Abstract:We investigate phaseless inverse scattering problem for the Schrödinger equation and develop reconstruction methods based on the inverse Born series (IBS). We consider three types of phaseless data: the far-field total field, the total field and the far-field scattered field. For phaseless total-field data, we extend the IBS framework and analyze its radius of convergence. In the far-field setting, we propose a Fourier-based reconstruction method that exploits the scattering reciprocity between incident and observation directions to recover Fourier coefficients of the scattering potential. For phaseless scattered-field data, we employ a polarization-based approach to recover phase information and enable IBS reconstruction. Numerical experiments are conducted to validate the proposed methods.
| Subjects: | Mathematical Physics (math-ph) |
| Cite as: | arXiv:2605.23784 [math-ph] |
| (or arXiv:2605.23784v1 [math-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2605.23784 arXiv-issued DOI via DataCite (pending registration) |
From: John Schotland [view email]
[v1]
Fri, 22 May 2026 15:49:15 UTC (15,804 KB)
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