Multipoint Formulas for Phase Recovering from Phaseless Scattering Data


We give formulas for phase recovering from appropriate monochromatic phaseless scattering data at 2n points in dimension \(d=3\) and in dimension \(d=2\). These formulas are recurrent and explicit and their precision is proportional to n. By this result we continue studies of Novikov (Bulletin des Sciences Mathématiques 139(8):923–936, 2015), where formulas of such a type were given for \(n=1\), \(d\ge 2\).

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The author thanks B. Berndtsson and M. V. Klibanov for remarks on results of [12, 14], which stimulated studies of the present work.

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Correspondence to R. G. Novikov.

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Novikov, R.G. Multipoint Formulas for Phase Recovering from Phaseless Scattering Data. J Geom Anal 31, 1965–1991 (2021).

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  • Schrödinger equation
  • Helmholtz equation
  • Monochromatic scattering data
  • Phase recovering
  • Phaseless inverse scattering

Mathematics Subject Classification

  • 35J10
  • 35P25
  • 35R30
  • 81U40