The optical response of NbTiN superconducting single photon detectors is studied using quantum detector tomography which separates the detector response in single and multiple photon contributions. Three different NbTiN nanodetectors of 70, 100 and 150 nm width are compared based on their detector tomography curves. The energy dependent photon response for the 100 nm nanodetector at two different wavelengths is explored. The detectors present a non-linear behaviour, which complicates the comparison. For the first time, we find that tomography curves saturate above a certain bias current and we compare the current density required to achieve the single photon regime.