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Optimization Methods for In-Line Holography

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Carpio, Ana and Dimiduk, T. G. and Vidal, Perfecto and Selgas, V. (2018) Optimization Methods for In-Line Holography. SIAM Journal on Imaging Sciences, 11 (2). pp. 923-956. ISSN 1936-4954

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Official URL: https://doi.org/10.1137/17M1142740


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https://epubs.siam.org/loi/sjisbiUNSPECIFIED


Abstract

We present a procedure to reconstruct objects from holograms recorded in in-line holography settings. Working with one beam of polarized light, the topological derivatives and energies of functionals quantifying hologram deviations yield predictions of the number, location, shape and size of objects with nanometer resolution. When the permittivity of the objects is unknown, we approximate it by parameter optimization techniques. Iterative procedures combining topological field based geometry corrections and parameter optimization sharpen the initial predictions.
Additionally, we devise a strategy which exploits the measured holograms to produce numerical approximations of the full electric field (amplitude and phase) at the screen where the hologram is recorded. Shape and parameter optimization of functionals employing such approximations of the electric field also yield images of the holographied objects.


Item Type:Article
Uncontrolled Keywords:Holography, light imaging, inverse scattering, topological energy, topological derivative, cellular structures, soft matter, microscale, nanoscale.
Subjects:Sciences > Physics > Optics
Sciences > Mathematics > Functional analysis and Operator theory
Sciences > Mathematics > Numerical analysis
Sciences > Mathematics > Differential equations
ID Code:55887
Deposited On:18 Jul 2019 10:34
Last Modified:18 Jul 2019 10:52

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