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A novel target-field method for finite-length magnetic resonance shim coils: II. Tesseral shims

This paper presents a new approach for the design of finite-length shim and gradient coils of the type that are used in magnetic resonance imaging applications. A cylindrical target region is located arbitrarily within the coil, and the exact geometry of the coil is treated without approximation. Target fields of any desired type may be specified, and may involve zonal and tesseral harmonics. The method presented here then designs the coil windings needed to produce the specified target field. In this new approach, there is complete freedom in the choice of target field, with no requirement to restrict the target field to any one spherical harmonic. The method is therefore able to design coils in which the region of interest is located asymmetrically with respect to the coil length. In addition, to control the accuracy of the fields produced by the shim coil, the design methodology presented here is also extended to show how the desired target field can be matched at two or more different co-axial target radii. The method is illustrated for the design of shim coil that involves high-order tesseral fields located asymmetrically in a finite-length coil.