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We present a transfer-function approach to calculate the force on a magnetic force microscope tip and the stray field due to a perpendicularly magnetized medium having an arbitrary magnetization pattern. Under certain conditions, it is possible to calculate the magnetization pattern from the measured force data. We apply this transfer function theory to quantitatively simulate magnetic force microscopy data acquired on a CoNi/Pt multilayer and on an epitaxially grown Cu/Ni/Cu/Si(001) magnetic thin film. The method described here serves as an excellent basis for (i) the definition of the condition for achieving maximum resolution in a specific experiment, (ii) the differences of force and force z-derivative imaging, (iii) the artificial distinction between domain and domain wall contrast, and finally (iv) the influence of various tip shapes on image content

Quantitative magnetic force microscopy on perpendicularly magnetized samples