# Inductive Imaging of the Concealed Defects with Radio-Frequency Atomic Magnetometers
## 1 Introduction
For the uncovered defect, the amplitude of the defect signature increases with frequency, which is a simple consequence of the growth of induction with rf field frequency. Most of the observations reported in [22; 23; 24; 25; 26] have been performed with the rf primary field frequency in a range of tens of kHz. One of the main challenges for existing NDT methods is the detection of concealed defects; e.g., defects covered by an insulating material, buried within, or located on an inner surface of the object. In the case of electrically conductive objects, the detection requires a balance between two mutually exclusive regimes of coupling between the rf field and the object--(1) strong coupling; ensures the generation of a detectable response, and (2) weak coupling; enables significant penetration of the rf field within the object. Condition (1) is dependent on the combination of the secondary field amplitude produced by defect, which is proportional to the operating frequency, and the sensitivity of the magnetometer. To be specific, the sensor sensitivity defines the detectable limit of a defect's signature. Condition (2) limits the detection of defects located at depths below the surface. Coupling strength scales with rf field frequency and the object thickness and the optimal operational frequency occurs at the balance between the two regimes. In this paper, we evaluate the performance of an rf atomic magnetometer in various types of NDT measurement scenarios involving a concealed defect. Our main goal is to identify the optimum coupling between the rf field and the object, i.e., optimum operational frequency of the sensor, for detecting defects concealed by a conductive barrier or throughout the object's volume. The detection of objects has partially demonstrated the efficacy of NDT with an rf atomic magnetometer through conductive and ferromagnetic barriers [19]. The low operating frequency of the magnetometer enables the penetration of the rf field through the barrier. In the cited experiment, the rf primary field source and the sensor are located on opposite sides of the barrier, which might be impractical for in-the-field measurements. In contrast, we are exploring a more versatile detection geometry, Figure 1, over a frequency range where the skin depth spans the object thickness. In addition, it should be noted that studies of the sensor performance for various frequencies, rather than just a single frequency, could address the problem of operating the magnetometer at frequencies near noises in the ambient magnetic field. The studies discussed in this paper are mainly carried out in the so-called self-compensated configuration, where the primary rf field is parallel to the bias magnetic field [24]. In this configuration, the magnetometer signal is only produced by the secondary field components orthogonal to the primary field. These investigations have been carried out with electrically conductive, non-magnetic aluminium objects: (1) to investigate the how the skin depth, which is related to eddy currents and rf field frequency, impacts the measurements of defects at different depths, and (2) since the changes in the local field detected by the atomic magnetometer are negligible.