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Spatial light interference microscopy (SLIM) is a novel method developed in our laboratory that provides quantitative phase images of transparent structures with a 0.3 nm spatial and 0.03 nm temporal accuracy owing to the white light illumination and its common path interferometric geometry. We exploit these features and demonstrate SLIM's ability to perform topography at a single atomic layer in graphene. Further, using a decoupling procedure that we developed for cylindrical structures, we extract the axially averaged refractive index of semiconductor nanotubes and a neurite of a live hippocampal neuron in culture. We believe that this study will set the basis for novel high-throughput topography and refractometry of man-made and biological nanostructures.