Sub-diffraction limit focusing through a complex medium by virtual Fourier filtering

We have recently reported on a method to design at will the spatial profile of transmitted coherent light after propagation through a strongly scattering sample, exploiting wavefront shaping in combination with a transmission matrix approach. In this paper, we explore experimentally and theoretically the ability of this approach to generate foci whose full width at half maximum are smaller than the diffraction-limited speckle grain size, using (Bessels) beam variations implemented with virtual annular filters.