Wavefront shaping to improve beam quality: converting a speckle pattern into a Gaussian spot

A perfectly collimated beam can be spread out by multiple scattering, creating a speckle pattern and increasing the etendue of the system. Standard optical systems conserve etendue, and thus are unable to reverse the process by transforming a speckle pattern into a collimated beam or, equivalently, into a sharp focus. Wavefront shaping is a technique that is able to manipulate the amplitude and/or phase of a light beam, thus controlling its propagation through such media. Wavefront shaping can thus break the conservation of etendue and, in principle, reduce it. In this work we study how much of the energy contained in a fully developed speckle pattern can be converted into a high quality (low M (2)) beam, we support it with a theoretical framework and discuss the advantages and limitations of this approach.