Focusing of light by random scattering

Random scattering of light is what makes materials such as white paint, clouds and biological tissue opaque. We show that although light propagating in these media is diffuse, a high degree of control is possible as phase information is not irreversibly lost. Opaque objects such as eggshell or white paint focus coherent light as sharply as a lens when illuminated with a wavefront that inverts the wave diffusion. We demonstrate the construction of such wavefronts using feedback, achieving a focus that is 1000 times brighter than the diffusely transmitted light. Our results are explained quantitatively by a universal relation based on statistical optics.