Momentum selection for enhanced adaptive focusing through semi-transparent media

Adaptive optics can focus light through opaque media by compensating the random phase delay acquired while crossing a scattering curtain. The technique is commonly exploited in many fields, including astrophysics, microscopy, biomedicine and biology. A turbid lens has the capability of producing foci with a resolution higher than conventional optics, however it has a fundamental limit: to obtain a sharp focus one has to introduce a strongly scattering medium in the optical path. Indeed a tight focusing needs strong scattering and, as a consequence, high resolution focusing is obtained only for weakly transmitting samples. Here we disclose an unprecedented phenomenon which allows to obtain highly concentrated optical spots even by introducing a minimum amount of scattering in the beam path that is with semi-transparent materials. By filtering the pseudo-ballistic components of the transmitted beam we are able to experimentally overcome the limits of the adaptive focus resolution, gathering light on a spot with a diameter which is one third of the original speckle grain.