  We present a Coherent X-ray Diffraction study of the antiferrodistortive
displacive transition of SrTiO$_3$, a prototypical example of a phase
transition for which the critical fluctuations exhibit two length scales and
two time scales. From the microbeam x-ray coherent diffraction patterns, we
show that the broad (short-length scale) and the narrow (long-length scale)
components can be spatially disentangled, due to 100 $\mu$m-scale spatial
variations of the latter. Moreover, both components exhibit a speckle pattern,
which is static on a $\sim$10 mn time-scale. This gives evidence that the
narrow component corresponds to static ordered domains. We interpret the
speckles in the broad component as due to a very slow dynamical process,
corresponding to the well-known \emph{central} peak seen in inelastic neutron
scattering.
