A phaseless inverse scattering problem for the 3-D Helmholtz equation

Michael V. Klibanov

doi:10.3934/ipi.2017013

Article Contents

2017, Volume 11, Issue 2: 263-276. Doi: 10.3934/ipi.2017013

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A phaseless inverse scattering problem for the 3-D Helmholtz equation

Michael V. Klibanov

Department of Mathematics and Statistics, University of North Carolina at Charlotte Charlotte, NC 28213, USA

Received: August 2016

Revised: November 2016

Published: May 2017

This work was supported by US Army Research Laboratory and US Army Research Office grant W911NF-15-1-0233 as well as by the Office of Naval Research grant N00014-15-1-2330.

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Abstract

An inverse scattering problem for the 3-D Helmholtz equation is considered. Only the modulus of the complex valued scattered wave field is assumed to be measured and the phase is not measured. This problem naturally arises in the lensless quality control of fabricated nanostructures. Uniqueness theorem is proved.

Keywords:

Lensless quality control of fabricated nanostructures,
high frequencies,
phaseless inverse scattering,
uniqueness.

Mathematics Subject Classification: 35R30.

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References

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