The tomography of single-particle-resolved detectors is of primary importance for characterizing particle correlations, with applications in quantum metrology, quantum simulation, and quantum computing. However, it is a nontrivial task in practice due to the uncertainties on the statistics of the state impinging on the detector and to the unavoidable presence of noise that affects the measurement but does not originate from the detector. In this work, we address this problem for a three-dimensional single-atom-resolved detector where shot-to-shot atom-number fluctuations are a central issue in performing a quantum detector tomography. We overcome this difficulty by exploiting the parallel measurement of the counting statistics in subvolumes of the detector, from which we evaluate the effect of shot-to-shot fluctuations and perform a local tomography of the detector. In addition, we illustrate the validity of our method from applying it to Gaussian quantum states with different number statistics. Finally, we show that the response of microchannel plate detectors is well described by using a binomial distribution with the detection efficiency as a single parameter. Published by the American Physical Society 2024