  We developed a microscopy technique that can measure the local refractive
index without sampling the optical phase delay of the electromagnetic
radiation. To do this, we designed and experimentally demonstrated a setup with
two co-localized Brillouin scattering interactions that couple to a common
acoustic phonon axis; in this scenario, the ratio of Brillouin frequency shifts
depends on the refractive index, but not on any other mechanical and/or optical
properties of the sample. Integrating the spectral measurement within a
confocal microscope, the refractive index is mapped at micron-scale
three-dimensional resolution. As the refractive index is probed in
epi-detection and without assumptions on the geometrical dimensions of the
sample, this method may prove useful to characterize biological cells and
tissues.
