# Fixed-distance multipoint formulas for the scattering amplitude from phaseless measurements

Abstract : 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].
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https://hal.archives-ouvertes.fr/hal-03263803
Submitted on : Thursday, June 17, 2021 - 3:38:36 PM
Last modification on : Saturday, June 19, 2021 - 4:06:35 AM

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Multipoint recovering.pdf
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• HAL Id : hal-03263803, version 1

### Citation

Roman Novikov, Vladimir Sivkin. Fixed-distance multipoint formulas for the scattering amplitude from phaseless measurements. 2021. ⟨hal-03263803⟩

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