  Entangled photons generated by spontaneous parametric down conversion inside
a nonlinear crystal exhibit a complex spatial photon count distribution. A
quantitative description of this distribution helps with the interpretation of
experiments that depend on this structure. We developed a theoretical model and
an accompanying numerical calculation that includes the effects of phase
matching and the crystal properties to describe a wide range of spatial effects
in two-photon experiments. The numerical calculation was tested against
selected analytical approximations. We furthermore performed a double-slit
experiment where we measured the visibility V and the distinguishability D and
obtained $D^2 + V^2 = 1.43$. The numerical model accurately predicts these
experimental results.
