中文摘要：

针对全开放磁共振成像系统的特点，提出了一种单平面梯度线圈的新型设计方法。将电流密度用二维傅立叶级数展开，根据误差平方和与一个惩罚函数建立目标函数。使目标函数最小化，得到电流密度的表达式。应用流函数技术离散电流密度，得到线圈的绕线形式。为了验证理论的正确性，利用Biot—Savart积分方程计算该线圈绕线产生的梯度磁场。采用这种方法，设计了梯度强度为40mT／m，电流为114．474A的x梯度线圈。结果表明，应用所提出的方法设计的线圈可以产生所需要的线性度很好的磁场。该方法也可以用于双平面或者双平面自屏蔽梯度线圈的设计。

英文摘要：

Aiming at the feature of fully open magnetic resonance imaging system, a new approach to the design of uniplanar gradient coils was proposed. In this new design methodology, the surface current density was represented by a two-dimensional Fourier series expansion. We constructed a cost function in terms of the squared error and a penalty function. By minimizing the cost function, we obtained the continuous current density distribution for the uniplanar gradient coil. Applying the stream function technique to the resulting continuous current distribution, the discrete current pattern could be generated. Employing the Biot-Savart integral equation to the discrete current loops, the gradient magnetic field was re-evaluated in order to validate the proposed method. Using this approach, we designed a uniplanar x-gradient coil which is capable of generating a field with 40mT/m in gradient and 114.474 A in current. The results indicated that the produced field was with high linearity. The above mentioned methodology can also be used to the design of biplanar or biplanar self-shielded gradient coils.