  As a tutorial to the spatial aspects of Spontaneous Parametric Downconversion
(SPDC), we present a detailed first-principles derivation of the transverse
correlation width of photon pairs in degenerate collinear SPDC. This width
defines the size of a biphoton birth zone, the region where the signal and
idler photons are likely to be found when conditioning on the position of the
destroyed pump photon. Along the way, we discuss the quantum-optical
calculation of the amplitude for the SPDC process, as well as its simplified
form for nearly collinear degenerate phase matching. Following this, we show
how this biphoton amplitude can be approximated with a Double-Gaussian
wavefunction, and give a brief discussion of the measurement statistics (and
subsequent convenience) of such Double-Gaussian wavefunctions. Next, we use
this approximation to get a simplified estimation of the transverse correlation
width, and compare it to more accurate calculations as well as experimental
results. We then conclude with a discussion of the concept of a biphoton birth
zone, using it to develop intuition for the tradeoff between the first-order
spatial coherence and bipohoton correlations in SPDC.
