{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T15:14:56Z","timestamp":1777389296577,"version":"3.51.4"},"reference-count":38,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,4,15]],"date-time":"2022-04-15T00:00:00Z","timestamp":1649980800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000070","name":"National Institute of Biomedical Imaging and Bioengineering","doi-asserted-by":"publisher","award":["U01EB028656"],"award-info":[{"award-number":["U01EB028656"]}],"id":[{"id":"10.13039\/100000070","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["678578"],"award-info":[{"award-number":["678578"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we propose a method to estimate the position, orientation, and gain of a magnetic field sensor using a set of (large) electromagnetic coils. We apply the method for calibrating an array of optically pumped magnetometers (OPMs) for magnetoencephalography (MEG). We first measure the magnetic fields of the coils at multiple known positions using a well-calibrated triaxial magnetometer, and model these discreetly sampled fields using vector spherical harmonics (VSH) functions. We then localize and calibrate an OPM by minimizing the sum of squared errors between the model signals and the OPM responses to the coil fields. We show that by using homogeneous and first-order gradient fields, the OPM sensor parameters (gain, position, and orientation) can be obtained from a set of linear equations with pseudo-inverses of two matrices. The currents that should be applied to the coils for approximating these low-order field components can be determined based on the VSH models. Computationally simple initial estimates of the OPM sensor parameters follow. As a first test of the method, we placed a fluxgate magnetometer at multiple positions and estimated the RMS position, orientation, and gain errors of the method to be 1.0 mm, 0.2\u00b0, and 0.8%, respectively. Lastly, we calibrated a 48-channel OPM array. The accuracy of the OPM calibration was tested by using the OPM array to localize magnetic dipoles in a phantom, which resulted in an average dipole position error of 3.3 mm. The results demonstrate the feasibility of using electromagnetic coils to calibrate and localize OPMs for MEG.<\/jats:p>","DOI":"10.3390\/s22083059","type":"journal-article","created":{"date-parts":[[2022,4,19]],"date-time":"2022-04-19T02:39:31Z","timestamp":1650335971000},"page":"3059","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Calibration and Localization of Optically Pumped Magnetometers Using Electromagnetic Coils"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6034-4604","authenticated-orcid":false,"given":"Joonas","family":"Iivanainen","sequence":"first","affiliation":[{"name":"Sandia National Laboratories, Albuquerque, NM 87185, USA"},{"name":"Department of Neuroscience and Biomedical Engineering, Aalto University School of Science, FI-00076 Aalto, Finland"}]},{"given":"Amir","family":"Borna","sequence":"additional","affiliation":[{"name":"Sandia National Laboratories, Albuquerque, NM 87185, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5331-2521","authenticated-orcid":false,"given":"Rasmus","family":"Zetter","sequence":"additional","affiliation":[{"name":"Department of Neuroscience and Biomedical Engineering, Aalto University School of Science, FI-00076 Aalto, Finland"}]},{"given":"Tony R.","family":"Carter","sequence":"additional","affiliation":[{"name":"Sandia National Laboratories, Albuquerque, NM 87185, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2486-747X","authenticated-orcid":false,"given":"Julia M.","family":"Stephen","sequence":"additional","affiliation":[{"name":"Mind Research Network a Division of Lovelace Biomedical Research Institute, Albuquerque, NM 87106, USA"}]},{"given":"Jim","family":"McKay","sequence":"additional","affiliation":[{"name":"Candoo Systems Inc., Port Coquitlam, BC V3C 5M2, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0130-0801","authenticated-orcid":false,"given":"Lauri","family":"Parkkonen","sequence":"additional","affiliation":[{"name":"Department of Neuroscience and Biomedical Engineering, Aalto University School of Science, FI-00076 Aalto, Finland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6164-3366","authenticated-orcid":false,"given":"Samu","family":"Taulu","sequence":"additional","affiliation":[{"name":"University of Washington, Seattle, WA 98195, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7570-1229","authenticated-orcid":false,"given":"Peter D. D.","family":"Schwindt","sequence":"additional","affiliation":[{"name":"Sandia National Laboratories, Albuquerque, NM 87185, USA"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1103\/RevModPhys.65.413","article-title":"Magnetoencephalography\u2014theory, instrumentation, and applications to noninvasive studies of the working human brain","volume":"65","author":"Hari","year":"1993","journal-title":"Rev. Mod. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1330","DOI":"10.1016\/j.measurement.2009.04.003","article-title":"Calibration of low frequency magnetic field meters using a Helmholtz coil","volume":"42","author":"Ardjomand","year":"2009","journal-title":"Measurement"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"068501","DOI":"10.1088\/1674-1056\/25\/6\/068501","article-title":"An efficient calibration method for SQUID measurement system using three orthogonal Helmholtz coils","volume":"25","author":"Li","year":"2016","journal-title":"Chin. Phys. B"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4855","DOI":"10.1088\/0031-9155\/57\/15\/4855","article-title":"Calibration of a multichannel MEG system based on the Signal Space Separation method","volume":"57","author":"Chella","year":"2012","journal-title":"Phys. Med. Biol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5001304","DOI":"10.1109\/TMAG.2014.2326869","article-title":"Calibration for a multichannel magnetic sensor array of a magnetospinography system","volume":"50","author":"Adachi","year":"2014","journal-title":"IEEE Trans. Magn."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5000506","DOI":"10.1109\/TMAG.2019.2895355","article-title":"Calibration of room temperature magnetic sensor array for biomagnetic measurement","volume":"55","author":"Adachi","year":"2019","journal-title":"IEEE Trans. Magn."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ahlfors, S., and Ilmoniemi, R.J. (1989). Magnetometer position indicator for multichannel MEG. Advances in Biomagnetism, Springer.","DOI":"10.1007\/978-1-4613-0581-1_155"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Hansen, P., Kringelbach, M., and Salmelin, R. (2010). MEG: An Introduction to Methods, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780195307238.001.0001"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Boto, E., Bowtell, R., Kr\u00fcger, P., Fromhold, T.M., Morris, P.G., Meyer, S.S., Barnes, G.R., and Brookes, M.J. (2016). On the potential of a new generation of magnetometers for MEG: A beamformer simulation study. PLoS ONE, 11.","DOI":"10.1371\/journal.pone.0157655"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"542","DOI":"10.1016\/j.neuroimage.2016.12.048","article-title":"Measuring MEG closer to the brain: Performance of on-scalp sensor arrays","volume":"147","author":"Iivanainen","year":"2017","journal-title":"NeuroImage"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5490","DOI":"10.1038\/s41598-019-41763-4","article-title":"Optical Co-registration of MRI and On-scalp MEG","volume":"9","author":"Zetter","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"118747","DOI":"10.1016\/j.neuroimage.2021.118747","article-title":"Spatial sampling of MEG and EEG based on generalized spatial-frequency analysis and optimal design","volume":"245","author":"Iivanainen","year":"2021","journal-title":"NeuroImage"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"116995","DOI":"10.1016\/j.neuroimage.2020.116995","article-title":"Multi-channel whole-head OPM-MEG: Helmet design and a comparison with a conventional system","volume":"219","author":"Hill","year":"2020","journal-title":"NeuroImage"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"109181","DOI":"10.1016\/j.jneumeth.2021.109181","article-title":"Automatic coregistration of MRI and on-scalp MEG","volume":"358","author":"Gu","year":"2021","journal-title":"J. Neurosci. Methods"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"706785","DOI":"10.3389\/fnins.2021.706785","article-title":"Co-registration Comparison of On-Scalp Magnetoencephalography and Magnetic Resonance Imaging","volume":"15","author":"Cao","year":"2021","journal-title":"Front. Neurosci."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Pfeiffer, C., Andersen, L.M., Lundqvist, D., H\u00e4m\u00e4l\u00e4inen, M., Schneiderman, J.F., and Oostenveld, R. (2018). Localizing on-scalp MEG sensors using an array of magnetic dipole coils. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0191111"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"116686","DOI":"10.1016\/j.neuroimage.2020.116686","article-title":"On-scalp MEG sensor localization using magnetic dipole-like coils: A method for highly accurate co-registration","volume":"212","author":"Pfeiffer","year":"2020","journal-title":"NeuroImage"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"8909","DOI":"10.1088\/1361-6560\/aa93d1","article-title":"A 20-channel magnetoencephalography system based on optically pumped magnetometers","volume":"62","author":"Borna","year":"2017","journal-title":"Phys. Med. Biol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1016\/j.neuroimage.2018.07.028","article-title":"A bi-planar coil system for nulling background magnetic fields in scalp mounted magnetoencephalography","volume":"181","author":"Holmes","year":"2018","journal-title":"NeuroImage"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/j.neuroimage.2019.03.022","article-title":"On-scalp MEG system utilizing an actively shielded array of optically-pumped magnetometers","volume":"194","author":"Iivanainen","year":"2019","journal-title":"NeuroImage"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1119\/1.1933682","article-title":"The theory of vector spherical harmonics","volume":"22","author":"Hill","year":"1954","journal-title":"Am. J. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"124905","DOI":"10.1063\/1.1935742","article-title":"Presentation of electromagnetic multichannel data: The signal space separation method","volume":"97","author":"Taulu","year":"2005","journal-title":"J. Appl. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1023\/B:BRAT.0000032864.93890.f9","article-title":"Suppression of interference and artifacts by the signal space separation method","volume":"16","author":"Taulu","year":"2004","journal-title":"Brain Topogr."},{"key":"ref_24","unstructured":"Simola, J., and Taulu, S. (2018). Method for Designing Coil Systems for Generation of Magnetic Fields of Desired Geometry, a Magnetic Resonance Imaging or Magnetoencephalography Apparatus with a Coil Assembly and a Computer Program. (No. 9,977,764), U.S. Patent."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Borna, A., Carter, T.R., Colombo, A.P., Jau, Y.Y., McKay, J., Weisend, M., Taulu, S., Stephen, J.M., and Schwindt, P.D. (2020). Non-invasive functional-brain-imaging with an OPM-based magnetoencephalography system. PLoS ONE, 15.","DOI":"10.1371\/journal.pone.0227684"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"243703","DOI":"10.1063\/1.3522648","article-title":"Magnetoencephalography with a two-color pump-probe, fiber-coupled atomic magnetometer","volume":"97","author":"Johnson","year":"2010","journal-title":"Appl. Phys. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"15403","DOI":"10.1364\/OE.24.015403","article-title":"Four-channel optically pumped atomic magnetometer for magnetoencephalography","volume":"24","author":"Colombo","year":"2016","journal-title":"Opt. Express"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"063906","DOI":"10.1063\/5.0016087","article-title":"Magnetic-field modeling with surface currents. Part I. Physical and computational principles of bfieldtools","volume":"128","author":"Zetter","year":"2020","journal-title":"J. Appl. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"063905","DOI":"10.1063\/5.0016087","article-title":"Magnetic field modeling with surface currents. Part II. Implementation and usage of bfieldtools","volume":"128","author":"Zetter","year":"2020","journal-title":"J. Appl. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","article-title":"SciPy 1.0: Fundamental algorithms for scientific computing in Python","volume":"17","author":"Virtanen","year":"2020","journal-title":"Nat. Methods"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1109\/34.88573","article-title":"Least-squares estimation of transformation parameters between two point patterns","volume":"13","author":"Umeyama","year":"1991","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"156869","DOI":"10.1155\/2011\/156869","article-title":"FieldTrip: Open source software for advanced analysis of MEG, EEG, and invasive electrophysiological data","volume":"2011","author":"Oostenveld","year":"2011","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"118818","DOI":"10.1016\/j.neuroimage.2021.118818","article-title":"Cross-Axis Projection Error in Optically Pumped Magnetometers and its Implication for Magnetoencephalography Systems","volume":"247","author":"Borna","year":"2021","journal-title":"NeuroImage"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1109\/10.245606","article-title":"Sampling theory for neuromagnetic detector arrays","volume":"40","author":"Ahonen","year":"1993","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"931","DOI":"10.1007\/s10548-018-0656-5","article-title":"Requirements for coregistration accuracy in on-scalp MEG","volume":"31","author":"Zetter","year":"2018","journal-title":"Brain Topogr."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"119027","DOI":"10.1016\/j.neuroimage.2022.119027","article-title":"Triaxial detection of the neuromagnetic field using optically-pumped magnetometry: Feasibility and application in children","volume":"252","author":"Boto","year":"2022","journal-title":"NeuroImage"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1109\/TBME.2021.3100770","article-title":"Magnetic Field Mapping and Correction for Moving OP-MEG","volume":"69","author":"Mellor","year":"2022","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"118401","DOI":"10.1016\/j.neuroimage.2021.118401","article-title":"Precision magnetic field modelling and control for wearable magnetoencephalography","volume":"241","author":"Rea","year":"2021","journal-title":"NeuroImage"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/8\/3059\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:55:03Z","timestamp":1760136903000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/8\/3059"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,15]]},"references-count":38,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["s22083059"],"URL":"https:\/\/doi.org\/10.3390\/s22083059","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,15]]}}}