  The refractive index of a y-cut SiO$_2$ crystal surface is reconstructed from
polarization dependent soft X-ray reflectometry measurements in the energy
range from 45 eV to 620 eV. Due to the anisotropy of the crystal structure in
the (100) and (001) directions, we observe a significant deviation of the
measured reflectance at the Si-L$_{2,3}$ and O-K absorption edges. The
anisotropy in the optical constants reconstructed from these data is also
confirmed by ab initio Bethe-Salpeter Equation calculations of the O-K edge.
This new experimental dataset expands the existing literature data for quartz
optical constants significantly, particularly in the near-edge regions.
