  Here we show how time-resolved broadband optical spectroscopy can be used to
quantify, with femtometer resolution, the oscillation amplitudes of coherent
phonons through a displacive model without free tuning parameters, except an
overall scaling factor determined by comparison between experimental data and
density functional theory calculations. $WTe_2$ is used to benchmark this
approach. In this semimetal, the response is anisotropic and provides the
spectral fingerprints of two $A_1$ optical phonons at $\sim$8 and $\sim$80
$cm^-$$^1$. In principle, this methodology can be extended to any material in
which an ultrafast excitation triggers coherent lattice modes modulating the
high-energy optical properties.
