An Inverse Uniqueness of a Phaseless Scattering Problem by Zero-Crossings

We discuss the inverse uniqueness problem in phaseless scattering by counting the zeros of its modulus of the scattering amplitude. The phase linearization of scattered wave field disturbs the originally uniform distribution of the zero set. There is a connection between the perturbation of the index of refraction and the zero distribution of the modulus. We conclude the inverse uniqueness of the phaseless problem from the point of view of interior transmission problem.