  The ability to determine the joint spectral properties of photon pairs
produced by the processes of spontaneous parametric downconversion (SPDC) and
spontaneous four wave mixing (SFWM) is crucial for guaranteeing the usability
of heralded single photons and polarization-entangled pairs for multi-photon
protocols. In this paper, we compare six different techniques that yield either
a characterization of the joint spectral intensity or of the closely-related
purity of heralded single photons. These six techniques include: i) scanning
monochromator measurements, ii) a variant of Fourier transform spectroscopy
designed to extract the desired information exploiting a resource-optimized
technique, iii) dispersive fibre spectroscopy, iv) stimulated-emission-based
measurement, v) measurement of the second-order correlation function $g^{(2)}$
for one of the two photons, and vi) two-source Hong-Ou-Mandel interferometry.
We discuss the relative performance of these techniques for the specific cases
of a SPDC source designed to be factorable and SFWM sources of varying purity,
and compare the techniques' relative advantages and disadvantages.
