• Corpus ID: 249191573

Magnetisation moment of a bounded 3D sample: asymptotic recovery from planar measurements on a large disk using Fourier analysis

@inproceedings{Ponomarev2022MagnetisationMO,
  title={Magnetisation moment of a bounded 3D sample: asymptotic recovery from planar measurements on a large disk using Fourier analysis},
  author={Dmitry Ponomarev},
  year={2022}
}

• D. Ponomarev
• Published 29 May 2022
• Mathematics

. We consider the problem of reconstruction of the overall magnetisation vector (net moment) of a sample from partial data of the magnetic field. Namely, motivated by a concrete experimental set-up, we deal with a situation when the magnetic field is measured on a portion of the plane in vicinity of the sample and only one (normal to the plane) component of the field is available. We assume the measurement area to be a sufficiently large disk (lying in a horizontal plane above the sample) and we obtain a set of estimates for the components of the net moment vector with the accuracy asymptotically improving with the increase of the radius of the measurement disk. Compared to our previous preliminary results, the asymptotic estimates are now rigorously justified and higher-order estimates are given. The presented approach also elucidates the derivation of asymptotic estimates of an arbitrary order. The obtained results are illustrated numerically and their robustness with respect to noise is discussed.