  In this work we propose and analyse a scheme where the full spatio-temporal
correlation of twin photons/beams generated by parametric down-conversion is
detected by using its inverse process, i.e. sum frequency generation. Our main
result is that, by imposing independently a temporal delay \Delta t and a
transverse spatial shift \Delta x between two twin components of PDC light, the
up-converted light intensity provides information on the correlation of the PDC
light in the full spatio-temporal domain, and should enable the reconstruction
of the peculiar X-shaped structure of the correlation predicted in
[gatti2009,caspani2010,brambilla2010]. Through both a semi-analytical and a
numerical modeling of the proposed optical system, we analyse the feasibility
of the experiment and identify the best conditions to implement it. In
particular, the tolerance of the phase-sensitive measurement against the
presence of dispersive elements, imperfect imaging conditions and possible
misalignments of the two crystals is evaluated.
