Three Dimensional Polarimetric Neutron Tomography of Magnetic Fields

Sales, Morten; Ströbl, Markus; Shinohara, T.; Tremsin, Anton S.; Kuhn, Luise Theil; Lionheart, William R B; Desai, Naeem; Dahl, Anders Bjorholm; Schmidt, Søren

doi:10.1038/s41598-018-20461-7

Cited by 36 publications

(37 citation statements)

References 18 publications

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“…Earlier attempts at reconstruction were presented using the ad hoc method of scalar Radon transform inversion applied to polarized neutron data [5,8,7]. The linearized problem about a zero magnetic field was presented in [13]. We show that the problem can be formulated as a non-Abelian ray transform and that sufficiently smooth magnetic fields are uniquely determined by polarimetric neutron tomography data.…”

Section: Introductionmentioning

confidence: 93%

Polarimetric neutron tomography of magnetic fields: uniqueness of solution and reconstruction

et al. 2020

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We consider the problem of determination of a magnetic field from three dimensional polarimetric neutron tomography data. We see that this is an example of a non-Abelian ray transform and that the problem has a globally unique solution for smooth magnetic fields with compact support, and a locally unique solution for less smooth fields. We derive the linearization of the problem and note that the derivative is injective. We go on to show that the linearised problem about a zero magnetic field reduces to plane Radon transforms and suggest a modified Newton Kantarovich method (MNKM) type algorithm for the numerical solution of the non-linear problem, in which the forward problem is re-solved but the same derivative used each time. Numerical experiments demonstrate that MNKM works for small enough fields (or large enough velocities) and show an example where it fails to reconstruct a slice of the simulated data set. Lastly we show viewed as an optimization problem the inverse problem is non-convex so we expect gradient based methods may fail.

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Section: Introductionmentioning

confidence: 93%

Polarimetric neutron tomography of magnetic fields: uniqueness of solution and reconstruction

et al. 2020

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“…An iterative procedure based on simulations (Biot-Savart law) shows a good agreement with the experimental data and allows for a 3D visualization of the field produced by the solenoid [7]. A different approach using a pulsed neutron beam combined with a time-of-flight method was proposed recently and first experiments show promising reconstructions of the magnetic vector field produced by a current driven solenoid obtained by the Filtered-Back-Projection tomographic reconstruction algorithm [15]. In general, the calculated and experimental results agree very well, though some deviations can be seen.…”

Section: Simulation and Quantification Of Magnetic Fieldsmentioning

confidence: 99%

Imaging with Polarized Neutrons

et al. 2018

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Owing to their zero charge, neutrons are able to pass through thick layers of matter (typically several centimeters) while being sensitive to magnetic fields due to their intrinsic magnetic moment. Therefore, in addition to the conventional attenuation contrast image, the magnetic field inside and around a sample can be visualized by detecting changes of polarization in a transmitted beam. The method is based on the spatially resolved measurement of the cumulative precession angles of a collimated, polarized, monochromatic neutron beam that traverses a magnetic field or sample.

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“…In other non-Abelian tomography problems the transport equation cannot be solved using an exponential and we have a non-linear integral operator along rays. Polarimetric neutron spin tomography provides an example [21]. The problems we treat in this paper of a quite a different nature.…”

Section: Introductionmentioning

confidence: 99%

Histogram tomography

Lionheart

2020

Mathematics in Engineering

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In many tomographic imaging problems the data consist of integrals along lines or curves. Increasingly we encounter "rich tomography" problems where the quantity imaged is higher dimensional than a scalar per voxel, including vectors tensors and functions. The data can also be higher dimensional and in many cases consists of a one or two dimensional spectrum for each ray. In many such cases the data contain not just integrals along rays but the distribution of values along the ray. If this is discretized into bins we can think of this as a histogram. In this paper we introduce the concept of "histogram tomography". For scalar problems with histogram data this holds the possibility of reconstruction with fewer rays. In vector and tensor problems it holds the promise of reconstruction of images that are in the null space of related integral transforms. For scalar histogram tomography problems we show how bins in the histogram correspond to reconstructing level sets of function, while moments of the distribution are the x-ray transform of powers of the unknown function. In the vector case we give a reconstruction procedure for potential components of the field. We demonstrate how the histogram longitudinal ray transform data can be extracted from Bragg edge neutron spectral data and hence, using moments, a non-linear system of partial differential equations derived for the strain tensor. In x-ray diffraction tomography of strain the transverse ray transform can be deduced from the diffraction pattern the full histogram transverse ray transform cannot. We give an explicit example of distributions of strain along a line that produce the same diffraction pattern, and characterize the null space of the relevant transform.

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Three Dimensional Polarimetric Neutron Tomography of Magnetic Fields

Cited by 36 publications

References 18 publications

Polarimetric neutron tomography of magnetic fields: uniqueness of solution and reconstruction

Polarimetric neutron tomography of magnetic fields: uniqueness of solution and reconstruction

Imaging with Polarized Neutrons

Histogram tomography

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