A cylindrical basis set for shim coil design in magnetic resonance imaging

Shim coils used in magnetic resonance imaging and NMR to produce magnetic fields are commonly designed to generate spherical harmonics, and thus achieve accuracy over a spherical region. Herein a cylindrical basis set is presented as an alternative to spherical harmonics, so as to better suit the cylindrical coil geometry and, in cases where it more closely matches a cylinder, the imaging region of interest. Example coil winding patterns for a selection of functions in this new set are derived using the target field method. A computational approach is taken to determine their accuracy, and it is found the basis functions are generated with high accuracy over cylindrical imaging regions within the coil. The basis set is also applied to a double-coil configuration with active shielding, which results in slightly reduced accuracy within the coil but highly effective field nullification beyond the coil radius.