A holographic global uniqueness in passive imaging
Résumé
We consider a radiation solution psi for the Helmholtz equation in an exterior region in 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, arXiv:2310.11127].
In particular, these and known results imply a holographic type global uniqueness in passive imaging and for the
Gelfand-Krein-Levitan inverse problem in the monochromatic case.
Some other surfaces for measurements instead of the planes X are also considered.
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