  A theory of correlations between N photons of given frequencies and detected
at given time delays is presented. These correlation functions are usually too
cumbersome to be computed explicitly. We show that they are obtained exactly
through intensity correlations between two-level sensors in the limit of their
vanishing coupling to the system. This allows the computation of correlation
functions hitherto unreachable. The uncertainties in time and frequency of the
detection, which are necessary variables to describe the system, are intrinsic
to the theory. We illustrate the formalism with the Jaynes--Cummings model,
showing how correlations of various peaks at zero or finite time delays bring
new insights into the dynamics of open quantum systems.
