A long-standing goal in biomedical imaging, the control of light inside turbid media, requires knowledge of how the phase and amplitude of an illuminating wavefront are transformed as the electric field propagates inside a scattering sample onto a target plane. So far, it has proved challenging to non-invasively characterize the scattered optical wavefront inside a disordered medium. Here, we present a non-invasive scattering compensation method, termed F-SHARP, which allows us to measure the scattered electric-field point spread function (E-field PSF) in three dimensions. Knowledge of the phase and amplitude of the E-field PSF makes it possible to optically cancel sample turbulence. We demonstrate the imaging capabilities of this technique on a variety of samples and notably through vertebrate brains and across thinned skull in vivo.
