We introduce the concept of computerized tomographic microscopy in magnetic
resonance imaging using the magnetic fields and field gradients from a
ferromagnetic probe. We investigate a configuration where a two-dimensional
sample is under the influence of a large static polarizing field, a small
perpendicular radio-frequency field, and a magnetic field from a ferromagnetic
sphere. We demonstrate that, despite the non-uniform and non-linear nature of
the fields from a microscopic magnetic sphere, the concepts of computerized
tomography can be applied to obtain proper image reconstruction from the
original spectral data by sequentially varying the relative sample-sphere
angular orientation. The analysis shows that the recent proposal for atomic
resolution magnetic resonance imaging of discrete periodic crystal lattice
planes using ferromagnetic probes can also be extended to two-dimensional
imaging of non-crystalline samples with resolution ranging from micrometer to
Angstrom scales.Comment: 9 pages, 11 figure
