Shim coils can be formed from combinations of small numbers of simple “building block” coils (loops and saddles). In a seminal 1984 paper, Romeo and Hoult, showed how to combine building blocks to produce coils that generate a given spherical harmonic, whilst eliminating contamination from as many unwanted spherical harmonic terms as possible. By applying updated numerical optimisation approaches to this problem, we show how to produce improved zonal shim coils. Designs of Z2, Z3 and Z4 coils formed from three pairs of loops, which are shorter than previously reported coils while having large regions of conformity are described.
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