An apparatus for producing magnetic field gradients includes (a) a first planar electromagnet coil set configured to produce a first magnetic field gradient with respect to a first axis, (b) a second planar electromagnet coil set configured to produce a second magnetic field gradient with respect to a second axis that is orthogonal to the first axis, (c) a third planar electromagnet coil set configured to produce a third magnetic field gradient with respect to a third axis that is orthogonal to the first and second axes, and (d) a controller configured to selectively provide power to the first, second, and/or third electromagnet coil sets to sequentially produce a localization magnetic field gradient with respect to each of the first, second, and third axes, at least a portion of each localization magnetic field gradient having a monotonically-varying magnetic field magnitude along a respective axis.