  Optical diffraction tomography (ODT) has emerged as a powerful label-free
three-dimensional (3D) bioimaging techniques for observing living cells and
thin tissue layers. We report a new reflection-mode ODT (rODT) method for
imaging thick biological specimens with 500 nm lateral resolution and 1 {\mu}m
axial resolution. In rODT, multiple scattering background is rejected through
spatio-temporal gating provided by dynamic speckle-field interferometry, while
depth-resolved refractive index maps are reconstructed by developing a
comprehensive inverse scattering model that also considers specimen-induced
aberration. Benefiting from the high-resolution and full-field quantitative
imaging capabilities of rODT, we succeeded in imaging red blood cells and
quantifying their membrane fluctuations behind a turbid sample with a thickness
of 2.8 scattering mean-free-paths. We further realized volumetric imaging of
cornea inside an ex vivo rat eye and quantified its optical properties,
including mapping the topography of Dua's and Descemet's membrane surfaces on
the nanometer scale.
