**3.1 Spatial resolution**

Besides the lack of an excitation coil, one of the main advantages of wire-core fluxgates is the diameter of the wire, usually very narrow (several tens of µm). A narrow diameter is advantageous not only for miniaturization, but also for improvement of spatial resolution in magnetic field measurement. Let us consider, for instance, a magnetic field HZ with constant gradient along the x direction, as shown in Fig. 5. Parallel fluxgates must use either a ring or a racetrack core to reduce the demagnetizing factor and compensate voltage peaks for zero measured fields. Such core has two sensitive sections in the measurement direction (namely A and B in Fig.5, left) which sense different fields HZA and HZB. The total field measured by the parallel fluxgate will be the average of HZA and HZB.

Parallel fluxgates rarely have a core narrower than 1÷2 cm, limiting the spatial resolution to such level. On the contrary, orthogonal fluxgates have the sensitive cross section of a single wire making it possible to measure the magnetic field HZ in the single spot, with resolution limited by the diameter. Since typical wires used for orthogonal fluxgates have diameters up to 100 µm, the spatial resolution of orthogonal fluxgates is two orders of magnitude better than conventional parallel fluxgates. To this extent, they were successfully employed for applications such as magnetic imaging. For instance, in (Terashima & Sasada, 2002) a gradiometer based on a wire-core orthogonal flux is presented. The gradiometer is used to measure magnetic fields emerging from a specimen of 3% grain oriented silicon steel, with steps of 50 µm (the diameter of the amorphous wire used as a core is 120 µm). Since the spatial resolution of the sensor is very high it was possible to measure the magnetic field emerging from a single domain, and then graphically represent the domain's topology of the sample.

Parallel fluxgates, based on PCB technology, with an ultra thin core (50 µm) have also been proposed (Kubik et al., 2007). In this case, the spatial resolution is remarkably improved in y direction, but it is still poor in the x direction.

Fig. 5. Spatial resolution in parallel (left) and orthogonal fluxgates (right).
