The field maps used here for unwarping, like any other field map, can be corrected as
proposed through Eqs 11–13. A 1D
profile as marked in inset is plotted here, for the corrected as well as the non-corrected
field map. In this particular case, the manually-introduced shim was linear (Fig. 3b); for this reason and as seen here, the field
error was simply proportional to the field itself, so that treated and untreated results
appear here as straight lines intersecting at a zero field offset.