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Noninvasive imaging of three-dimensional micro and nanostructures by topological methods

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Carpio, Ana and Dimiduk, T. G. and Rapún, M. L. and Selgas, V. (2016) Noninvasive imaging of three-dimensional micro and nanostructures by topological methods. SIAM Journal on Imaging Sciences, 9 (3). pp. 1324-1354. ISSN 19364954

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Official URL: http://epubs.siam.org/doi/abs/10.1137/16M1068669


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Abstract

We present topological derivative and energy based procedures for the imaging of micro and nano structures using one beam of visible light of a single wavelength. Objects with diameters as small as 10 nm can be located and their position tracked with nanometer precision. Multiple objects dis-tributed either on planes perpendicular to the incidence direction or along axial lines in the incidence direction are distinguishable. More precisely, the shape and size of plane sections perpendicular to the incidence direction can be clearly determined, even for asymmetric and nonconvex scatterers. Axial resolution improves as the size of the objects decreases. Initial reconstructions may proceed by gluing together two-dimensional horizontal slices between axial peaks or by locating objects at three-dimensional peaks of topological energies, depending on the effective wavenumber. Below a threshold size, topological derivative based iterative schemes improve initial predictions of the lo-cation, size, and shape of objects by postprocessing fixed measured data. For larger sizes, tracking the peaks of topological energy fields that average information from additional incident light beams seems to be more effective.


Item Type:Article
Uncontrolled Keywords:Cellular structures; Holography; Inverse scattering; Microscale; Nanoscale; Topological derivative; Topological energy; Visible light imaging
Subjects:Sciences > Mathematics > Topology
ID Code:39733
Deposited On:28 Oct 2016 11:03
Last Modified:12 Dec 2018 15:06

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