The magnetic force microscope (MFM) is an established experimental tool for imaging stray fields with high spatial resolution and sensitivity. The MFM contrast can however contain contributions from the sample topography, variations in the surface Kelvin potential and magnetic contributions arising from grain-to-grain variations of the areal density of the magnetic moment, apart from the contrast generated by the micromagnetic pattern of the sample. Differential imaging techniques can be used to disentangle these contrast contributions. The calibration of the response of the MFM tip on different spatial wavelengths of the field allows a quantitative determination of the magnetic vector field in the plane parallel to the sample surface scanned by the tip. Generally, the tip becomes less sensitive for smaller spatial wavelengths. Obtaining a high spatial resolution thus requires a high measurement sensitivity that can be obtained by MFM operation in vacuum and by using high-quality factor cantilevers. As a result, field sensitivities better than 80 mu T/root Hz can be obtained, even with low magnetic moment tips.