Two-dimensional current density imaging

Imaging of electrical current by measuring the magnetic field which it produces requires the solution of the magnetic inverse problem. For a current restricted to a plane, the inverse problem can theoretically be solved by a linear spatial filtering method. Experimental results indicate that currents restricted to the surface of a printed circuit board can be imaged using this method. To measure the magnetic field, a magnetic resonance imaging technique is used. The reconstructed current density images illustrate that a tradeoff exists between the spatial resolution and the signal-to-noise ratio (S/N). The currents were restricted to the surface of a printed circuit board set in the xy plane. The circuit board was bathed in a nonconducting mineral oil to provide a magnetic resonance (MR) signal. The z component of the magnetic field produced by the current was measured using the magnetic resonance technique, and a spatial filtering technique was used to find the current density (J). The spatial resolution with which one can measure electric current density depends strongly on the distance at which the magnetic field from these currents can be measured. Magnetic resonance imaging offers a way to measure magnetic fields noninvasively and thus the possibility of reducing this distance to zero (if the current flows in an appropriate medium). While less sensitive than a superconducting quantum interference device (SQUID), the MR imaging method might, under certain circumstances, be capable of higher spatial resolution.<
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