A holographic uniqueness theorem for the two-dimensional Helmholtz equation
Résumé
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 $\mathbb R^2$.
We consider a straight line in this region, such that the direction of propagation of the plane wave
is not parallel to this line.
We show that the radiation solution in the exterior region is uniquely determined by the intensity of
the total solution on an interval of this line.
In particular, this result solves one of the old mathematical questions of holography in its two-dimensional setting. Our proofs also contribute to the theory of the Karp expansion of radiation solutions in two dimensions.
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