  When building a parametric downconversion photon-pair source with spectrally
separable photons, e.g. for making high-purity heralded single photons, two
practical issues must be accounted for: the design of the experiment, and its
characterization. To address experiment design, we study the impact on spectral
separability of realistic (sech shaped and chirped) pump fields, realistic
nonlinear crystals with fabrication imperfections, and undesirable PDC
generation far from the central PMF peak coming from nonlinearity shaping
methods. To address experiment characterization, we study the effect of
discretization and spectral range of the measured bi-photon joint spectrum, the
difference between inferring separability from the joint spectral amplitude vs.
the joint spectral intensity, and advantages of interference experiments for
purity characterization over methods based on the joint spectral intensity.
This study will be of practical interest to researchers building the next
generation of nonlinear sources of separable photon pairs.
