A method, consisting of generating, using a plurality of magnetic transmitters, a magnetic field in a region and introducing a field perturbing element into the region. The method includes characterizing multiple images of each magnetic transmitter in the field perturbing element, and calculating a reaction magnetic field in the region based on the characterized images. The method further includes positioning a probe in the region and measuring a perturbed magnetic field at the probe, and determining a location of the probe in response to the measured perturbed magnetic field and the calculated reaction magnetic field.
