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The ferrite magnetic shield can provide a low-noise magnetic environment for various ultrahigh-sensitivity measurements. The low-frequency complex permeability, which determines the magnetic hysteresis noise and the shielding factor, is a key parameter of the ferrite shield and thus should be measured accurately. In this paper, the measurement error of conventional coil method is analyzed at low frequency, and an improved method is proposed which could eliminate the measurement error introduced by the wire resistance. Using this method, four ferrite samples made of PC40 and PC47 materials are measured. The measurement accuracy of the low-frequency complex permeability has improved by two orders of magnitude. On the basis of the measurement results, magnetic hysteresis noise and the shielding factor of ferrite shields are calculated. The calculated results of the noise analysis indicate that the PC40 material has lower magnetic hysteresis noise. This study can help select the ferrite materials and estimate the performance for low-noise magnetic shield design.

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Ultra-sensitive multi-channel optically pumped atomic magnetometers based on the spin-exchange relaxation-free (SERF) effect are powerful tools for applications in the field of magnetic imaging. To simultaneously achieve ultra-high spatial resolution and ultra-high magnetic field sensitivity, we proposed a high-resolution multi-channel SERF atomic magnetometer for two-dimensional magnetic field measurements based on a digital micro-mirror device (DMD) as the spatial light modulator for a single vapor cell. Under the optimal experimental conditions obtained via spatial and temporal modulation of the probe light, we first demonstrated that the average sensitivity of the proposed 25-channel magnetometer was approximately 25fT/Hz1/2 with a spatial resolution of 216µm. Then, we measured the magnetic field distribution generated by a gradient coil and compared the experimentally obtained distributions with those calculated via finite element simulation. The obtained g value of 99.2% indicated good agreement between our experimental results and the theoretical calculations, thereby confirming that our proposed multi-channel SERF magnetometer was effective at measuring magnetic field distributions with an ultra-high spatial resolution.