  We present a complete method to characterize multiphoton detectors with a
small overall detection efficiency. We do this by separating the nonlinear
action of the multiphoton detection event from linear losses in the detector.
Such a characterization is a necessary step for quantum information protocols
with single and multiphoton detectors and can provide quantitative information
to understand the underlying physics of a given detector. This characterization
is applied to a superconducting multiphoton nanodetector, consisting of an NbN
nanowire with a bowtie-shaped subwavelength constriction. Depending on the bias
current, this detector has regimes with single and multiphoton sensitivity. We
present the first full experimental characterization of such a detector.
