Wang J, Reykowski A, Dickas J
Siemens AG, Medical Engineering Group, Erlangen, Germany.
IEEE Trans Biomed Eng. 1995 Sep;42(9):908-17. doi: 10.1109/10.412657.
This paper describes a new method to calculate the signal-to-noise ratio (SNR) of MR signals obtained from single receiver coils and arrays of receiver coils. The coils are assumed to be place on the surface of a conducting half-space and the SNR is sample-noise dominated. While in conventional methods line integrals over the electric currents in the coils are chosen to calculate the electric and magnetic fields, this new method uses surface integrals over magnetic dipoles covering the area enclosed by the antenna to derive these fields. Using this method, the SNR for simple circular and square coils was analytically calculated. The calculations show that the theoretical difference in SNR between circular and square antennas is very low. Furthermore, based on the new method, a derivation of the ultimate gain in SNR for arrays of surface coils is presented. The SNR of such an array approaches a limit even if the total number of coils is increased to infinity. This ultimate SNR of a coil array is 35.8% above that of a single circular-shaped, size-optimized and linear polarized coil.
本文描述了一种计算从单接收线圈和接收线圈阵列获得的磁共振信号信噪比（SNR）的新方法。假设线圈放置在导电半空间表面，且信噪比以样本噪声为主。在传统方法中，通过对线圈中的电流进行线积分来计算电场和磁场，而这种新方法使用覆盖天线所围区域的磁偶极子的面积分来推导这些场。利用该方法，对简单圆形和方形线圈的信噪比进行了解析计算。计算结果表明，圆形和方形天线之间信噪比的理论差异非常小。此外，基于新方法，给出了表面线圈阵列信噪比最终增益的推导。即使线圈总数增加到无穷大，这种阵列的信噪比也会趋近于一个极限。线圈阵列的这个最终信噪比比单个圆形、尺寸优化且线极化的线圈的信噪比高35.8%。
