A new approach to the design of uniplanar gradient coils for fully open magnetic resonance imaging (MRI) system is proposed to build a specified gradient magnetic field in a target region. In this new methodology, the surface current density of the coil is represented by a two-dimensional Fourier series expansion. A cost function is constructed in terms of the summation of squared error and a penalty function. Minimizing the cost function, the continuous current density distribution for the uniplanar gradient coil is obtained. Applying the stream function technique to the resulting continuous current distribution, discrete current patterns can be generated. Employing the Biot-Savart law to the discrete current loops, the gradient magnetic field has been re-evaluated in order to validate the method proposed. Using this approach, a uniplanar x-gradient coil with high level of linearity is designed.
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