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The paper [1] considers a spherical cloak described by three radially varyingacoustical quantities. For a given radial mass density in the cloak thequestion posed is whether the remaining two parameters, tangential density andcompressibility, are uniquely determined. A method is proposed in [1] to solvethis inverse question based upon the solution of a Riemann-Hilbert probleminvolving spectral properties of a one-dimensional inhomogeneous Schr\"odingerequation. However, no constructive examples of the solution procedure aregiven. This comment provides explicit solutions for any radial mass densitythat conforms with the requirements of transformation acoustics [2]. A validform of the compatibility condition [1, eq. (22)] for $n=0$ is derived.

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