Noninvasive nonlinear focusing and imaging through strongly scattering turbid layers

Diffraction-limited imaging through complex scattering media is a long sought after goal with important applications in biomedical research. In recent years, high resolution wavefront-shaping has emerged as a powerful approach to generate a sharp focus through highly scattering, visually opaque samples. However, it requires a localized feedback signal from the target point of interest, which necessitates an invasive procedure in all-optical techniques. Here, we show that by exploiting optical nonlinearities, a diffraction-limited focus can be formed inside or through a complex sample, even when the feedback signal is not localized. We prove our approach theoretically and numerically, and experimentally demonstrate it with a two-photon fluorescence signal through highly scattering biological samples. We use the formed focus to perform two-photon microscopy through highly scattering, visually opaque layers.