Abstract
We study to determine the scattering source given certain knowledge of potential scatterer. In one-dimensional problem, the scattering matrix consists of entries of meromorphic functions. Comparing other methods in problems of compactly supported perturbation, we are able to precisely and quantitatively estimate the zeros and poles of each meromorphic entry. The size of potential support is connected to the zero density of scattered wave field. Assuming that the known part of potential is supported more significantly than the unknown part, the latter is uniquely determined from the magnitude of transmission coefficient which is the magnitude of certain Fourier transform of traveling wave. We show that recovering of the unknown perturbation is possible through single direction measurements under certain assumptions.
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