  The exponential growth of photonic quantum technologies is driving the demand
of tools for measuring the quality of their information carriers. One of the
most prominent is Stimulated Emission Tomography (SET), which uses classical
coherent fields to measure the Joint Spectral Amplitude (JSA) of photon pairs
with high speed and resolution. While the modulus of the JSA can be directly
addressed from a single intensity measurement, the retrieval of the Joint
Spectral Phase (JSP) is far more challenging and received minor attentions.
However, a wide class of spontaneous sources of technological relevance, as
chip integrated micro-resonators, have a JSP with a rich structure, that
carries correlations hidden in the intensity domain. Here, using a compact and
reconfigurable silicon photonic chip, it is measured for the first time the
complex JSA of a micro-ring resonator photon pair source. The photonic circuit
coherently excites the ring and a reference waveguide, and the interferogram
formed by their stimulated fields is used to map the ring JSP through a novel
phase reconstruction technique. This tool complements the traditionally bulky
and sophisticated methods implemented so far, simultaneously minimizing the set
of required resources.
