Scattering compensation through Fourier-domain intensity coupling in two-photon microscopy

Light penetration depth in biological tissue is limited by tissue scattering. Correcting scattering becomes particularly challenging in scenarios with limited photon availability and when access to the transmission side of the scattering tissue is not possible. Here, we introduce a new two-photon microscopy system with Fourier-domain intensity coupling for scattering correction (2P-FOCUS). 2P-FOCUS corrects scattering by intensity modulation in the Fourier domain, leveraging the nonlinearity of multiple-beam interference and two-photon excitation, eliminating the need for a guide star, iterative optimization, or measuring transmission or reflection matrices. 2P-FOCUS uses random patterns to probe scattering properties, combined with a single-shot algorithm to rapidly generate the correction mask. 2P-FOCUS can also correct scattering beyond the limitation of the memory effect by automatically customizing correction masks for each subregion in a large field-of-view. We provide several proof-of-principle demonstrations here, including focusing and imaging through a bone sample, and imaging neurons and cerebral blood vessels in the mouse brain ex vivo. 2P-FOCUS significantly enhances two-photon fluorescence signals by several tens of folds compared to cases without scattering correction at the same excitation power. 2P-FOCUS can also correct tissue scattering over a 230x230x500 um\textsuperscript{3} volume, which is beyond the memory effect range. 2P-FOCUS is able to measure, calculate, and correct scattering within a few seconds, effectively delivering more light deep into the scattering tissue. 2P-FOCUS could be broadly adopted for deep tissue imaging owing to its powerful combination of effectiveness, speed, and cost.