  Light penetration depth in biological tissue is limited by tissue scattering.
There is an urgent need for scattering compensation in vivo focusing and
imaging, particularly challenging in photon-starved scenarios, without access
to the transmission side of the scattering tissue. Here, we introduce a
two-photon microscopy system with Fourier-domain open-channel coupling for
scattering correction (2P-FOCUS). 2P-FOCUS corrects scattering by utilizing the
non-linearity of multiple-beam interference and two-photon excitation,
eliminating the need for a guide star, iterative optimization, or measuring
transmission or reflection matrices. We demonstrate that 2P-FOCUS significantly
enhances two-photon fluorescence signals by several tens of folds when focusing
through a bone sample, compared to cases without scattering compensation at
equivalent excitation power. We also show that 2P-FOCUS can correct scattering
over large volumes by imaging neurons and cerebral blood vessels within a
230x230x500 um\textsuperscript{3} volume in the mouse brain in vitro. 2P-FOCUS
could serve as a powerful tool for deep tissue imaging in bulky organisms or
live animals.
