Focusing through random media: Eigenchannel participation number and intensity correlation

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 ₍=1+N₄₅₅, where N₄₅₅ is the eigenchannel participation number for the transmission matrix. For diffusive waves, N₄₅₅ is the inverse of the degree of intensity correlation. 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 () and. These results are demonstrated in microwave experiments and provide the parameters for optimal focusing and the limits of imaging.