Design of Highly Linear Gradient Field Coils Based on an Improved Target-Field Method

An improved approach for designing highly linear gradient coils based on the target-field method is presented for application in a magnetoencephalography system. With this method, two novel current density functions are expanded in a trigonometric series with single-Fourier coefficients that need to be determined. Their determination is resolved by selecting field points and desired field values in the target area of interest. The coil winding patterns are then given by the level contours of the stream function. Compared with the discrete-wire design method, the advantage of this method is that the coil size is predetermined prior to the calculation and better linearity in the field is obtained that overcomes size constraints. A numerical simulation shows that in a cube with a side length of 0.5 R, the field linearity of the proposed transverse gradient coil is improved by 2.5 times that of the Golay coil, and the designed longitudinal gradient coil by 1.2 times that of the Maxwell coil. Moreover, with the optimized transverse gradient coil being manufactured by flexible printed circuit technology, the magnetic field generated by it matches that produced in theoretical simulations. Measurement results show that the linearity of this transverse gradient coil is 6×10
^{- 3}
along the z-axis in the range of ±0.25 R.