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/Si͑001͒ magnetic thin film. The method described here serves as an excellent basis for ͑i͒ the definition of the condition for achieving maximum resolution in a specific experiment, ͑ii͒ the differences of force and force z-derivative imaging, ͑iii͒ the artificial distinction between domain and domain wall contrast, and finally ͑iv͒ the influence of various tip shapes on image content.

Measurements of effective magnetic anisotropy energy of epitaxial Cu/Ni/Cu͑001͒ sandwiches are analyzed as a function of Ni film thickness h. The magnetization easy axis is perpendicular to the films for 20ϽhϽ140 Å. The magnetic anisotropy is best described by inclusion in the effective anisotropy energy of the straindependent magnetic surface anisotropy term, predicted by the strain-dependent Néel model, along with the usual magnetostatic, magnetocrystalline, and bulk magnetoelastic energies. The surface magnetocrystalline and surface magnetoelastic anisotropy energies of the Ni/Cu͑001͒ interface are determined to be ϩ0.9 erg/cm 2 and Ϫ52 erg/cm 2 , respectively. The effective magnetoelastic coupling coefficient ͑bulk plus surface͒ of Cu/Ni/Cu͑001͒ is predicted to change sign at hϭ80 Å. The two observed magnetization easy-axis reversals are also well described by this model.