  We investigate the nonlinear refraction induced by Rydberg excitons in
$\mathrm{Cu_2O}$. Using a high-precision interferometry imaging technique that
spatially resolves the nonlinear phase shift, we observe significant shifts at
extremely low laser intensity near each exciton resonance. From this, we derive
the nonlinear index $\mathrm{n_2}$, present the $\mathrm{n_2}$ spectrum for
$n\geq 5$ and report large $\mathrm{n_2}$ values of order $10^{-3}$ mm$^2$/mW.
Moreover, we observe a rapid saturation of the Kerr nonlinearity and find that
the saturation intensity $\mathrm{I_{sat}}$ decreases as $n^{-7}$. We explain
this with the Rydberg blockade mechanism, whereby giant Rydberg interactions
limit the exciton density, resulting in a maximum phase shift of 0.5 rad in our
setup.
