Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantitative magneto-optical imaging with ferrite garnets   Magneto-optical imaging is a powerful technique for studying qualitative
features of magnetic flux distributions in superconductors and other magnetic
samples. However, magneto-optical imaging does not automatically return
two-dimensional maps with the actual values of the magnetic field, due to the
non-linear response functions of magneto-optical indicator films and in
practice also non-uniform illumination. A quantitative treatment is needed in
order to achieve such a calibration. After calibration, one can proceed to
deduce the corresponding two-dimensional maps of the current density
distribution from inversion of the Biot-Savart law. While there has been
published a large amount of work on quantitative magneto-optical imaging, the
material is scattered and notation differs significantly between different
authors. These notes originate from parts of the Ph. D. thesis of the author
and collect the most important materials into a unified and updated treatment.
Basic aspects of magnetic flux penetration in superconductors including the
Bean model are reviewed briefly in chapter 1. In chapter 2, the method of
magneto-optical imaging using the Faraday effect is introduced, together with
practical aspects of magneto-optical experiments at low temperatures and the
semi-qualitative technique of RGB addition for checking the reproducibility of
flux patterns. The physics of magneto-optical indicator films and calibration
of magneto-optical images into maps of magnetic field values are discussed in
chapter 3. Next, in chapter 4 the Biot-Savart law and fast Fourier
transformations are discussed before proceeding to inversion of magnetic field
maps into current density maps. Finally, magnetometry with Faraday
magneto-optical imaging is treated. MATLAB codes for several of the discussed
concepts can be found at https://github.com/atlejq/Magneto-optics

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The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
2
The categories of this paper are: math
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat