  We show that intensity of a wave created by a source embedded inside a
three-dimensional disordered medium exhibits a non-universal space-time
correlation which depends explicitly on the short-distance properties of
disorder, source size, and dynamics of disorder in the immediate neighborhood
of the source. This correlation has an infinite spatial range and is
long-ranged in time. We suggest that a technique of "diffuse microscopy" might
be developed employing spatially-selective sensitivity of the considered
correlation to the disorder properties.
