Study of the Magnetic Film Materials by Horizontal Scanning Mode for the   Magnetic Force Microscopy in Magnetostatic and ac Regimes
  The magnetic force microscopy inverse problem for the case of horizontal scanning of a tip on a linear magnetic film is introduced. We show the possibility to recover the magnetic permeability of the material from the experimental data by using the Hankel (Fourier-Bessel) transform inverse method (HIM). This method is applied to the case of a layered slab film as well. The inverse problem related to the ac MFM is introduced. 
Artorix de la Cruz de Ona and Nibaldo Alvarez Moraga