Carpio Rodríguez, Ana MaríaDimiduk, T. G.Vidal Lloret, PerfectoSelgas, V.2023-06-172023-06-172018Carpio 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/10.1137/17M1142740.1936-495410.1137/17M1142740https://hdl.handle.net/20.500.14352/13415We 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.engjournal articlehttps://doi.org/10.1137/17M1142740https://epubs.siam.org/loi/sjisbiopen access517.9HolographyLight imagingInverse scatteringTopological energyTopological derivativeCellular structuresSoft matterMicroscaleNanoscaleÓptica (Física)Análisis funcional y teoría de operadoresAnálisis numéricoEcuaciones diferenciales2209.19 Óptica Física1206 Análisis Numérico1202.07 Ecuaciones en Diferencias