  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 non-trivial task in
practice due 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 to perform a quantum detector
tomography. We overcome this difficulty by exploiting the parallel measurement
of counting statistics in sub-volumes 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 Micro-Channel Plate detectors is well-described from
using a binomial distribution with the detection efficiency as a single
parameter.
