  We consider a class of one-dimensional nonlinear Schr\"odinger equations of
the form \[ (i\partial_t+\Delta)u = [1+a]|u|^2 u. \] For suitable localized
functions $a$, such equations admit a small-data modified scattering theory,
which incorporates the standard logarithmic phase correction. In this work, we
prove that the small-data modified scattering behavior uniquely determines the
inhomogeneity $a$.
