Uncertainty Propagation in Quantitative Magnetic Force Microscopy Using a Monte-Carlo Method

A Monte-Carlo (MC)-type method is utilized for the propagation of uncertainties in quantitative magnetic force microscopy (qMFM). In qMFM, quantitative magnetic field distributions are inferred from magnetic force microscopy (MFM) raw data using a calibration of the instrument point spread function and a subsequent inversion process. The two stages of calibration and measurement may be subject to a variety of uncertainties that naturally arise in practice. Identifying these sources of uncertainties and quantifying their impact on the reconstruction of the measurand is crucial for reliable quantitative studies of nanomagnetic materials and devices. So far, the propagation of variance method has been applied to determine the uncertainty budget for a complete calibration and measurement process. In this work, we are able to improve the uncertainty description in terms of structure and magnitude by application of an MC method. We demonstrate the importance of correlations and show possible side effects of model linearizations.