By combining a finite element tip model and numerical simulations of the ti
p-sample interaction, it is shown that magnetic force microscopy images of
patterned soft elements may be quantitatively compared to experiments, even
when performed at low lift heights, while preserving physically realistic
tip characteristics. The analysis framework relies on variational principle
s. Assuming magnetically hard tips, the model is both exact and numerically
more accurate than hitherto achieved. (C) 2001 American Institute of Physi
cs.