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arXiv · 1703.03742

The phase retrieval problem for solutions of the Helmholtz equation

Philippe Jaming·Salvador Pérez-Esteva
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Abstract

In this paper we consider the phase retrieval problem for Herglotz functions, that is, solutions of the Helmholtz equation $Δu+λ^2u=0$ on domains $Ω\subset\mathbb{R}^d$, $d\geq2$. In dimension $d=2$, if $u,v$ are two such solutions then $|u|=|v|$ implies that either $u=cv$ or $u=c\bar v$ for some $c\in\mathbb{C}$ with $|c|=1$. In dimension $d\geq3$, the same conclusion holds under some restriction on $u$ and $v$: either they are real valued or zonal functions or have non vanishing mean.

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Philippe Jaming, Salvador Pérez-Esteva. 2017-03-10. The phase retrieval problem for solutions of the Helmholtz equation. https://doi.org/10.1088/1361-6420%2Faa8640

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