Nonparametric inference of photon energy distribution from indirect measurement

We consider a density estimation problem arising in nuclear physics. Gamma photons are impinging on a semiconduc- tor detector, producing pulses of current. The integral of this pulse is equal to the total amount of charges created by the photon in the detector, which is linearly related to the photon energy. Be- cause the inter-arrival of photons can be shorter than the charge collection time, pulses associated to different photons may over- lap leading to a phenomenon known as pileup. The distortions on the photon energy spectrum estimate due to pileup becomes worst when the photon rate increases, making pileup correction techniques a must for high-counting rate experiments. In this pa- per, we present a novel technique to correct pileup, which extends a method introduced in Hall and Park (2004) for the estimation of the service time from the busy period in M/G/∞ models. It is based on a novel formula linking the joint distribution of the energy and duration of the cluster of pulses and the distribution of the energy of the photons. We then assess the performance of this estimator by providing an expression of its integrated square error. A limited Monte-Carlo experiment is presented to illustrate on practical examples the benefits of the pileup correction.

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