When light passes through a disordered medium, its wavefront is scrambled, resulting in a seemingly random speckle pattern. In the multiple scattering regime, it is commonly assumed that this randomization removes any memory about the original wavefront, effectively destroying all its information content. But as linear elastic scattering is a purely deterministic process, information is not destroyed, but just hidden and redistributed within these patterns. We present an experimental observation of the correlations between reflected and transmitted speckle patterns, which indicate that information can survive even very strong scattering. We show that there are two distinct contributions to the correlation function - a narrow positive peak and a broad negative dip, which depend in a different way on the system parameters. We study the dependence of this correlation on the thickness of the scattering medium and the mean free path of the light in the sample, probing different regimes from ballistic to diffusive scattering. We propose an experimental procedure, based on the ghost imaging technique, that allows to use this correlation for imaging of the objects hidden behind the scattering media.
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