# Inductive Imaging of the Concealed Defects with Radio-Frequency Atomic Magnetometers
## 5 Detection of Concealed Defects  
The measurement of a series of cavities (holes drilled in the side of an aluminium plate) offset from the surface of the plate at various distances represent the detection of concealed defects, as depicted by the inset in Figure 1. The cavities are 2 mm in diameter and drilled to a length of 40 mm in the side of a 10 mm-thick plate with an area of 140 \(\times\) 140 mm\({}^{2}\). The cavities run parallel to the surface of the plate. The centre of the holes on one (front) side of the plate are offset by 1.5 mm and 2 mm from the surface, while the holes on the opposite (back) side are offset by 3 mm and 4 mm. The measurement is in the self-compensated configuration, i.e., with the rf primary field coil and the bias field axis orthogonal to the surface of the plate. The geometry of these cavities present no hard edge to the penetrating rf field so it will produce a secondary field with a different spatial distribution to those generated by the circular recesses examined earlier.  
Figure 7 shows the amplitude (a) and phase (b) change of the rf atomic magnetometer signal produced by scanning a 165.6 \(\times\) 165.6 mm\({}^{2}\) area over the plate with cavities. To remove the spatial modulation of the measured amplitude and phase [already discussed in description of Figure 2 and seen prominently in Figure 6a], the images were bandstop filtered (within range 15/pix-25/pix) along the direction parallel to the cavities axis. The plate edges and the positions of the cavities are marked with dotted lines and arrows, respectively. The rf atomic magnetometer was operated at 1.6 kHz. The signatures of all four cavities are visible in both amplitude and phase images. The character of the amplitude of the secondary field in this measurement is similar to that reported in the literature [31]. The signatures of the two holes in the upper part of Figure 7a indicate that, due to the proximity of the plate edge, the compensation of the rf magnetic field is achieved only locally within the area of the defect. Imperfection in rf field compensation is visible as a dark stripe within the defect signature.  
Figure 7c shows the dependence of the magnetometer frequency on the amplitude contrast (\(C_{\mathrm{R}}\)) while (d) shows the phase contrast, \(C_{\mathrm{GE}}\). Consistent with results shown in Figure 4d, the frequency dependence of \(C_{\mathrm{R}}\) reaches a broad maximum within 1 kHz-2 kHz range for of the cavities that lie 0.5 mm (blue dots) and 1 mm (green diamonds) under the object surface. The dependencies for cavities that are 2 (yellow triangles) and 3 mm (red squares) deep indicate the presence of a maximum for frequencies below 1 kHz. The spatial extent of the profiles representing the cavity edge is defined by the coil diameter, lift-off distance, operating rf frequency and conductivity of the plate. Since the size of the cavity is comparable to the diameter of the rf primary field coil, the profiles from the opposite edge of the cavities overlap. This overlap results in a reduction of the observed contrast with respect to the values shown in Figure 4d [23]. Imperfections in rf field cancellation are visible in the relatively large variation in the frequency dependence of the phase contrast, \(C_{\mathrm{GE}}\). Nevertheless, the general trend mirrors that of the frequency dependence of the amplitude contrast. The advantage of \(C_{\mathrm{GE}}\) is the large dynamic range of the defect signatures measured, even for frequencies outside the optimum range, i.e., 1 kHz-2 kHz, where the maximum value of the \(C_{\mathrm{R}}\) and \(C_{\mathrm{GE}}\) are reached.