A two-point phase recovering from holographic data on a single plane

2025/09/26 by Novikov, Roman, Sivkin, Vladimir
#Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2509.22048

Abstract

We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for the Helmholtz equation in an exterior region in ℝ^d, d≥ 2. In this region, we consider a hyperplane X with sufficiently large distance s from the origin in \mathbb R^d. We give two-point local formulas for approximate recovering the radiation solution restricted to the plane X from the intensity of the total solution at X, that is, from holographic data. The recovering is given in terms of the far-field pattern of the radiation solution with a decaying error term as s → +∞. A numerical implementation is also presented.

Citations

• Inverse scattering for the multipoint potentials of Bethe-Peierls-Thomas-Fermi type
• A holographic uniqueness theorem for the two-dimensional Helmholtz equation
• A holographic uniqueness theorem
• A numerical method to solve a phaseless coefficient inverse problem from a single measurement of experimental data
• Reconstruction procedures for two inverse scattering problems without\n the phase information
• Formulas for phase recovering from phaseless scattering data at fixed\n frequency

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