  Using random matrix calculations, we show that, the contrast between
maximally focused intensity through random media and the background of the
transmitted speckle pattern for diffusive waves is, \mu_N =1 +N_{eff}, where N
eff is the eigenchannel participation number for the transmission matrix. For
diffusive waves, N_{eff} is the inverse of the degree of intensity correlation,
\kappa. The profile of the focused beam relative to the ensemble average
intensity is expressed in terms of the square of the normalized spatial field
correlation function, F(\Delta r), and \kappa. These results are demonstrated
in microwaves experiments and provide the parameters for optimal focusing and
the limits of imaging.
