Determination of the Spatial Resolution in the Case of Imaging Magnetic Fields by Polarized Neutrons
One of the most important parameters characterizing imaging systems (neutrons, X-rays, etc.) is their spatial resolution. In magnetic field imaging, the spatial resolution depends on the (magnetic) resolution of the depolarization of spin-polarized neutrons. This should be realized by different meth...
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MDPI AG
2021-07-01
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| Online Access: | https://www.mdpi.com/2076-3417/11/15/6973 |
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| author | Wolfgang Treimer Ralf Köhler |
| author_facet | Wolfgang Treimer Ralf Köhler |
| author_sort | Wolfgang Treimer |
| collection | DOAJ |
| description | One of the most important parameters characterizing imaging systems (neutrons, X-rays, etc.) is their spatial resolution. In magnetic field imaging, the spatial resolution depends on the (magnetic) resolution of the depolarization of spin-polarized neutrons. This should be realized by different methods, but they all have in common that a spin-polarizing and spin-analyzing system is part of the resolution function. First a simple and useful method for determining the spatial resolution for unpolarized neutrons is presented, and then methods in the case of imaging with polarized neutrons. Spatial resolution in the case of polarized neutron imaging is fundamentally different from ‘classical’ spatial resolution. Because of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula>-periodicity, the shortest path along which a spin-flip can occur is a measure of ‘magnetic’ spatial resolution. Conversely, the largest detectable magnetic field (B-field) within a given path length is also a measure of magnetic spatial resolution. This refers to the spatial resolution in the flight direction of the neutrons (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>y</mi></mrow></semantics></math></inline-formula>). The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>x</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>z</mi></mrow></semantics></math></inline-formula> refers to the spatial resolution in x- or z-direction; however, in these cases a different method must be used. Therefore, two independent methods are used to distinguish longitudinal and lateral spatial resolution, one method to determine the modulation transfer function (MTF) by recording the frequency-dependent fringe contrast of magnetic field images of a coil (longitudinal spatial resolution), and the second method, to observe the fringe displacement at the detector as a function of magnetic motion, provided that the accuracy of the motion is much better than the pixel size (at least half the pixel size) of the detector (lateral spatial resolution). The second method is a convolution of the fringe pattern with the pixel array of the detector. |
| first_indexed | 2024-03-10T09:18:45Z |
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| language | English |
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| spelling | doaj.art-5c3c6087741248679825035ff343e1022023-11-22T05:22:27ZengMDPI AGApplied Sciences2076-34172021-07-011115697310.3390/app11156973Determination of the Spatial Resolution in the Case of Imaging Magnetic Fields by Polarized NeutronsWolfgang Treimer0Ralf Köhler1Department of Mathematics, Physics & Chemistry, University of Applied Sciences, Berliner Hochschule für Technik Berlin, 13353 Berlin, GermanyDepartment of Mathematics, Physics & Chemistry, University of Applied Sciences, Berliner Hochschule für Technik Berlin, 13353 Berlin, GermanyOne of the most important parameters characterizing imaging systems (neutrons, X-rays, etc.) is their spatial resolution. In magnetic field imaging, the spatial resolution depends on the (magnetic) resolution of the depolarization of spin-polarized neutrons. This should be realized by different methods, but they all have in common that a spin-polarizing and spin-analyzing system is part of the resolution function. First a simple and useful method for determining the spatial resolution for unpolarized neutrons is presented, and then methods in the case of imaging with polarized neutrons. Spatial resolution in the case of polarized neutron imaging is fundamentally different from ‘classical’ spatial resolution. Because of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula>-periodicity, the shortest path along which a spin-flip can occur is a measure of ‘magnetic’ spatial resolution. Conversely, the largest detectable magnetic field (B-field) within a given path length is also a measure of magnetic spatial resolution. This refers to the spatial resolution in the flight direction of the neutrons (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>y</mi></mrow></semantics></math></inline-formula>). The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>x</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>z</mi></mrow></semantics></math></inline-formula> refers to the spatial resolution in x- or z-direction; however, in these cases a different method must be used. Therefore, two independent methods are used to distinguish longitudinal and lateral spatial resolution, one method to determine the modulation transfer function (MTF) by recording the frequency-dependent fringe contrast of magnetic field images of a coil (longitudinal spatial resolution), and the second method, to observe the fringe displacement at the detector as a function of magnetic motion, provided that the accuracy of the motion is much better than the pixel size (at least half the pixel size) of the detector (lateral spatial resolution). The second method is a convolution of the fringe pattern with the pixel array of the detector.https://www.mdpi.com/2076-3417/11/15/6973neutron imagingpolarized neutronsmagnetic fieldsspatial resolution |
| spellingShingle | Wolfgang Treimer Ralf Köhler Determination of the Spatial Resolution in the Case of Imaging Magnetic Fields by Polarized Neutrons Applied Sciences neutron imaging polarized neutrons magnetic fields spatial resolution |
| title | Determination of the Spatial Resolution in the Case of Imaging Magnetic Fields by Polarized Neutrons |
| title_full | Determination of the Spatial Resolution in the Case of Imaging Magnetic Fields by Polarized Neutrons |
| title_fullStr | Determination of the Spatial Resolution in the Case of Imaging Magnetic Fields by Polarized Neutrons |
| title_full_unstemmed | Determination of the Spatial Resolution in the Case of Imaging Magnetic Fields by Polarized Neutrons |
| title_short | Determination of the Spatial Resolution in the Case of Imaging Magnetic Fields by Polarized Neutrons |
| title_sort | determination of the spatial resolution in the case of imaging magnetic fields by polarized neutrons |
| topic | neutron imaging polarized neutrons magnetic fields spatial resolution |
| url | https://www.mdpi.com/2076-3417/11/15/6973 |
| work_keys_str_mv | AT wolfgangtreimer determinationofthespatialresolutioninthecaseofimagingmagneticfieldsbypolarizedneutrons AT ralfkohler determinationofthespatialresolutioninthecaseofimagingmagneticfieldsbypolarizedneutrons |