Spatiotemporal Grouping of Photons in Spontaneous Parametric Scattering of Light. A. A. Malygin, A. N. Penin and A. V. Sergienko in Sov. Phys. Dokl. 30:227 (1985). What the paper says!?
This is, according to Jost et al.[1], the first spatial imaging of SPDC correlated photon pairs (here they call it "PSL" for "parametric scattering of light"). They, in turn, refer to Klyshko[2] for the probability of detecting the two parametric photons:[3]
Here $\rho\equiv|\vec\rho_1-\vec\rho_2|$ is the transverse distance, which they break later into a radial $\rho$ and azimuthal $y$ component.
The «spatial (transverse) and temporal (longitudinal)» aspect is a nice spacetime viewpoint, and indeed, both are measured (time in Fig. 2, space in Fig. 3, even frequency in Fig. 4).
They map emission angle—and therefore momentum, and therefore frequency—to radius in the back focal plane ($\rho=F\tan\vartheta$). Therefore, each frequency lands on its own ring and the whole emission becomes a set of concentric coloured rings. Momentum conservation $k_0=k_1+k_2$ then places the two photons of a pair diametrically opposite on the ring. And only there, so in contrast to our correlations in vortices, here the SPDC structure restricts the correlations very much.
The state of the art at the time:
Ref. 7 (Klyshko[2]) is a must-read as it contains the theory (and first prediction, apparently) of spatial correlations.
Their setup at the time:
The boxes on the right are an abstract way to sketch the HBT correlation setup. They measured them by scanning the detector.
They confirm the expected correlations, with beautiful figures:
Here only the spatial case is shown. The top curves are one-photon observables, the curves below are two-photon coincidences. The perpendicular curves of the right panel shows that one looses correlations in all the directions. The left panel is radial only but for different diameters, showing that different frequencies (different rings) are correlated with different radii.
They also show (with unfortunate notations, their $g^{(2)}$ is not $g^{(2)}$) that the amount of pairs in the signal is close to 100%: all the emission is correlated.
A very nice, early demonstration of spatial (in fact, spatio-temporal) SPDC correlations, through heroic scanning at point at a time!