The deflections of the probe tip of a magnetic force scanning tunneling microscope are calculated for 3-D magnetic fields. The magnetic fields are calculated for a thin film whose magnetization is uniform through the thickness of the film and can be expressed by Fourier series in the other two dimensions. The deflections are calculated from the energy of interaction between the probe and the 3-D fields. The magnetization is modeled for recorded patterns with arctan transitions. Experimental data can be compared to the theory using the transition lengths as adjustable parameters. The magnetic fields can be determined at all points: along, across, and between the recorded tracks. An example is given for data on guard bands of a recorded track.
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