# Inductive Imaging of the Concealed Defects with Radio-Frequency Atomic Magnetometers
## 2 Experimental Setup  
The measurements are performed in a magnetically unshielded environment [22; 23; 24; 25; 26]. The bias magnetic field is actively stabilised by three pairs of nested, orthogonal, square Helmholtz coils. The bias magnetic field amplitude sets the operating frequency of the system (i.e., the magnetic resonance frequency). Caesium atomic vapour is housed in a paraffin-coated cell at ambient temperature (atomic density \(n_{\text{Cs}}=0.33\times 10^{11}\,\text{cm}^{-3}\)). Atoms are optically pumped by a circularly polarised laser beam propagating along the direction of the bias field, Figure 1. This pump beam is provided by a diode laser, frequency stabilized to the \(6\,^{2}\text{S}_{1/2}\) F = 3\(\rightarrow\)\(6\,^{2}\text{P}_{3/2}\) F\({}^{\prime}\) = 2 transition (D2 line, 852 nm). The evolution of the collective atomic spin is mapped through the paramagnetic Faraday effect onto the polarisation state of the linearly polarised probe beam [27; 28; 29]. The probe beam is phase-offset-locked to the pump beam, bringing it 800 MHz blue-shifted from the \(6\,^{2}\text{S}_{1/2}\) F = 4\(\rightarrow\)\(6\,^{2}\text{P}_{3/2}\) F\({}^{\prime}\) = 5 transition. The laser light transmitted through the cell is analysed by a polarimeter consisting of a zero-order half-wave plate, a crystal polariser and a commercial balanced photodetector. The resulting signal is measured by a lock-in amplifier referenced to the driving rf field frequency. In all the measurements, the internal rf field source of the lock-in drives the rf primary field coil. The frequency of the primary rf field is set at the operating frequency. An acoustic amplifier is added to increase the current of the lock-in rf output. The signal output of the photodetector, i.e., gain, is limited to the dynamic range of the lock-in (1 V). All the measurements rely on monitoring the response of the magnetometer while the frequency of the lock-in source is scanned through the rf resonance. The two quadrature components of the rf signal, \(X\) and \(Y\), are recorded by the lock-in referenced to the first harmonic of the internal source (some results are expressed in terms of the amplitude \(R=\sqrt{(X)^{2}+(Y)^{2}}\) and phase \(\phi=\arctan(\frac{Y}{X})\)). For aluminium objects, the rf atomic magnetometer signal (polarisation rotation caused by atomic ground state coherences) is produced by the secondary magnetic field created by eddy currents within the test object (a \(150\times 150\) mm\({}^{2}\) and 6 mm thick plate, unless stated otherwise). Eddy currents are excited by the rf coil (300 turns of 0.02 mm diameter copper, wound length of 3 mm, 2 mm and 3.5 mm inner and outer diameters). The coil has a ferrite core length 6 mm and diameter 2 mm. The coil is placed 2-7 mm from the object (coil lift-off) on the same axis as the cell and 200 mm from the atomic  
Figure 1: (colour online) Magnetic induction tomography with a radio-frequency atomic magnetometer. An rf coil produces the rf primary field that excites the object response (secondary field). The area enclosed by the dashed box shows the components that make up the rf atomic magnetometer and solid box details the geometry of the holes in the object used for the validation of concealed defect detection. magnetometer. The object is placed on a 2D translation stage actuated by two computer controlled stepper motors with 0.184 mm positioning precision. Detection of the Secondary Field with an rf Atomic Magnetometer in the Self-Compensated Configuration  
Use of an rf magnetometer enables the vectorial measurement of the secondary field [23]. The realisations of this idea in the so-called self-compensated configuration were demonstrated in [24]. It relies on the alignment of the rf primary and bias field such that they are both parallel to the surface normal of the studied object. Hence, the rf primary field is absent from the magnetometer signal.