Adaptive Optical Multi-Spectral Matrix Approach for Label-free High-resolution Imaging through Complex Scattering Media

Imaging through complex scattering media is severely limited by aberrations and scattering which obscure images and reduce resolution. Confocal and temporal gatings partly filter out multiple scattering but are severely degraded by wavefront distortions. Adaptive optics restore resolution by correcting low-order aberrations and matrix-based imaging enables more complex wavefront corrections. However, they struggle to undo high-order aberrations under strong scattering, preventing imaging at greater depths. To address these challenges, we present Scattering Matrix Tomography (SMT), an approach that makes full use of the wavefront engineering capability of scattering matrix and extreme adaptive optics. SMT reformulates imaging through complex media as a numerical optimization and employs Zernike-mode wavefront regularization and coarse-to-fine nonconvex optimization strategy to reverse severe aberrations, enabling noninvasive high-resolution volumetric imaging in multiple scattering regime. Based on the spectrally-resolved matrix measurement, SMT achieves a depth-over-resolution ratio above 900 beneath $ex~vivo$ mouse brain tissue and volumetric imaging at over three transport mean free paths inside an opaque colloid, where conventional methods fail to correct strong aberrations under these challenging conditions. SMT is noninvasive, label-free, and works both inside and outside the scattering media, making it suitable for various applications, including medical imaging, biological science, device inspection, and colloidal physics.