Optimization Methods for In-Line Holography

Carpio Rodríguez, Ana María; Dimiduk, T. G.; Vidal Lloret, Perfecto; Selgas, V.

Optimization Methods for In-Line Holography

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Official URL

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

Publication date

2018

Authors

Carpio Rodríguez, Ana María

Dimiduk, T. G.

Vidal Lloret, Perfecto

Selgas, V.

Publisher

Society for Industrial and Applied Mathematics

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URI

https://hdl.handle.net/20.500.14352/13415

Citation

Carpio Rodríguez, A. M., Dimiduk, T. G., Vidal Lloret, P. y Selgas, V. «Optimization Methods for In-Line Holography». SIAM Journal on Imaging Sciences, vol. 11, n.o 2, enero de 2018, pp. 923-56. DOI.org (Crossref), https://doi.org/10.1137/17M1142740.

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.