Abstract:
The plane wave, the radiation solution, and the sum of these solutions (the complete solution) for the Helmholtz equation in the outer domain in R^3 are considered. For a beam in this region such that its direction differs from the direction of propagation of a plane wave, it is shown that the limitation of the radiation solution to this beam is uniquely determined by the intensity of the complete solution at an arbitrary interval of this beam. As a consequence, it is also established that the limitation of the radiation solution to any plane in the outer region is uniquely determined by the intensity of the complete solution on an arbitrary open area in this plane. In particular, these results solve one of the old mathematical questions of holography. The report will also present further results, including applications to the inverse scattering problem without phase information.
|
