  PURPOSE: To extend magnitude-based PDFF (Proton Density Fat Fraction) and
$R_2^*$ mapping with resolved water-fat ambiguity to calculate field
inhomogeneity (field map) using the phase images.
  THEORY: The estimation is formulated in matrix form, resolving the field map
in a least-squares sense. PDFF and $R_2^*$ from magnitude fitting may be
updated using the estimated field maps.
  METHODS: The limits of quantification of our voxel-independent implementation
were assessed. Bland-Altman was used to compare PDFF and field maps from our
method against a reference complex-based method on 152 UK Biobank subjects (1.5
T Siemens). A separate acquisition (3 T Siemens) presenting field
inhomogeneities was also used.
  RESULTS: The proposed field mapping was accurate beyond double the
complex-based limit range. High agreement was obtained between the proposed
method and the reference in UK Biobank (PDFF bias = -0.03 %, LoA (limits of
agreement) [-0.1,0.1] %; Field map bias = 0.06 Hz, LoA = [-0.2,0.3] Hz). Robust
field mapping was observed at 3 T, for inhomogeneities over 300 Hz including
rapid variation across edges.
  CONCLUSION: Field mapping following magnitude-based water-fat separation with
resolved water-fat ambiguity was demonstrated in-vivo and showed potential at
high field.
