  We present a theoretical and experimental analysis of the joint effects of
the transverse electric field distribution and of the nonlinear crystal
characteristics on the properties of photon pairs generated by spontaneous
parametric downconversion (SPDC). While it is known that for a sufficiently
short crystal the pump electric field distribution fully determines the joint
signal-idler properties, for longer crystals the nonlinear crystal properties
also play an important role. In this paper we present experimental measurements
of the angular spectrum (AS) and of the conditional angular spectrum (CAS) of
photon pairs produced by spontaneous parametric downconversion (SPDC), carried
out through spatially-resolved photon counting. In our experiment we control
whether or not the source operates in the short-crystal regime through the
degree of pump focusing, and explicitly show how the AS and CAS measurements
differ in these two regimes. Our theory provides an understanding of the
boundary between these two regimes and also predicts the corresponding
differing behaviors.
