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However, the existing magnetic-field-based Fourier Transform back-evolution method is limited by its mono-function of imaging the magnitude of current density in devices under test, and subject to background noise distortion. Here, we developed a novel vectorial current density imaging method based on the detection of the magnetic field gradient generated by current carrying conductors. A closed form solution of current density inversion was analytically derived and numerically verified. Experiments were conducted by scanning tri-axial fluxgate sensor over different shapes of electrical wires. The results show that a current density resolution of 24.15 mA\/mm2, probe-to-sample separation of 2 mm, and spatial resolution of 0.69 mm were achieved over a maximum scanning area of 300 mm \u00d7 300 mm. Such a method is verified to be capable of simultaneously imaging both magnitude and directions of current density, which is a promising technique for in situ noninvasive inspection for the power electronic and semiconductor industry.<\/jats:p>","DOI":"10.3390\/s23135859","type":"journal-article","created":{"date-parts":[[2023,6,26]],"date-time":"2023-06-26T05:11:54Z","timestamp":1687756314000},"page":"5859","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Vectorial Current Density Imaging Method Based on Magnetic Gradient Tensor"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-7036-4294","authenticated-orcid":false,"given":"Yangjing","family":"Wu","sequence":"first","affiliation":[{"name":"Sino-German College of Intelligent Manufacturing, Shenzhen Technology University, Shenzhen 518118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingji","family":"Zhang","sequence":"additional","affiliation":[{"name":"Sino-German College of Intelligent Manufacturing, Shenzhen Technology University, Shenzhen 518118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chengyuan","family":"Peng","sequence":"additional","affiliation":[{"name":"Sino-German College of Intelligent Manufacturing, Shenzhen Technology University, Shenzhen 518118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-2051-8080","authenticated-orcid":false,"given":"Zehuang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Sino-German College of Intelligent Manufacturing, Shenzhen Technology University, Shenzhen 518118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yichen","family":"He","sequence":"additional","affiliation":[{"name":"Sino-German College of Intelligent Manufacturing, Shenzhen Technology University, Shenzhen 518118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenwei","family":"Zhang","sequence":"additional","affiliation":[{"name":"Sino-German College of Intelligent Manufacturing, Shenzhen Technology University, Shenzhen 518118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liang","family":"Chang","sequence":"additional","affiliation":[{"name":"State Grid Liaoning Electric Power Co., Ltd., Huludao 125000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"14","DOI":"10.31399\/asm.edfa.2009-4.p014","article-title":"Magnetic Current Imaging in Failure Analysis","volume":"11","author":"Orozco","year":"2009","journal-title":"EDFA Tech. 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