Fig. 4: Comparison of a simulated MRI gradient field and its approximation using harmonic expansions.
Shown are the experimental results of the MRI gradient field in the x, y-plane. The simulated gradient field is labeled as Ground Truth and includes the cylindrical field of view as green dashed line. Heatmaps of the calculated gradient fields using ellipsoidal and spherical harmonics are shown and labeled accordingly. The reference ellipsoid and the spheres are indicated as green dashed lines within the field plots. A joint color bar indicating the z-component of the field values from −0.05 mT (dark blue) to 0.05 mT (dark red) is provided. The relative errors (as defined in (2)) to the ground truth are shown for both cases, labeled as Difference EHE for the ellipsoidal harmonic expansion and Difference SHE for the spherical harmonic expansion. The reference ellipsoid and the spheres are indicated as blue dashed lines within the difference plots. A joint color bar for the difference plots indicating the relative error within six bins from 0 to 1% (light pink) to > 30% (dark red) is provided. Moreover, the Bz values of the ground truth, the spherical harmonic expansion (SHE) and the ellipsoidal harmonic expansion (EHE) at y = z = 0 are compared in a separate line-plot labeled as Gradient at y = z = 0. The border of the ellipsoid and the spheres in x − direction are displayed as gray dashed lines.
