  Quasiparticle interference (QPI) patterns in momentum space are often assumed
to be independent of the strength of the impurity potential when compared with
other quantities, such as the joint density of states. Here, using the
$T$-matrix theory, we show that this assumption breaks down completely even in
the simplest case of a single-site impurity on the square lattice with an $s$
orbital per site. Then, we predict from first-principles, a very rich,
impurity-strength-dependent structure in the QPI pattern of TaAs, an archetype
Weyl semimetal. This study thus demonstrates that the consideration of the
details of the scattering impurity including the impurity strength is essential
for interpreting Fourier-transform scanning tunneling spectroscopy experiments
in general.
