Comment on "Characterization of an acoustic spherical cloak", Inverse Problems 31(3):035001, 2015

The paper [1] considers a spherical cloak described by three radially varying acoustical quantities. For a given radial mass density in the cloak the question posed is whether the remaining two parameters, tangential density and compressibility, are uniquely determined. A method is proposed in [1] to solve this inverse question based upon the solution of a Riemann-Hilbert problem involving spectral properties of a one-dimensional inhomogeneous Schr\"odinger equation. However, no constructive examples of the solution procedure are given. This comment provides explicit solutions for any radial mass density that conforms with the requirements of transformation acoustics [2]. A valid form of the compatibility condition [1, eq. (22)] for $n=0$ is derived.