Progress in the development of high-sensitivity magnetic-field measurements has stimulated interest in understanding the magnetic noise of conductive materials, especially of magnetic shields based on high-permeability materials and/or high-conductivity materials. For example, SQUIDs and atomic magnetometers have been used in many experiments with mu-metal shields, and additionally SQUID systems frequently have radio frequency shielding based on thin conductive materials. Typical existing approaches to modeling noise only work with simple shield and sensor geometries while common experimental setups today consist of multiple sensor systems with complex shield geometries. With complex sensor arrays used in, for example, MEG and Ultra Low Field MRI studies, knowledge of the noise correlation between sensors is as important as knowledge of the noise itself. This is crucial for incorporating efficient noise cancelation schemes for the system. We developed an approach that allows us to calculate the Johnson noise for arbitrary shaped shields and multiple sensor systems. The approach is efficient enough to be able to run on a single PC system and return results on a minute scale. With a multiple sensor system our approach calculates not only the noise for each sensor but also the noise correlation matrix between sensors. Here we will show how the algorithm can be implemented.

中文翻译：

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使用基尔霍夫方程对导电屏蔽进行噪声建模

高灵敏度磁场测量发展的进展激发了人们对了解导电材料的磁噪声的兴趣，尤其是基于高磁导率材料和/或高电导率材料的磁屏蔽。例如，SQUID 和原子磁力计已用于许多具有 mu 金属屏蔽的实验，此外，SQUID 系统通常具有基于薄导电材料的射频屏蔽。现有的典型噪声建模方法仅适用于简单的屏蔽和传感器几何形状，而当今常见的实验设置由多个具有复杂屏蔽几何形状的传​​感器系统组成。例如，在 MEG 和超低场 MRI 研究中使用复杂的传感器阵列，了解传感器之间的噪声相关性与了解噪声本身一样重要。这对于将有效的噪声消除方案纳入系统至关重要。我们开发了一种方法，允许我们计算任意形状的屏蔽和多个传感器系统的约翰逊噪声。该方法足够高效，能够在单个 PC 系统上运行并以分钟为单位返回结果。对于多传感器系统，我们的方法不仅计算每个传感器的噪声，还计算传感器之间的噪声相关矩阵。在这里，我们将展示如何实现该算法。该方法足够高效，能够在单个 PC 系统上运行并以分钟为单位返回结果。对于多传感器系统，我们的方法不仅计算每个传感器的噪声，还计算传感器之间的噪声相关矩阵。在这里，我们将展示如何实现该算法。该方法足够高效，能够在单个 PC 系统上运行并以分钟为单位返回结果。对于多传感器系统，我们的方法不仅计算每个传感器的噪声，还计算传感器之间的噪声相关矩阵。在这里，我们将展示如何实现该算法。