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Multipoint Formulas for Phase Recovering from Phaseless Scattering Data

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Abstract

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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Acknowledgements

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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  1. CMAP, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91128, Palaiseau, France

    R. G. Novikov

  2. IEPT RAS, Moscow, Russia, 117997

    R. G. Novikov

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  1. R. G. Novikov
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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). https://doi.org/10.1007/s12220-019-00329-6

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  • DOI: https://doi.org/10.1007/s12220-019-00329-6

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