  Any characterization of a single-photon source is not complete without
specifying its second-order degree of coherence, i.e., its $g^{(2)}$ function.
An accurate measurement of such coherence functions commonly requires
high-precision single-photon detectors, in whose absence, only time-averaged
measurements are possible. It is not clear, however, how the resulting
time-averaged quantities can be used to properly characterize the source. In
this paper, we investigate this issue for a heralded source of single photons
that relies on continuous-wave parametric down-conversion. By accounting for
major shortcomings of the source and the detectors--i.e., the multiple-photon
emissions of the source, the time resolution of photodetectors, and our chosen
width of coincidence window--our theory enables us to infer the true source
properties from imperfect measurements. Our theoretical results are
corroborated by an experimental demonstration using a PPKTP crystal pumped by a
blue laser, that results in a single-photon generation rate about 1.2 millions
per second per milliwatt of pump power. This work takes an important step
toward the standardization of such heralded single-photon sources.
