A holographic global uniqueness in passive imaging

Roman Novikov

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arXiv · 2405.10333

A holographic global uniqueness in passive imaging

Roman Novikov

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Abstract

We consider a radiation solution $\psi$ for the Helmholtz equation in an exterior region in $\mathbb R^3$. We show that the restriction of $\psi$ to any ray $L$ in the exterior region is uniquely determined by its imaginary part $\Im\psi$ on an interval of this ray. As a corollary, the restriction of $\psi$ to any plane $X$ in the exterior region is uniquely determined by $\Im\psi$ on an open domain in this plane. These results have holographic prototypes in the recent work Novikov (2024, Proc. Steklov Inst. Math. 325, 218-223). In particular, these and known results imply a holographic type global uniqueness in passive imaging and for the Gelfand-Krein-Levitan inverse problem (from boundary values of the spectral measure in the whole space) in the monochromatic case. Some other surfaces for measurements instead of the planes $X$ are also considered.

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Roman Novikov. 2024-05-12. A holographic global uniqueness in passive imaging. https://arxiv.org/abs/2405.10333

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