In magnetopneumography (MPG), we scan weak remanent magnetic fields (in the range of nT) of ferromagnetic dust deposited in the lungs of affected workers. This is carried out in an unshielded lab. Variations of the background field during the scanning period bias the inversion process, i.e., the estimation of the magnetic sources from the measured field. We present an innovative mathematical technique of finding a field equation uniquely describing the magnetic moments in the nodes of the measurement space. Simultaneously, it enables the tracking of the values of the disturbing gradient created by external distant sources during the time of scanning. Our method preserves the first-order gradients obtained in multiple layers (scan heights above the object) instead of losing data with the higher order gradients which are not effective here. Six coaxially aligned fluxgates were used for scanning the field maps. The obtained five first-order gradients for each node give us the parameters of the respective ldquoequivalentrdquo magnetic sources. Furthermore, we obtain a parameter describing the error originating mainly from the background field. The main limits of the presented method are: 1) the alignment of the probes; 2) their number being limited by a minimum distance; and 3) nonhomogeneity of the external field.
