Reflection-mode diffraction tomography of multiple-scattering samples on a reflective substrate from intensity images

We introduce a novel reflection-mode diffraction tomography technique that enables simultaneous recovery of forward and backward scattering information for high-resolution 3D refractive index reconstruction. Our technique works by imaging a sample on a highly reflective substrate and employing a novel multiple-scattering model and reconstruction algorithm. It combines the modified Born series as the forward model, Bloch and perfect electric conductor boundary conditions to handle oblique incidence and substrate reflections, and the adjoint method for efficient gradient computation in solving the inverse-scattering problem. We validate the technique through simulations and experiments, achieving accurate reconstructions in samples with high refractive index contrasts and complex geometries. Forward scattering captures smooth axial features, while backward scattering reveals complementary interfacial details. Experimental results on dual-layer resolution targets, 3D randomly distributed beads, phase structures obscured by highly scattering fibers, fixed breast cancer cells, and fixed \emph{C. elegans} demonstrate its robustness and versatility. This technique holds promise for applications in semiconductor metrology and biomedical imaging.