Abstract: An apparatus includes an enclosure having a wall defining an interior of the enclosure and having a layer of a magnetically permeable material disposed such that there is no layer of an electrically conductive material located closer to the interior of the enclosure than the layer of the magnetically permeable material. A background-field magnetometer and an electrical coil structure are positioned within the enclosure. The electrical coil structure is driven by a controllable electrical current source. A background-field-reducing feedback controller has a controller input responsive to a background-field magnetometer output signal, and a controller output in communication with the current source command signal input. A signal magnetometer, such as a biomagnetometer, within the enclosure detects a magnetic field produced by a source within the enclosure.