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We report a method to design at will the spatial profile of transmittedcoherent light after propagation through a scattering sample. We compute anoperator based on the experimentally measured transmission matrix, obtained bynumerically adding an arbitrary mask in the Fourier domain prior to focusing.We demonstrate the strength of the technique through several examples:propagating Bessel beams, thus generating foci smaller than the diffractionlimited speckle grain, donut beams, and helical beams. We characterize the 3Dprofile of the achieved foci and analyze the fundamental limitations of thetechnique. Our approach generalizes Fourier optics concepts for random media,and opens in particular interesting perspectives for super-resolution imagingthrough turbid media.

Transmission-matrix-based point-spread-function engineering through a complex medium