Singular spectrum analysis filtering and Fourier inversion: an efficient and fast way to improve resolution and quality of current density maps with low-cost Hall scanning systems

We provide a Biot–Savart inversion scheme that, for any two-dimensional, or bulk with planar crystallization, high-temperature superconducting (HTS) sample, determines current density maps with a higher resolution and accuracy than previous procedures and at a fraction of its computational cost. The...

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Autores: Amorós, Jaume, Duran, Arnau, Carrera, Miquel, López, Josep, Granados, Xavier
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2019
País:España
Recursos:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/177819
Acesso em linha:http://hdl.handle.net/10261/177819
Access Level:acceso abierto
Palavra-chave:Biot-Savart inversion
SSA filtering
Fast Fourier Transform
Hall magnetometry
High Temperature Superconducting tapes
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dc.title.none.fl_str_mv Singular spectrum analysis filtering and Fourier inversion: an efficient and fast way to improve resolution and quality of current density maps with low-cost Hall scanning systems
title Singular spectrum analysis filtering and Fourier inversion: an efficient and fast way to improve resolution and quality of current density maps with low-cost Hall scanning systems
spellingShingle Singular spectrum analysis filtering and Fourier inversion: an efficient and fast way to improve resolution and quality of current density maps with low-cost Hall scanning systems
Amorós, Jaume
Biot-Savart inversion
SSA filtering
Fast Fourier Transform
Hall magnetometry
High Temperature Superconducting tapes
title_short Singular spectrum analysis filtering and Fourier inversion: an efficient and fast way to improve resolution and quality of current density maps with low-cost Hall scanning systems
title_full Singular spectrum analysis filtering and Fourier inversion: an efficient and fast way to improve resolution and quality of current density maps with low-cost Hall scanning systems
title_fullStr Singular spectrum analysis filtering and Fourier inversion: an efficient and fast way to improve resolution and quality of current density maps with low-cost Hall scanning systems
title_full_unstemmed Singular spectrum analysis filtering and Fourier inversion: an efficient and fast way to improve resolution and quality of current density maps with low-cost Hall scanning systems
title_sort Singular spectrum analysis filtering and Fourier inversion: an efficient and fast way to improve resolution and quality of current density maps with low-cost Hall scanning systems
dc.creator.none.fl_str_mv Amorós, Jaume
Duran, Arnau
Carrera, Miquel
López, Josep
Granados, Xavier
author Amorós, Jaume
author_facet Amorós, Jaume
Duran, Arnau
Carrera, Miquel
López, Josep
Granados, Xavier
author_role author
author2 Duran, Arnau
Carrera, Miquel
López, Josep
Granados, Xavier
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Ministerio de Economía y Competitividad (España)
European Commission
Generalitat de Catalunya
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Biot-Savart inversion
SSA filtering
Fast Fourier Transform
Hall magnetometry
High Temperature Superconducting tapes
topic Biot-Savart inversion
SSA filtering
Fast Fourier Transform
Hall magnetometry
High Temperature Superconducting tapes
description We provide a Biot–Savart inversion scheme that, for any two-dimensional, or bulk with planar crystallization, high-temperature superconducting (HTS) sample, determines current density maps with a higher resolution and accuracy than previous procedures and at a fraction of its computational cost. The starting point of our scheme is a Hall scanning microscopy map of the out-of-plane component of the magnetic field generated by the current. Such maps are noisy in scans of real samples with commercial-grade equipment, and their error is the limiting factor in any Biot–Savart inversion scheme. The main innovation of our proposed scheme is a singular spectrum analysis (SSA) filtering of the Hall probe maps, which cancels measurement errors such as noise or drifts without introducing any artifacts in the field map. The SSA filtering of the Hall probe data is so successful in this task that the resulting magnetic field map does not require an overdetermined QR inversion, allowing Fourier inversion of the Biot–Savart problem. Our implementation of SSA filtering of the Hall scan measurements, followed by Biot–Savart inversion using the fast Fourier transform (FFT), is applied to both simulations and real samples of HTS tape stacks. The algorithm works in cases where ill conditioning ruled out the application of Fourier inversion, and achieves a finer resolution for a fraction of the cost of the QR inversion used to date. The computation passes physical and statistical validity tests in all cases, and in three-dimensional samples it is shown to yield the average, with a depth-dependent weight, of the current density circulating in the different layers of the sample.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019
2019
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dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/177819
url http://hdl.handle.net/10261/177819
dc.language.none.fl_str_mv Inglés
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info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/SEV-2015-0496
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info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MAT2014-51778-C2-1-R
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dc.publisher.none.fl_str_mv Institute of Physics (Great Britain)
publisher.none.fl_str_mv Institute of Physics (Great Britain)
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spelling Singular spectrum analysis filtering and Fourier inversion: an efficient and fast way to improve resolution and quality of current density maps with low-cost Hall scanning systemsAmorós, JaumeDuran, ArnauCarrera, MiquelLópez, JosepGranados, XavierBiot-Savart inversionSSA filteringFast Fourier TransformHall magnetometryHigh Temperature Superconducting tapesWe provide a Biot–Savart inversion scheme that, for any two-dimensional, or bulk with planar crystallization, high-temperature superconducting (HTS) sample, determines current density maps with a higher resolution and accuracy than previous procedures and at a fraction of its computational cost. The starting point of our scheme is a Hall scanning microscopy map of the out-of-plane component of the magnetic field generated by the current. Such maps are noisy in scans of real samples with commercial-grade equipment, and their error is the limiting factor in any Biot–Savart inversion scheme. The main innovation of our proposed scheme is a singular spectrum analysis (SSA) filtering of the Hall probe maps, which cancels measurement errors such as noise or drifts without introducing any artifacts in the field map. The SSA filtering of the Hall probe data is so successful in this task that the resulting magnetic field map does not require an overdetermined QR inversion, allowing Fourier inversion of the Biot–Savart problem. Our implementation of SSA filtering of the Hall scan measurements, followed by Biot–Savart inversion using the fast Fourier transform (FFT), is applied to both simulations and real samples of HTS tape stacks. The algorithm works in cases where ill conditioning ruled out the application of Fourier inversion, and achieves a finer resolution for a fraction of the cost of the QR inversion used to date. The computation passes physical and statistical validity tests in all cases, and in three-dimensional samples it is shown to yield the average, with a depth-dependent weight, of the current density circulating in the different layers of the sample.We acknowledge the financial support from the Spanish Ministry of Economy and Competitiveness through the Severo Ochoa Programme (SEV-2015-0496), CONSOLIDER Excellence Network (MAT2015-68994-REDC), COACHSUPENERGY project (MAT2014-51778-C2-1-R, co-financed by FEDER), GAP project (MTM2015-69135-P) and SUPERINKS project (RTC-2015-3640-3, co-financed by FEDER); the European Union for the FASTGRID project (H2020-NMBP-18-2016-IA-72109) and WPMAG 5 (H2020-EUROfusion); and the Catalan Government with 2017-SGR-932, 2014-SGR-753 and Xarmae.Peer reviewedInstitute of Physics (Great Britain)Ministerio de Economía y Competitividad (España)European CommissionGeneralitat de CatalunyaConsejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]201920192019info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Postprintinfo:eu-repo/semantics/acceptedVersionhttp://hdl.handle.net/10261/177819reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/SEV-2015-0496info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MAT2015-68994-REDCinfo:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MAT2014-51778-C2-1-Rinfo:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2015-69135-Pinfo:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/RTC-2015-3640-3info:eu-repo/grantAgreement/EC/H2020/721019info:eu-repo/grantAgreement/EC/H2020/633053http://dx.doi.org/10.1088/1361-6501/aaf13aSíinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/1778192026-05-22T06:33:51Z
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