  We consider the solution of a scalar Helmholtz equation where the potential
(or index) takes two positive values, one inside a disk of radius $\epsilon$
and another one outside. We derive sharp estimates of the size of the scattered
field caused by this disk inhomogeneity, for any frequencies and any contrast.
We also provide a broadband estimate, that is, a uniform bound for the
scattered field for any contrast, and any frequencies outside of a set which
tend to zero with $\epsilon$.
