often unattainable. Here, we show that the DFT technique, coupled with a gamma function model for the single photoelectron response, produces rigorous calibration results and it can be used for gain determination with a good accuracy.
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