Fixed-distance multipoint formulas for the scattering amplitude from phaseless measurements
Résumé
We give explicit formulas for finding the complex (phased) scattering amplitude at fixed frequency and angles from absolute values of the scattering wave function given at 2n points in dimension d = 3, where distances between these points are fixed and satisfy a multiplicity condition. These formulas are asymptotic and their convergence rate is proportional to n. Our further results include: similar 2n point formulas without the aforementioned multiplicity condition in dimension d = 3 and in dimension d = 2 for the linearised case; related multipoint formulas without the multiplicity condition in dimension d = 3 and in dimension d = 2 for the general non-linearised case, but with somewhat more slow convergence. In particular, we continue studies going back to [Novikov, Bull. Sci. Math. 139(8), 923-936, 2015].
Origine : Fichiers produits par l'(les) auteur(s)