Wawefront shaping can overcome light scattering to focus deep inside turbid media, but it typically requires feedback from guidestars and is restricted by the isoplanatic patch size and modulation speed. Here, we present scattering matrix tomography (SMT) that uses the measured scattering matrix to perform virtual spatiotemporal wavefront shaping, with a digitally scanned confocal spatiotemporal focus and guidestar-free wavefront optimization for every isoplanatic patch. We experimentally use SMT to achieve diffraction-limited resolution behind one-millimeter-thick ex-vivo mouse brain tissue which reduces the target signal by over ten million-fold. We also realize 3D tomography with ideal transverse and axial resolutions inside a dense colloid, where conventional imaging methods fail due to multiple scattering, across a large depth of field of over 70 times the Rayleigh range.
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