## 3 Results
### Problem Statement
#### 3.1.3 Change of the rf Signal with Lift-Off  
To gain further insight, we measured the dependence on lift-off of the signal amplitude, Figure 5a, and phase, Figure 5b, for a square copper plates with side length of 40 mm (blue solid line), 20 mm (orange dashed line), 8 mm (yellow dotted line), and 4 mm (purple dash-dotted line). The data were recorded with plates angled at 30\({}^{\circ}\), while the black line represents the signal amplitude measured over a plate at 0\({}^{\circ}\). All amplitudes measured at 0\({}^{\circ}\) are at the same level for all plate sizes but only one data set (40 mm plate) is shown for clarity. These plots show that there is a decay in the measured rf resonance amplitude with increasing lift-off. This is due to the decrease in the primary field amplitude at the surface of the plate with increasing lift-off. In addition, at a single lift-off, i.e., 2 mm, the measured amplitude increases linearly with plate side length. The reason for this is more complex. The signal measured at the magnetometer reflects the strength of the secondary rf field, but is also related to the change in the spatial distribution of the primary field. The distribution of the primary field will change if it couples inductively to an object, i.e., field lines will deviate relative to the case where there is no object. This results in the generation of a horizontal component of the primary field. Larger objects will disrupt the field distribution more, which leads to an increase in the measured signal amplitude with plate size. Plate size will also influence the secondary rf field through the circumference of the secondary  
Figure 3: Amplitude (**a**) and phase (**b**) of the rf signal as a function of the angle between the normal to the object surface and the sensor axis recorded for a copper (red diamonds), steel (blue triangles), and ferrite (black squares) plate. Lines connecting points serve only to guide the eye. The measurement was performed at an operating frequency of 6 kHz. The primary rf field coil is located above the centre of the plate.  
field generating eddy currents, i.e., for the same eddy current density a small circumference imposed by a small plate will result in a smaller field measured at the cell (Biot-Savart law). For the coil and plate sizes used here, this is expected to be a small contribution.  
Figure 4: Amplitude (**a**) and phase (**b**) of the rf signal as a function of the angle between the normal to the object surface and the sensor axis recorded over the copper plates with lift-off values of 3 mm (red squares), 10 mm (orange diamonds), 20 mm (green triangles), and 30 mm (blue circles). Lines connecting points serve only to guide the eye. The measurement was performed at an operating frequency of 40 kHz. The plate was positioned so that it was centred along the axis of the primary rf field coil.  
Figure 5: Amplitude (**a**) and phase (**b**) of the rf resonance measured a function of coil lift-off (2 mm to 55 mm) for a single point over the centre of a square copper plate angled at 30\({}^{\circ}\), with a side length of 40 mm (blue solid line), 20 mm (orange dashed line), 8 mm (yellow dotted line), and 4 mm (purple dash-dotted line). The black line represents the signal measured over a 40 mm plate at 0\({}^{\circ}\). The measurement was performed at an operating frequency 40 kHz. Each point is an average of 50 measurements, and the errors bars represent one standard deviation.