Deep imaging inside scattering media through virtual spatiotemporal wavefront shaping

The multiple scattering of light makes materials opaque and obstructs imaging. Wavefront shaping can reverse the scattering process, but imaging with physical wavefront shaping has severe deficiencies such as requiring physical guidestars, limited within a small isoplanatic patch, restricted to planar targets outside the scattering media, and slow wavefront updates due to the hardware. Here, we introduce scattering matrix tomography (SMT): measure the hyperspectral scattering matrix of the sample, use it to digitally scan a synthesized confocal spatiotemporal focus and construct a volumetric image of the sample, and then use the synthesized image as many virtual guidestars to digitally optimize the pulse shape, input wavefront, and output wavefront to compensate for aberrations and scattering. The virtual feedback dispenses with physical guidestars and enables hardware-free spatiotemporal wavefront corrections across arbitrarily many isoplanatic patches. We demonstrate SMT with sub-micron diffraction-limited lateral resolution and one-micron bandwidth-limited axial resolution at one millimeter beneath ex vivo mouse brain tissue and inside a dense colloid, where all existing imaging methods fail due to the overwhelming multiple scattering. SMT translates imaging and wavefront shaping into a computational problem. It is noninvasive and label-free, provides multi-isoplanatic volumetric images inside and outside the scattering media, and can be applied to medical imaging, device inspection, biological science, and colloidal physics.