Here we present a reconstruction of the Positive Operator-Value Measurement of a photon-number-resolving detector comprised of three 50:50 beamsplitters in a tree configuration, terminated with four single-photon avalanche detectors. The four detectors' outputs are processed by an electronic board that discriminates detected photon number states from 0 to 4 and implements a "smart counting" routine to compensate for dead time issues at high count rates. c 2018 Optical Society of America OCIS codes: 270.0270, 270.5570, 270.5585.Photon-number-resolving (PNR) detectors [1, 2], i.e. photodetectors that can resolve the number of photons that are impinging on them, have achieved a critical role in a wide variety of research fields, ranging from quantum mechanics foundations experiments [3] to quantum metrology [4,5], imaging [6,7] and information [8,9]. As a consequence, a precise quantum characterization of these devices has become crucial [3][4][5][6][7][8][9][10][11]. In a quantum mechanical framework, a full operational description of a PNR device is its positive operator-valued measure (POVM), i.e. the set of operators Ξ n describing a physical process that leads to a particular measurement outcome n. A measurement of the elements of a detector's POVM can be quite non-trivial, because one has to carefully choose the best-suited technique for a tomographic reconstruction of the POVM of the device under test, depending on its particular properties [12][13][14][15][16][17][18].There exist different types of PNR detectors, e.g. photo-multiplier tubes [19,20] [28][29][30][31][32][33][34][35][36][37][38]. Some of those detector families hold a significant promise for future applications, even if their use at present is very difficult because of a large experimental overhead associated with their operation. On the other hand, even though traditional single-photon avalanche detectors (SPADs) are only capable to discriminate between zero and one (or more) detected photons, photon number resolution can be obtained by multiplexing those detectors spatially [39,40] or temporally [41][42][43][44]. At present, this solution is by far the easiest and cheapest way to achieve a photon number resolving capability, even though at a cost of sacrificing linearity due to detector saturation [45]. Here we present the POVM reconstruction of a multiplexed PNR detector (at 1550 nm) composed of four Indium/Gallium arsenide (InGaAs) SPADs connected to a beam-splitter (BS) tree made with three 50:50 fiber BSs. The output of the InGaAs SPADs is processed with a field-programmable gate array (FPGA) board, giving as output the detected photon number (up to 4 detected photons per pulse).Because this detector is not phase-sensitive, its POVM is diagonal in the Fock states basis:where the Ξ nm = m| Ξ n |m elements give the detector tree probability of counting n = 0, ..., 4 photons with m impinging photons per pulse. To reconstruct Ξ nm , we test the response of our device to a set of J coherent states. The response of our PNR detector to the j-th...