GB2575695A

GB2575695A - Method and system for detecting a material response

Info

Publication number: GB2575695A
Application number: GB1811928.9A
Authority: GB
Inventors: Chalupczak Witold; Gartman Rafal; Bevington Patrick
Original assignee: University of Strathclyde; NPL Management Ltd
Current assignee: University of Strathclyde; NPL Management Ltd
Priority date: 2018-07-20
Filing date: 2018-07-20
Publication date: 2020-01-22
Anticipated expiration: 2038-07-20
Also published as: GB2575695B; GB201811928D0

Abstract

Detecting a material response by providing an oscillating primary magnetic field to cause a sample 16 to produce a secondary magnetic field, and detecting the secondary magnetic field with the atomic magnetometer to detect the material response. In one aspect, the method involves reducing the effect on an atomic magnetometer of components of the primary and secondary magnetic fields in a direction orthogonal to a surface of a sample 16. In another aspect, the method involves modulating a bias magnetic field of an atomic magnetometer.

Description

METHOD AND SYSTEM FOR DETECTING A MATERIAL RESPONSE

The invention relates to method and systems for detecting a material response.

Aspects of the invention seek to provide an improved method and system for detecting a material response.

According to an aspect of the invention, there is provided a method of detecting a material response, including:

providing an oscillating primary magnetic field to cause the sample to produce a secondary magnetic field;

reducing the effect on an atomic magnetometer of components of the primary and secondary magnetic fields in a direction substantially orthogonal to a surface of a sample;

detecting the secondary magnetic field with the atomic magnetometer to detect the material response.

According to an aspect of the invention, there is provided a system for detecting a material response, including:

a magnetic field source for providing an oscillating primary magnetic field to cause a sample to produce a secondary magnetic field;

an atomic magnetometer for detecting the secondary magnetic field for detecting a material response;

wherein the system is configured to reduce the effect on the atomic magnetometer of components of the primary and secondary magnetic fields in a primary direction substantially orthogonal to a surface of the sample.

providing an oscillating primary magnetic field to cause a sample to produce a secondary magnetic field;

modulating a bias magnetic field of an atomic magnetometer; detecting the secondary magnetic field with the atomic magnetometer to detect the material response.

an atomic magnetometer for detecting a secondary magnetic field for detecting a material response, the atomic magnetometer including a bias magnetic field source for providing a bias magnetic field;

a modulator for modulating the bias magnetic field.

Optional features of embodiments of the invention are provided in the dependent claims.

The methods of the different independent method claims and optionally also the features of any one or more of their dependent claims can be combined in some embodiments of the invention.

The systems of the different independent system claims and optionally also the features of any one or more of their dependent claims can be combined in some embodiments of the invention.

Providing a compensatory magnetic field can include operating a compensation coil arrangement to produce the compensatory magnetic field.

In some embodiments, the method can include varying or tuning one or more distances from a detection cell of the atomic magnetometer of one or more coils of the compensation coil arrangement, so as to reduce the effect on the atomic magnetometer of one or more components of the primary and/or secondary magnetic fields. For example, to reduce the effect on the atomic magnetometer of any component of the primary and/or secondary magnetic field, the method can include varying or tuning a distance from the detection cell of a compensation coil having an axis in a direction of that component.

Preferably, the compensatory magnetic field is an oscillating magnetic field.

Preferably, the compensatory magnetic field is made to oscillate with the same frequency as the primary magnetic field to keep a constant phase difference therebetween.

Providing an oscillating primary magnetic field substantially orthogonal to the surface of the sample to cause the sample to produce a secondary magnetic field can include operating an rf coil arrangement to provide the primary magnetic field.

In embodiments, the magnetic field source for providing an oscillating primary magnetic field includes an rf coil with or without a solid core.

In embodiments, the primary magnetic field is oscillated at an rf frequency, for example in the range 1 Hz to 1 GHz.

In some embodiments, the magnetic field source for providing an oscillating primary magnetic field can be configured to be disposed entirely on one side of a sample surface.

In some embodiments, the system can be configured to be disposed entirely on one side of the sample surface.

The method and/or system can be for detecting a material response for a variety of purposes, for example for material defects imaging and/or for detecting material electrical conductivity and magnetic permeability. In some embodiments the method and/or can be used for corrosion under insulation detection (CUI). In some embodiments, the method and/or system can be used for detection of the condition of reinforced concrete structures. In some embodiments, the method and/or system can be used for localisation of objects.

In embodiments, the atomic magnetometer is a radio-frequency atomic magnetometer.

In some embodiments, the sample has a high magnetic permeability and the secondary magnetic field is dominated by the secondary magnetisation. However, in other embodiments (highly conductive samples), the secondary magnetic field is dominated by the field generated by eddy currents.

Some embodiments can provide improving of material defects imaging with a radio-frequency atomic magnetometer

Embodiments of the invention are described below, by way of example only, with reference to the accompanying drawings.

Figure 1(a) shows a system for detecting a material response according to an embodiment of the invention.

Figure 1(b) shows a Caesium transition.

Figure 1(c) shows how secondary magnetic fields are formed in some instances.

Figure 2 shows a simulation of secondary field components by and b_z(marked with dashed red and solid blue lines respectively) as coil is moved along y axis through the centre of the hole in the embodiment of Figure 1.

Figure 3 shows a modelled change in signal phase (dotted black line) and amplitude (solid red line) of magnetic resonance signal over a recess recorded by magnetometer for various amplitudes of the primary field components. Vertical axis of the image array represents changes in vertical component, while horizontal axis represents changes in horizontal component of the primary field.

Figure 4 shows (a) Amplitude and (b) phase contrast measured for different locations of a vertical coil (compensation coil above the vapour cell) from the compensation point. For each position of the vertical coil, position of the horizontal coil was adjusted to achieve symmetric profile. Green squares in (a) represent change of the rf spectroscopy signal amplitude. Solid blue/ red line shows the amplitude/ phase contrast in an absence of the compensation field.

Figure 6 shows an experimental setup according to another embodiment of the invention.

Figure 7 shows the measured change of the amplitude of rf spectroscopy signal over a 64x64 mm² area of a 6 mm thick Al plate containing a 24 mm diameter recess that is 2.4 mm deep recorded with three measurement configurations: (a) without rf field compensation, (b) with compensation performed with two rf coils (Fig. 1), (c) and with rotated bias magnetic field and compensation coils (Fig. 6).

Figure 8 is a system diagram of an embodiment of the invention.

Figure 9 shows graphs of scanning.

Figures 11 and 12 are system diagrams of embodiments of the invention.

Figures 13 to 18 are associated with Annex 1.

Figure 13: Main components of the experimental setup. The oscillating primary magnetic field is generated by rf coil. The secondary magnetic field is produced by eddy currents excited in a sample (Al plate with recess) by the primary field. The atomic magnetometer signal monitors contributions from the primary as well as the secondary magnetic field.

Figure 14: The measured change in signal phase (a) and amplitude (b) of the rf resonance over a 64x64 mm² area of a 6 mm thick Al plate containing a 48 mm diameter recess that is 2.4 mm deep. Below, results of simulation of the phase (c) and amplitude (d).

Figure 15: Calculated b field components generated in a 64x64 mm²conductive area, a with 48 mm diameter recesses, (a), (b), and (c) refer to x, y and z component respectively.

Figure 16: The change in phase (a, b, c, d) and amplitude (e, f, g, h) of rf resonance over a 64x64 mm² area of 6 mm thick Al plates with 48 mm (a, e), 24 mm (b, f), 12 mm (c, g) and 2 mm (d, h) diameter recesses that are 2.4 mm deep.

Figure 17: Dependence of measured feature size (blue diamonds) and phase contrast (red points) on actual size of circular recesses. Dashed lines represent the modelling.

Figure 18: (a) Drawing of the aluminium plate used for a contrast calibration. White contour indicates the area of the scan. The change in phase (b) and amplitude (c) of rf resonance over a recess edge (main plot)/ a 70x70 mm² area of a 6 mm Al plates (inset).

In embodiments of the invention, imaging of the structural defects can be realized with radio-frequency atomic magnetometer by recording a material response to the radio-frequency excitation field. Described below are two examples of measurement configurations that enable an increase of the amplitude and phase contrast of the images representing a structural defect in paramagnetic and ferromagnetic samples. Both examples involve an elimination of the excitation field component from the atomic magnetometer signal. First example is implemented with a set of coils that directly compensates excitation field in magnetometer signal. Second example takes advantage of the fact that the radio-frequency magnetometer is not sensitive to the magnetic field oscillating along one of its axis. Results of the modelling that confirm experimental observation are discussed in detail.

Reference is made to Bevington, Patrick & Gartman, Rafal & Chalupczak, Witold & Deans, Cameron & Marmugi, Luca & Renzoni, Ferruccio. (2018) Non-Destructive Structural Imaging of Steelwork with Atomic Magnetometers (Paper 1), which can be found at , and the disclosure of which is incorporated herein by reference in its entirety.

Reference is also made to Annex 1 (Paper 2) at the end of this description.

Paper 1 and Paper 2 provide context to the invention and any of the structural or method features, or applications, described in Paper 1 or Paper 2 are applicable to embodiments of the invention, by way of modification or addition.

Implementation of radio-frequency magnetic fields in non-destructive testing provides cost-effective options for detection of structural defects, particularly in cases when there is no direct access to the surface of the studied sample. The technique can involve monitoring the material response to the so-called primary magnetic field (B) created by an rf coil [1]. The material response can be detected in a variety of ways. Traditionally this is achieved by monitoring the impedance of the rf coil (or a dedicated pickup coil) [1-5]. However, the simplicity of instrumentation in this type of measurement is outweighed by signal sensitivity degradation at low frequencies. Other options involve implementation of magnetic sensors such as giant magnetoresistance (GMR) magnetometers [6-8], superconducting quantum interference devices (SQUIDs) [9-10], and the radio-frequency magnetometers [1114]. The magnetic field sensors directly monitor the response of the socalled secondary magnetic field (b) in the medium. The secondary field is produced by the primary magnetic field through eddy currents excited in highly conductive samples, or magnetisation induced in samples with high permeability [15], and contains signatures of the inhomogeneities/ structural defects within the sample.

Embodiments of the present invention utilise rf atomic magnetometers and can be used for material defects imaging.

As described above embodiments of the present invention increase the amplitude and/or phase contrast of the output of the system.

In some embodiments, this is achieved by reducing the effect on the atomic magnetometer of components of the primary and secondary magnetic fields in a direction substantially orthogonal to the surface of a sample. This is described below in connection with two embodiments, both of which involve an elimination of the primary and secondary field components in a direction substantially orthogonal to the surface of the sample from the atomic magnetometer signal.

It is shown herein that the elimination of the primary field component from the magnetometer signal significantly increases the phase/ amplitude contrast of the images. This can provide a relatively quick indication of a defect in non-destructive tests of large area samples. The concepts are explored in context of paramagnetic (aluminium) and ferromagnetic (carbon steel) samples.

As can be seen in Figure 1(a), an embodiment of the invention includes a system 10 including a radio-frequency atomic magnetometer 12 and a primary magnetic field source 14 for providing a primary magnetic field oscillating at rf frequency. In this embodiment, the primary magnetic field source 14 is an rf coil; however, other magnetic field sources can be used in other embodiments.

In this embodiment, the rf coil 14 is a 1000 turn coil with 0.02 mm wire, wound on a 2 mm plastic core (inside diameter) and with a 4 mm width (outside diameter) and a 10 mm length.

Samples should be electrically conductive (although not necessarily highly electrically conductive) and/or should have a magnetic permeability such that they can be magnetised.

The rf coil 14 is configured so that it can be placed adjacent to a sample 16, but entirely on one side thereof and in a non-overlapping relationship therewith, and can be operated to generate an oscillating primary magnetic field to cause the sample to produce a secondary magnetic field. The secondary magnetic field is indicative of a material response of the sample. Reference is made to Figure 1(c).

The atomic magnetometer is configured to detect the secondary magnetic field.

It is worth noting that ferromagnetic targets produce 2 types of secondary fields:

• a secondary magnetic field in the same direction as the applied primary field - the secondary magnetisation, and • eddy current induced magnetic field in the opposite direction to the applied primary field - the eddy current induced magnetic field.

Figure 1(a) shows the main components of an experimental setup. In this example, secondary magnetic field is produced by eddy currents excited in a sample (in this case an Al plate with recess having a 48 mm diameter and a 2.4 mm depth) by primary field created by the rf coil. Atomic magnetometer signal would normally combine components created by primary field generated by rf coil and secondary magnetic field.

In this description, the z direction is the direction orthogonal to the surface of the sample, and the x and y directions are mutually orthogonal directions that are parallel to the surface of the sample.

Details of the atomic magnetometer are described in W. Chalupczak, R. M. Godun, S. Pustelny, and W. Gawlik, Appl. Phys. Lett. 100, 242401 (2012), which is incorporated herein by reference in its entirety. Since the experimental setup is similar to that described in [17,15] only essential components will be briefly discussed here.

The atomic magnetometer 12 includes a detection cell 20, which in this embodiment is a 1 cm³ paraffin coated glass cell containing room temperature cesium atomic vapour (for which atomic density n_Cs = 3.3 x 10¹⁰cm'³).

The magnetometer includes a bias magnetic field source 24 (not shown in Figure 1(a)) configured to provide a bias magnetic field 26 at the detection cell 20 in a bias magnetic field direction.

To perform active compensation of the ambient field and any residual DC magnetic field created by the sample, the magnetometer includes a fluxgate 25 located next to the vapour cell 20 and three PID units (in this embodiment SRS 960). In this embodiment, the fluxgate is Bartington Mag690. With passive and active compensation of the ambient field, the linewidth of the rf spectral profile is approximately 30 Hz. The small size of the detection cell 20 can provide partial immunity to ambient field gradients.

The magnetometer includes a pump laser 22 configured to pump the atoms in the detection cell 20 with a circularly polarised pump laser beam 28, in this embodiment at 377 pW, frequency locked to the cesium 6 ²Si/2 F=3^ 6 ²P3/2 F'=2 transition (D2 line, 852 nm) propagating along the bias magnetic field 26.

The atomic magnetometer includes a probe laser 30 configured to probe atomic spin precession in the detection cell 20 with a linearly polarised probe laser beam 32 phase-offset-locked to the pump beam and orthogonal to the bias magnetic field 26.

The atomic magnetometer includes a balanced polarimeter 34 configured to receive the probe laser beam after passing through the detection cell 20 and detect Faraday rotation. The balanced polarimeter is configured to provide an electronic output signal representing the Faraday rotation detection.

The rf coil 14 axis is orthogonal to both the pump and probe beam.

The system 10 includes a primary field oscillation controller in the form of a lock-in amplifier 36 (not shown in Figure 1(a)) configured to operate the rf coil 14 by providing current therein oscillating at an rf frequency to generate the primary magnetic field and to control the frequency and phase of the current in the rf coil 14 and thereby also of the primary magnetic field, and includes a receiver to receive the output signal from the balanced polarimeter of the atomic magnetometer. The lock-in amplifier 36 may be configured to provide frequency modulated current in the rf coil to provide a frequency modulated primary magnetic field, although this is not necessary in every embodiment. The lock-in amplifier is configured to demodulate the output signal from the balanced polarimeter with reference to the current frequency or modulation of the rf coil 14, and to provide a first output signal for example to a computer to obtain an amplitude and/or phase of the signal. The lock-in amplifier thereby serves as a demodulator. The computer can use the amplitude of the signal to detect a material response of the sample, and in some cases to perform material defects imaging.

In some embodiments, the computer can include a receiver to receive the first output signal from the lock-in amplifier 36 and to determine therefrom changes in conductivity and/or permeability of the sample.

This embodiment uses a magnetically unshielded environment where static fields along y and z directions are nulled and a bias field along the x direction is created by three pairs of mutually orthogonal nested square Helmholtz coils [18] with dimensions 1 m, 0.94 m and 0.88 m respectively (largest coil length 1 m) The Helmholtz coils form a coil arrangement for active and passive compensation of the ambient magnetic field, for lowering noises, and for stabilising and adjusting the direction and strength of the bias magnetic field. In other words, the coil arrangement provides the bias magnetic field source.

The measurement signal comes from the phase and amplitude change in the rf resonance spectra registered by the rf atomic magnetometer as a sample is moved under the rf coil (Fig. 1(a)). The rf coil producing B is driven by the output of the internal reference of the lock-in amplifier 36.

In the experimental set-up shown and described, the samples are fixed to a 2D, computer controlled translation stage. The sample 16 is located approximately 30 cm from the cell and the coil is placed 1 mm - 2 mm above the sample surface on the same axis as the cell.

The strength of the bias field {B_bias} defines the operating frequency of the system (12.6 kHz in this embodiment, although other frequencies can be used, typically in the range 10 kHz - 20 kHz), in other words the frequency of the magnetic resonance and the required primary field frequency.

In operation, coherent atomic spin precession is driven by the rf field. The superposition of the primary and the secondary fields alters this motion, which is probed with the linearly polarized probe laser beam 32 propagating orthogonally to the bias magnetic field 26. Cs atoms are optically pumped into the stretched state (F=4, mf=4) with the circularly polarised pump laser 22 locked to the Cs 6 F=3^6

P3/2 F'=2 transition (D2 line, 852 nm) propagating along the bias magnetic field B_hia'. The probe beam (30 pW) is phase-offset-locked to the pump beam, bringing it 580MHz blue shifted from the 6 ²Si/₂ F=4-> 6 ²P3/2 F'=5 transition (D2 line, 852 nm). Coherent spin precession of the Cs atoms is coupled to the polarisation of the probe beam (Faraday rotation) which is detected with the balanced polarimeter, whose signal is then processed by the lock-in amplifier 36 referenced to the phase of the rf field.

For imaging, this can be performed for each pixel of the sample surface, as the sample or system is moved.

The skilled person will appreciate that the particular atomic magnetometer described above is not the only type of atomic magnetometer that can be used; for example, different detection cells, different dimensions, different powers, different laser frequencies, and different transitions can be employed as appropriate.

The inventors have previously analysed the shape of the spatial profiles generated by the recess in aluminium plates [15]. The profile represents variations in phase and amplitude of the rf spectroscopy signal recorded by the atomic magnetometer. It contains contributions from the primary and secondary magnetic field. A strong primary field contribution in the magnetometer signal results in the mapping of two orthogonal components of the secondary field, b_z and by, onto the amplitude and phase of the rf spectroscopy signal respectively. The inventors have noted that the component of the secondary field, by, parallel to the sample surface changes its sign in the vicinity of the surface crack (recess). As a consequence of a strong primary field, variations in the resultant field recorded by the rf atomic magnetometer measure the direction flip of the secondary field component, however the observed rf signal phase change is smaller than actual change in by.

Referring again to Figure 1(a), in this embodiment of the invention, the system includes a compensatory magnetic field source 40 for providing an oscillating compensatory magnetic field, also called a compensation magnetic field, at the atomic magnetometer, specifically at the detection cell 20, including a component substantially orthogonal to the surface of the sample 16 reducing and preferably eliminating the effect on the atomic magnetometer of magnetic field components of the primary and secondary fields in that direction. In particular, the compensatory magnetic field compensates the primary field contribution to the resultant field monitored by the atomic magnetometer vapour cell, without changing efficiency of b excitation.

As can be seen from Figure 1(a), in this embodiment the compensatory magnetic field source 40 is a compensation coil arrangement including a first compensation coil 42 and a second compensation coil 44.

The first compensation coil 42 has an axis substantially aligned with z, a direction orthogonal to the surface of the sample 16 so as to provide a magnetic field at the atomic magnetometer, specifically at the detection cell 20, which is substantially orthogonal to the surface of the sample

16.

In this embodiment, the detection cell 20 is located between the rf coil 14 and the first compensation coil 42, although this is not necessary in all embodiments.

The second compensation coil 44 has an axis substantially aligned with y, a direction parallel to the surface of the sample 16 and substantially orthogonal to the bias field direction so as to provide a magnetic field at the atomic magnetometer, specifically at the detection cell 20 which is substantially parallel to the surface of the sample 16 and substantially orthogonal to the bias field direction.

In this embodiment, the detection cell 20 is located between the probe laser 30 and the second compensation coil 44, and the second compensation coil 44 is located between the detection cell 20 and the balanced polarimeter 34, although this is not necessary in all embodiments.

The compensatory coil arrangement 40 is configured to provide, at the detection cell 20, a compensatory magnetic field b/.

In other words, a set of two rf coils oriented along z and y directions (Fig.1(a)) creates an oscillating magnetic field, B^, that compensates the primary field seen by the atomic magnetometer. The coils are driven by the output of the internal reference of the same lock-in amplifier 36 used to generate B. This keeps a constant phase difference between the fields B and B^.

In other words, the primary field is compensated in vapour cell by a set of two rf coils oriented along z and y direction.

However, for reasons explained below, the component of the secondary magnetic field in the z direction is also compensated.

The amplitudes of the two components of B^ can be varied by changing the distance of the relevant coils from the vapour cell.

The resultant magnetic field monitored by the rf atomic magnetometer includes components from the primary, secondary and compensation field, in other words b + B + B^ = b + B⁷.

The configuration allows determination of amplitude and phase (orientation) of the rf in yz plane. The amplitude

I 5“ 5 b_y+B _y (R=^(b_/+B^,/)^z+(bz+B'_z)^z) and the phase (cp=arctan( J _+β, )) of the rf spectroscopy signal describes changes in the resultant field, where b_z+B'_z and b_y+B'_y are the two quadrature components of the rf signal.

We begin with a model of b in the case of a ID scan of the rf coil position in y direction across the centre of the recess (Fig. 1(a)) in conductive samples (the skilled person will appreciate that a similar argument, as below, could be done based on magnetisation for samples with a high magnetic permeability). In this geometry only by and b_zcomponents are produced. Figure 2 shows the dependence of the secondary rf field components on rf coil position. In a homogeneous sample eddy current flow has circular symmetry and b has only one non-zero component, b_z [solid blue line in Fig. 2]. In vicinity of the recess, the symmetry of eddy currents flow is broken and non-zero component b is produced in the yz plane [dashed red line in Fig. 2]. The asymmetry of eddy current flow is mirrored on the other side of the recess, which results in the opposite sign of by. In the case of an rf coil above the recess, due to bigger lift off magnetic field flux through the plate becomes smaller, and consequently b decreases.

As we have shown previously [15], in the presence of a strong primary field B along z, changes in the secondary field components are mapped onto the amplitude (b₇) and phase (by) of the rf spectroscopy signal. Changes in the resultant magnetic field monitored by the atomic magnetometer are relatively small as they appear on top of a much bigger primary field.

To provide better insight, we consider the case where |b|~||b| along both z and y. Here, the observed amplitude and phase contrasts are estimated to be £^<0.05 and £^<4° respectively, where ^cR⁼^Max~^Min^^Max⁺^Min^ ^anc* ^C(p⁼^^>Max~^^>Min^{i wit}^ ^Max'^Min'^Max' ^anc^ ^Min being max/ min values of relevant variables (see corner graphs in Fig. 3 (c). These values are significantly lower than their maximum of C^=l and 0^=180°.

Figure 3 shows the simulated dependence of the amplitude and phase of the rf spectroscopy signal measured by the atomic magnetometer on the resultant magnetic field. Complete compensation of the primary field component in the resultant magnetic field monitored by the atomic magnetometer (|b'|~0) leads to an increase in amplitude and phase contrast [C^=0.44 and £φ=124°, central plot in Fig. 3] but does not produce maximum contrast values. The reason being that for |β'|=0 the /~2 2 signal amplitude becomes where the high contrast component by is reduced by the slowly varying offset of b_z (Figure 2).

The phase of the rf spectroscopy signal (cp=arctan( . ,_R, )) changes by 180° only when there is a change of the sign in the nominator and a singularity in the denominator. This indicates that the condition for achieving maximum contrast is B'_z+b_z=0 and B'y=0. In the following, we refer to these conditions as the compensation point. Fig. 3 confirms that maximum amplitude and phase contrast is observed for a non-zero value of B'_z. Figure 3 shows that changes in the vertical and horizontal components of S' induce changes in the shape of the phase and amplitude profiles. In particular, when B'_z is changed (with By=0) the shape of the amplitude profile evolves from 'dip' (for B'_z—13), through 'ring' (for B'_z=0) to 'top hat' (for B'_z~ 13). This evolution in amplitude profile is accompanied with the change of sign in dispersive phase profile. Variation of the z (in this case vertical) component of B' results in modifications of the amplitude and phase profiles. In the vicinity of the compensation point, modelling predicts phase jumps in the magnetic resonance signal by nearly 180° over the recess area. The reason for sudden phase change is a presence of z component of resultant rf field in the denominator of the arctan function that defines phase of rf spectroscopy signal.

The inventors adapted as a testbed for the experimental exploration of rf magnetic field compensation, changes in the amplitude and phase of the rf spectroscopy signal recorded with an rf coil scanned across a defect in the form of a recess (24.5 mm diameter, 2.4 mm deep) in 6 mm thick aluminium and carbon steel plate [15]. We begin from the realization ofthe compensation point. Experimentally, this is achieved by tuning the distance between the compensation coils and the vapour cell 20 (Fig. 1(a)). The coil located above the vapour cell 20 (the first compensation coil 42) is positioned on axes with the rf coil 14 producing the primary field. The optimum location of this coil along z is established by minimising the amplitude of the rf spectroscopy signal. The position of the other compensation coil (the second compensation coil 44) can be adjusted in all three directions. The presence of this coil is particularly important in measurements with ferromagnetic objects, where a significant rf field is produced in the plane parallel to the sample surface (the horizontal plane in this instance) by the sample. Figure 3 indicates that compensation in the horizontal direction results in symmetric amplitude and phase profiles. This factor is utilised in searches for the compensation point.

Figure 4 shows the changes in (a) amplitude, Cr (blue diamonds), and (b) phase, C^, contrast as a function of the distance of the vertical coil from the compensation point along z. The measurement has been performed with a 6 mm thick aluminium plate. Green squares in Fig. 4 (a) represent the change of the rf spectroscopy signal measured in the centre of the recess. Both plots confirm the presence of the maximum contrast at the compensation point. For reference, we show the amplitude/ phase contrast value recorded without rf compensation fields [blue/ red solid line in Fig. 4 (a)/ (b)].

The benefit of rf compensation can be demonstrated in the experiment with increased lift-off distance, 6 mm - 7 mm. Starting point for this is a measurement of the phase contrast in a standard configuration (the rf coil producing the primary field located 1 mm - 2 mm above the sample surface, no rf compensation). The phase contrast for a case of a 12 mm diameter recess that is 2.4 mm deep in 6 mm thick aluminium plate is ϋφ=40°. An increase of the lift off (6 mm - 7 mm) results in a reduction of the strength of the primary at the sample, and consequently, secondary field. At the same time, for a fixed distance between the vapour cell and the sample, Fig. 1(a), the primary field component monitored by the atomic magnetometer increases. This causes a reduction of the recorded phase contrast to ^=20°. With the adjustments of the compensation rf field we were able not only to recover the initial phase contrast value but even increase it to its maximum value, ^=180°.

Although in the embodiment above, B_c has components in direction y as well as z, this is not necessary in every embodiment. For example, it is possible to compensate only in the z direction. In the above embodiment, this means that the second compensation coil 44 can be omitted.

Another embodiment is shown in Figure 6. In the embodiment of Figure 6, the effect on the atomic magnetometer of components of the primary and secondary fields in a direction substantially orthogonal to the surface of the sample is reduced by aligning an insensitive axis of the atomic magnetometer with a direction substantially orthogonal to the surface of the sample.

The method of this embodiment benefits from fact that the rf atomic magnetometer is not sensitive to magnetic field oscillating along static bias field axes, B_bias (Fig. 1(a)) [16]. For the B_bias oriented along z, which is preferably also the B direction, B_z will be absent in the rf atomic magnetometer signal and the measurement configuration becomes equivalent to one with the compensated primary field component.

The atomic magnetometer evaluates the oscillating magnetic field strength through measurement of the atomic Zeeman coherence amplitude produced by this field in the atomic vapour polarized along direction of the static magnetic field, B_bias [19]. Since only magnetic fields oscillating orthogonally to b/ direction can generate atomic coherences, magnetometer is insensitive to the rf fields along B_biasdirection. For the B_bias aligned along z, this property of the atomic magnetometer is equivalent to first part of the compensation condition,

B'_z+b_z=0_f in other words an absence of the z-component of the resultant rf field in the magnetometer signal.

The embodiment of Figure 6 is in many respects the same as the embodiment of Figure 1(a) except as discussed. Static bias magnetic field 26 is directed along z and set to the same strength used in previous measurements (equivalent to Larmor frequency about 12.6 kHz). The pump laser beam 28 is aligned along bias magnetic field 26. The Helmholtz coils are adjusted accordingly and configured to null static fields along x and y directions.

Although not necessary in all embodiments, in the embodiment of Figure 6, the system also includes a set of rf coils 40' for providing a compensatory magnetic field for compensating for components of the primary field which are parallel to the sample surface (horizontal components of the primary field in this instance). The position of these compensating coils are varied such that the rf spectroscopy signal is minimised. The compensating coils 40' include a first compensation coil 46 and the second compensation coil 44, the second compensation coil 44 being as discussed above. The first compensation coil 46 has an axis substantially parallel to the sample surface and substantially orthogonal to the bias field direction and the direction of the probe laser. In this embodiment, the axis of the first compensation coil 46 is substantially aligned with direction x. The current though the compensation coils 40' is adjusted to minimize the rf spectroscopy signal without sample, in other words to compensate horizontal components of the primary field (B'_x=0 and B'^=0). As before, the resultant magnetic field monitored by the rf atomic magnetometer includes components from the primary, secondary and compensation field, in other words b + B + = b + B'.

In the embodiment of Figure 6, the amplitude (R=^y(b_x) ²+(b_y)²) and ^bx the phase (q>=arctan( ~r~)) of the rf spectroscopy signal reflect y variations of the amplitude and phase of the horizontal components of the secondary field.

In other words, the embodiment of Figure 6 has B_bias along z. The pump laser beams orients atomic vapour along direction of the bias field. Horizontal components of the primary field is compensated in vapour cell by a set of two rf coils oriented along x and y direction.

Figure 7 illustrates benefits of and differences between two discussed compensation schemes. It shows the images of 64x64 mm² area of a 6 mm thick Al plate containing a 24 mm diameter recess that is 2.4 mm deep recorded in three different configurations: (a) without compensation, (b) with compensation performed with two rf coils, and (c) with rotated bias magnetic field and compensation coils. Images represent the change of the amplitude of the rf spectroscopy signal. As mentioned before, for the uncompensated case (a) the recorded profile shows variation of the vertical component of the secondary field. In compensated cases the images show horizontal component (b)/ components (c) of the secondary field. The difference in symmetry of the image results from the change of the direction of the bias field. In case shown in Fig. 7 (b) B_biag is directed along x axis and therefore only signatures produced by the recess edges parallel to that direction are present in the recorded profile (in other words, the edge parallel to B_biasproduces oscillating secondary field perpendicular to B_bias that could be seen by the magnetometer). In case shown in Fig. 7 (c) B_bias\s directed along z axis and the recorded profile shows whole contour of the recess. We have calculated the amplitude contrast, Cr, as defined previously for the three images. The numbers confirm [(a) C^=0.04; (b) C^=0.77; (c) C^=0.79] that implementation of the compensation schemes allows easier identification of the structural defects in the amplitude images. In case of the modified geometry, the phase of the rf spectroscopy signal shows a vortex centered on the recess.

Demonstrated above are two methods for improvement of the contrast in the images representing the variations of the amplitude and phase of the rf spectroscopy signal recorded by the atomic magnetometer in eddy currents NDT measurement. The methods are based on compensation of the components of the resultant rf magnetic field monitored by the atomic magnetometer implemented in the above examples by either a set of coils or the geometry of the measurement. Reduction of the amplitude of the rf signal monitored by the atomic magnetometer through compensation process does not compromise ability for a defect detection. On contrary, monitoring of the signal phase in compensated configuration provides with the option of clear (180° phase change) signature of the inhomogeneity.

In another embodiment for increasing the amplitude and/or phase contrast of the output of the system, the bias magnetic field is modulated. This can be in addition to or instead of reducing the effect on the magnetometer of components of the primary and secondary magnetic fields in a direction substantially orthogonal to the sample. In other respects, the embodiment is substantially as described for the first or second embodiments.

Figure 8 shows a schematic system diagram of the system of Figures 1(a) and 6. The system works in the following way.

1. Output of the internal reference of the lock-in amplifier (1) 36 generates frequency modulated current in the rf coil 14.

2. The coil 14 produces (primary) rf field, which drives precession of atomic spins in the detection cell in the bias magnetic field (8_6/as).

3. Bias magnetic field strength defines the value of resonant Larmor frequency (o)_L = y 8e_/as), the frequency for which there is a maximum coupling between atomic spins and rf field.

4. To observe the precession of the atomic spins, off-resonant linearly polarised probe beam 32 is used. Beam polarisation direction is coupled to the atomic spins oscillation via Faraday's effect. The polarisation oscillation is transferred to electronic signal by balanced polarimeter 34. Amplitude and phase of the oscillation is read by lock-in amplifier 36 (referenced to the rf coil current modulation).

5. To see resonant behaviour of atomic spins precession we can either scan the primary field frequency for given bias magnetic field (left plot of Figure 9) or scan bias magnetic field for the chosen primary field frequency (right plot of Figure 9). Figure 9 shows how results would look like in both examples.

6. When the sample is placed in the vicinity of the rf coil, the atoms will additionally experience influence of the secondary field produced by a sample.

Phase and amplitude of the signal

When the sample is moved in vicinity of the rf coil, interference between primary and the secondary field causes change of amplitude and direction of the rf field driving the atoms. Change of rf amplitude transfers to change of strength of atomic response, whereas change of direction of rf field transfers to the change of the phase of atomic spin oscillation.

Single pixel on the scan

In the simplest and the fastest measurement scheme we could set rf field frequency to be on resonance and measure amplitude and phase of atomic signal while the sample is being moved. The inventors have done this with aluminium which is non-magnetic but steel samples are ferromagnetic and are strongly magnetised. This causes shifts of bias magnetic field and even with the active field compensation such as described above, the shift is typically bigger than the linewidth of the resonance. The shift is a consequence of nonzero distance between magnetic probe used for field compensation and the atomic cell.

One way to eliminate this problem is shown in Figure 11; however, this involves a slow measurement (time: 10s per pixel). This method is as follows:

1) Rf field frequency is scanned by scanning the current modulation frequency of rf coil 14.

2) Signal is demodulated by lock-in 1 and changes ofthe in-phase and the quadrature component of the signal are recorded.

3) Computer fits the data and from the fit amplitude and phase of the signal is extracted.

However, in an embodiment of the invention, an improved way to eliminate this problem is shown schematically in Figure 12, which provides fast measurement (< 1 s per pixel).

As described above, in most measurements, the frequency of the primary field is scanned across rf resonance, i.e. the whole resonance profile is recorded, for each point of the image [15]. The inventors have developed another mode of data aquisition, which enables significant decrease in image acquisition time. In this mode, the modulation of the B frequency is replaced with the low-frequency modulation (1-20 Hz in this example) of the amplitude of the B_bias component. In this case, the signal demodulated at the primary field frequency by the lock-in amplifier 36 (SR.S 865 in this embodiment) contains low-frequency oscillation with the amplitude equal to this of the rf resonance amplitude. The use of second lock-in amplifier referenced to the frequency of the B_bias amplitude modulation enables readout of the rf resonance amplitude. The extent of the B frequency modulation can balance an imperfection in the B_bias stabilisations such as a possible shift in resonance frequency for different sample locations. As a consequence of that the phase of the recorded signal contains information about the change of the secondary field as well the rf profile frequency shift.

In this embodiment, the system includes the second lock-in amplifier 38.

The bias magnetic field source 24 includes a modulator to modulate the bias magnetic field and to output a modulation signal to the second lock-in amplifier 38. The first output of the first lock-in amplifier (referenced to rf coil frequency) is connected to the input of the second lock-in amplifier (referenced to the bias field modulation). The second lock-in amplifier is configured to demodulate the output signal from the first lock-in amplifier 36 with reference to the modulation of the bias magnetic field and to provide an amplitude and phase of the signal. The second lock-in amplifier 38 thereby serves as a demodulator.

The method is as follows:

1) Frequency of the rf field is kept constant but the value of the bias magnetic field is slowly modulated. In this embodiment the frequency of bias field modulation is 1 -10 Hz (precession frequency is around 12kHz). However, it is preferable for the frequency of the bias field modulation to be as high as possible. This bias field modulation is preferably in the form of a sawtooth wave which periodically ramps the bias field either up or down.

2) In this case we observe amplitude modulated signal.

3) We measure amplitude of this oscillations with the first lock-in (we demodulate with reference to the primary field frequency).

4) Measurement of the amplitude of slow modulation is performed with the second lock-in referenced to the signal of bias magnetic field modulation. Amplitude measured by Lock-in 2 corresponds to the amplitude of atomic resonance.

Embodiments, for example such as any of the systems described above, can perform imaging with a sensitivity of 0.1 mm.

Embodiments can be used to image steelwork non-destructively in the presence of concealing conductive barriers at room temperature, in magnetically unscreened environments, with active compensation ofthe background fields, and compensation of the samples' magnetisation. This can be used for example for detection of corrosion in concealed pipes (CUI) and detection of structural anomalies in concrete structures.

Embodiments ofthe invention can be used for detecting corrosion under insulation. Embodiments ofthe invention can provide increased contrast to enable the imaging of sub-mm corrosion pits for example in pipes.

In some embodiments, the systems described above can be deployed on a robot to scan large areas for example of pipeline.

In some embodiments, the method and/or system can be used for detection of the condition of concrete structures.

Applications can be in manufacturing and construction, where quality of assemblies and welding is important, and often requires the use of potentially dangerous and expensive X-ray scans; materials manufacturing as part of a fabrication process; health and usage monitoring systems (HUMS), where timely and non-invasive identification of structural damages and fatigue is a primary target; nuclear; and in the utilities and/or energy sector, for example oil and gas, where spillage has economical as well as environmental costs. Applications also include detecting corrosion under insulation for energy sector, monitoring of the re-enforced concrete structures for transport sector, nuclear waste vessels monitoring.

Particular advantages are that the system and method may:

• Be safe and non-invasive (e.g. non-ionising radiations) • Detect corrosion on the inner-wall of a pipeline.

• Detect corrosion on the outer-wall of a pipeline.

• Be able to differentiate between corrosion and changes to pipeline geometries from bends/T-Junctions/welds in the pipe.

• Be able to scan through all insulation types.

• Be low cost.

• Provide improvements to current techniques (resolution, switch scanning-modes).

Although in the embodiments above, a lock-in amplifier 36 is described as providing the primary field controller, the primary field controller can include any current generator provided that the primary field oscillation controller includes a processor for demodulating the output signal from the balanced polarimeter with reference to the frequency or modulation of the current generator. Nevertheless, a lock-in amplifier is advantageous because they make the detection of the spectra easier as the source of the frequency/modulation and detector are inside one instrument (synchronisation, referencing, is automatically sorted out).

Although in the embodiments above, the material response detection is used for material defects imaging, this is not necessary in every embodiment. In some embodiments, the material response detection can be used for other purposes, for example to detect material conductivity and/or permeability.

All optional and preferred features and modifications of the described embodiments and dependent claims are usable in all aspects of the invention taught herein. Furthermore, the individual features of the dependent claims, as well as all optional and preferred features and modifications of the described embodiments are combinable and interchangeable with one another.

References [1] L. Ma and M. Soleimani, Meas. Sci. Techno/., 28, 072001 (2017).

[2] H. Griffiths, Meas. Sci. Technol., 12, 1126 (2001).

[3] B. A. Auld and J. C. Moulder, J. Nondestr. Eval. 18, 3 (1999).

[4] L. Perez, J. Le Hir, C. Dolabdjian, and L. Butin, J. Elec. Eng., 55, 73 (2004).

[5] A. Sophian, G. Tian, M. Fan, Chin. J. Meeh. Eng., 30, 500 (2017).

[6] T. Dogaru and S. T. Smith, Nondestr. Test. Eval., 16, 31 (2000).

[7] T. Dogaru and S. T. Smith, IEEE Transactions on Magnetics, 37, 5, 3831 (2001).

[8] P. Ripka, M. Janosek, IEEE Sensors J. 10, 1108 (2010).

[9] H. J. Krause and Μ. V. Kreutzbruck, Physica C, 368, 70 (2002).

[10] J. Storm, P. Hommen, D. Drung, R. Korber, App. Phys. Lett. 110 072603 (2017).

[11] A. Wickenbrock, S. Jurgilas, A. Dow, L. Marmugi, and F. Renzoni, Opt. Lett. 39, 6367 (2014).

[12] C. Deans, L. Marmugi, S. Hussain, and F. Renzoni, Appl. Phys. Lett. 108, 103503 (2016).

[13] A. Wickenbrock, N. Leefer, J. W. Blanchard, and D. Budker, Appl. Phys. Lett. 108, 183507 (2016).

[14] C. Deans, L. Marmugi, and F. Renzoni, Opt. Exp. 25, 17911 (2017).

[15] P. Bevington, R. Gartman, W. Chalupczak, C. Deans, L. Marmugi, and F. Renzoni submited to App. Phys. Lett..

[16] Orientation of the GMR sensitive axis paralel to the surface of the sample has been discussed in [7].

[17] W. Chalupczak, R. M. Godun, S. Pustelny, and W. Gawlik, Appl.

Phys. Lett. 100, 242401 (2012).

[18] G. Bevilacqua, V. Biancalana, P. Chesssa, Y. Dancheva, App. Phys. B 122 103 (2016).

[19] W. Chalupczak, R. M. Godun, S. Pustelny, Advances in At. Mol. and 10 Opt. Phys. 67, 297 (2018).

Annex 1 - Paper 2

Imaging of material defects with a radio-frequency atomic magnetometer

P. Bevington, R. Gartman, W. Chalupczak

National Physical Laboratory, Hampton Road, Teddington, TW11 OLW, United Kingdom

Department of Physics, University of Strathclyde, Glasgow G4 ONG, United Kingdom 20.7.18

Abstract

Non-destructive eddy current testing of defects in metal plates using the magnetic resonance signal of a radio-frequency atomic magnetometer is demonstrated. The shape and amplitude of the spatial profile of signal features that correspond to defects are explored. By comparing numerical and experimental results on a series of benchmark aluminium plates we demonstrate a robust process for determining defect dimensions. In particular, we show that the observed images represent the spatial distribution of the secondary field created by eddy currents in the sample. We also demonstrate that the amplitude and phase contrast of the observed profiles enables us to reliably measure defect depth.

33.35.+r, 32.70.Jz, 32.30.Dx

Accurate identification of structural flaws, such as corrosion in pipes or cracks in an aerofoil, has obvious benefits across many industries. In particular, the global cost of corrosion is estimated to be USD 2.5 trillion every year [1], Over 20% of the major oil and gas accidents reported within the EU since 1984 have been associated with corrosion under insulation [2], Monitoring the sample response to an oscillating magnetic primary field (B), provides a method of non-destructive testing (NDT) and detection of anomalies. Sample response, i.e. an oscillating secondary magnetic field (h), is created by eddy currents in samples with high conductivity, and magnetisation in ones with high permeability [3], The response carries information about the conductivity, permittivity and permeability of the conducting material, and these material properties can be mapped via the measurement of b [4],

Most eddy current NDT systems use an rf coil to generate b, but the material response can be detected in two ways, namely by measurement of coil inductance or with a magnetic sensor. Measurements based on coil inductance monitoring [4-7] benefit from simple instrumentation, but suffer from a decrease in signal sensitivity at low frequencies. Magnetic sensors offer higher sensitivity at low-frequencies and better spatial resolution [10]. This category of sensors includes giant magnetoresistance (GMR) magnetometers [8,9,10], superconducting quantum interference devices (SQUTDs) [11,12] and atomic magnetometers [13-16]. Atomic magnetometers are an attractive sensor type as they have sensitivities approaching those of GMR and SQUID sensors, can operate in an unshielded environment [18], do not require cryogenics, and have few restrictions of miniaturisation.

The ability to extract information about defects such as cracks, bends and pipe thinning from measurement signals lies at the heart of NDT. Therefore, understanding how the observed signal is created and linked to the anomaly is one of the first issues that needs to be addressed when developing an NDT system. In this paper we explore how the spatial variation in the signals recorded by an rf magnetometer correspond to the physical dimensions of structural defects in aluminium (Al) plates. Non-magnetic (paramagnetic) samples have been chosen to minimise changes in the local field detected by the atomic magnetometer. However, while we examine the spatial profiles generated by the thinning of Al targets, similar profiles have been observed in the case of ferromagnetic (carbon steel) plates [19]. The arguments presented here could, with some modifications, be extrapolated to measurements involving ferromagnetic materials. In addition to the characterisation of the measurement signal’s spatial profile, we calibrate measurements of sample thinning by monitoring the change of the rf signal phase/amplitude. This work presents a specific geometry, where the atomic sensor and coil are on the same side of the sample and are operated in an unshielded environment, representing a real-world sensing environment.

The measurement signal comes from the phase and amplitude change in the rf resonance spectra registered by an rf atomic magnetometer as a conductive sample is moved under the rf coil (Fig. 13). Since the experimental setup is similar to that described in [20,19] only essential components will be discussed here. Room temperature caesium vapour (atomic density n_Cs — 3.3 x IO¹⁰ cm^-3) atoms are optically pumped in to the stretched state (F=4,m=4 ) with a circularly polarised laser locked to the Cs 6 S F=3 —>6 P F’=2 transition (D2 line, 852nm) propagating along the bias magnetic field. The probe beam (30pW) is 580 MHz blue shifted from the 6 S F=4—>6 P_3/2 F’=5 transition via phase-offset-locking to the pump beam. Coherent spin precession of the Cs atoms is coupled to the polarisation of the probe beam (Faraday rotation) and is detected with a balanced polarimeter. This signal is then demodulated at radio-frequency by a lock-in amplifier (SRS 865). This work is carried out in a magnetically unshielded environment, where static fields along the y and z directions are nulled and a bias field is created by three pairs of nested, orthogonal, square Helmholtz coils, with dimensions Im, 0.94m and 0.88m respectively. The operating frequency of the system (i.e. the magnetic resonance frequency) is set to 12.6 kHz by the x component of the bias magnetic field (Fig. 13). The rf coil is a 1000 turn coil with 0.02 mm wire, wound on a 2 mm plastic core (inside diameter) and with a 4 mm width (outside diameter) and a 10 mm length. It is driven by an internally referenced rf output from the lock-in amplifier. The samples are fixed to a 2D, computer controlled translation stage that has a minimum step of 0.184 mm. The sample is located approximately 30 cm from the cell and the coil is placed 1 mm - 2 mm above the sample, on the same axis as the cell.

Figure 14 (a)/(b) shows the results of the scanned 64*64 mm² area of an Al plate with a defect in the form of a recess (48 mm diameter, 2.4 mm deep). Each pixel of the image represents the phase [Fig. 14 (a)] or amplitude [Fig. 14 (b)] of the rf resonance profile recorded by scanning the rf frequency through the magnetic resonance. These parameters are extracted through fitting of a Lorentzian and dispersive profile to the rf resonance line shapes. Although both plots contain traces of the sample thinning, the spatial signatures of the recess have different characteristics. The feature presented in Fig. 14 (a) shows that the phase changes as the rf coil scans over the falling and rising edges. The phase change measurement is most sensitive to the edges parallel to the bias field. Signatures from the parallel edges are also present in the amplitude data, Fig. 14 (b), but are superimposed on top of an increase in signal recorded over the whole recess.

In order to gain insight into the recorded images, we created a simple 2D model based on Faraday’s law, by calculating the coupling between the primary field B and the conductive sample containing an inhomogeneity. We model the spatial distribution of B with a step function that describes the rf coil diameter. The secondary field, b, changes linearly within the boundaries of the step function and decreases inversely with the distance outside of it. The eddy currents form closed loops that follow the path of least resistance. In the case of a uniform conductor surface, b will be produced parallel to the surface normal. However, the presence of inhomogeneities breaks the eddy currents symmetry and can change the orientation of b. Figure 15 shows the components of b generated in a conductive sample in the presence of a 48 mm diameter recess. Since the direction of b depends on the relative position of the induced eddy currents and the recess boundaries, b has opposite signs for rising and falling edges [Fig. 15(a, b)]. The components of b parallel to the conductor surface show complementary signatures of the recess (i.e. Fig. 15 (a)/(b) shows the change of the field sign due to a presence of part of the recess edges parallel to tlievA direction). The component of b orthogonal to the conductor surface decreases over the recess area, Fig. 15(c).

While Fig. 15 only shows the components of the secondary field, the signal measured by the magnetometer is a mixture of both the primary, B, and secondary field, b . The lock-in signal amplitude R= yj((B_+by-(B,-by) and phase B+b, <p-arctan( ^7^) correspond to the strength and orientation of the rf field component z z projected on the yz plain; where B-h_ and B +h are the two quadrature components of the rf signal. Tn our experiment B and B =^consf»b , hence B +b »B +b .

y z z z z y y

Therefore we can make the approximation that R~\B +b I and <p—/> /(B +b ) which z z y z y leads to mapping of b? onto Rv.b_ and b. onto φ<Χά . The latter approximation comes from the observation that for |B| » \b\, the function φ depends more strongly -I -2 on b ( dy/db ccB_z )than b? (d<^!dboiB_z ). It can be concluded that the presence of a strong B allows mapping of one horizontal component and the vertical component of b onto the amplitude and phase of the rf signal, as is shown in Figs. 14 and 15. Figure 14 (c)/(d) shows the results of the modelled signal with contributions from both the primary and secondary fields. Full reconstruction of b would require rotation of the sensor axis to measure the remaining horizontal component.

The minimum spatial extent of the profile representing the defect (recess) is defined by the coil diameter, lift off distance, operating rf frequency, and conductivity of the sample. The radial dimension of the rf coil defines the B spatial distribution and the size of the region containing the greatest density of eddy currents [9], There are two regimes in eddy current testing that are defined by the ratio between the dimensions of the rf coil and the size of the defect. When the defect is significantly larger than the coil, the observed profile in the image represents the spatial extent of the defect. If the defect is smaller than the coil size, the image represents the map of the field generated by the rf coil [5]. We explore these two regimes by recording the phase images of circular recesses of decreasing diameter in aluminium Al plates (Fig. 16). While the diameters of the features shown in Fig. 16 (a-c) follow the diameters of the actual recesses, the diameter of the profile shown in (d), which represent the phase image of a 2 mm recess, is defined by the 4 mm diameter of the rf coil, as shown in Fig. 17(a). We have observed the same behaviour with even smaller recesses. This confirms the initial assumption that the spatial resolution of our measurement is limited by the size of the coil and is not restricted by the sensor (vapour cell) dimensions. It is worth pointing out that while the 2 mm recess is clearly visible in the phase image it can’t be identified in the amplitude image. In the case of recesses with small diameters, the features in the phase image that represent edges overlap and the actual value of the phase contrast becomes a function of the recess diameter, as shown in Fig. 17(b).

To verify the dependence of the phase and amplitude contrast on the depth of the recess we have recorded phase and amplitude images generated by a 6 mm Al plate with a single recess, whose depth changes from 0 mm to 5 mm (scanned area marked with white square in Figure 18 (a)). Scanning the plate along the x-axis is equivalent to monitoring the signal response to a continuous change in the depth of the recess. The presence of only one recess in the scanned area ensures that the observed amplitude and phase changes are not affected by other inhomogeneities in the sample. Figure 18 shows the phase (b) and amplitude (c) change of the rf signal recorded over the recess. It indicates a linear change of the signal amplitude and a sinusoidal change of the signal phase with the depth of the recess. There is a change in a slope of linear dependence in amplitude variation for x <10 mm and x >60 mm in Fig. 18c. The central part of the plot comes from scan over the region with monotonic change of the recess height. The regions mentioned above include contributions from the flat parts outside scanning range due to finite size of the rf coil.

To conclude, monitoring the amplitude and phase changes of the rf resonance over the conductive sample provides a sensitive tool for the detection of a material defect. Implementation of atomic magnetometers in eddy current imaging is particularly interesting for studies of ferromagnetic samples at low operating frequencies, enabling penetration through the sample surface or under insulation barriers (e.g. corrosion under insulation). We have demonstrated that the phase and amplitude images could be used for estimations of sample thinning, although specific thickness estimation needs to take into account the size of the inhomogeneity. The tunability of the rf atomic magnetometer not only allows for the change of the penetration depth but also the choice of an operating frequency range free from external interferences.

This work was funded by the Innovate UK Energy Game Changer programme (IUK 132437).

References [1] International Measures of Prevention, Applications, and Economics of Corrosion Technologies Study, NACE International, 2016.

[2] Oil and Gas Technology Centre, Call for Ideas: Corrosion under insulation document, https://bit.ly/2IfwkJV.

[3] In ferromagnetic samples, the oscillation in magnetisation is much larger than the magnetic field generated by eddy currents. Measurement of the driven eddy current response is therefore aided by saturation of the magnetisation.

[4] H. Griffiths, Meas. Sci. Technol., 12, 1126 (2001).

[5] B. A. Auld and J. C. Moulder, J. Nondestr. Eval. 18, 3 (1999).

[6] L. Perez, J. Le Hir, C. Dolabdjian, and L. Butin, J. Elec. Eng., 55, 73 (2004).

[7] A. Sophian, G. Tian, M. Fan, Chin. J. Meeh. Eng., 30, 500 (2017).

[8] T. Dogaru and S. T. Smith, Nondestr. Test. Eval., 16, 31 (2000).

[9] T. Dogaru and S. T. Smith, IEEE Transactions on Magnetics, 37, 5, 3831 (2001).

[10] P. Ripka, M. Janosek, IEEE Sensors J. 10, 1108 (2010).

[11] H. J. Krause and Μ. V. Kreutzbruck, Physica C, 368, 70 (2002).

[12] J. Storm, P. Hommen, D. Drung, R. Korber, App. Phys. Lett. 110 072603 (2017).

[13] A. Wickenbrock, S. Jurgilas, A. Dow, L. Marmugi, and F. Renzoni, Opt. Lett. 39,6367 (2014).

[14] C. Deans, L. Marmugi, S. Hussain, and F. Renzoni, Appl. Phys. Lett. 108, 103503 (2016).

[15] A. Wickenbrock, N. Leefer, J. W. Blanchard, and D. Budker, Appl. Phys. Lett. 108,183507(2016).

[16] C. Deans, L. Marmugi, and F. Renzoni, Opt. Exp. 25, 17911 (2017).

[17] J. Belfi, G. Bevilacqua, V. Biancalana, R. Cecchi, Y, Dancheva, and L. Moi, Rev. sci. Instrum 81, 065103 (2010).

[19] P. Bevington, R. Gartman, W. Chalupczak, C. Deans, L. Marmugi, and F. Renzoni submited to App. Phys. Lett..

[20] W. Chalupczak, R. M. Godun, S. Pustelny, and W. Gawlik, Appl. Phys. Lett. 100, 242401 (2012).

Claims

1. A method of detecting a material response, including:

2. The method of claim 1, wherein the primary magnetic field is substantially orthogonal to the surface of the sample.

3. The method of any preceding claim, including detecting changes in electrical conductivity and/or magnetic permeability of the sample from the detection of the secondary magnetic field.

4. The method of any preceding claim, wherein reducing the effect on an atomic magnetometer of components of the primary and secondary magnetic fields in a direction substantially orthogonal to a surface of a sample includes:

providing a compensatory magnetic field at the atomic magnetometer including a component substantially orthogonal to the surface of the sample.

5. The method of claim 4, wherein the compensatory magnetic field is provided such that Bz' + bz = 0, wherein Bz' is a component of B' which is substantially orthogonal to the surface of the sample, bz is a component of the secondary magnetic field which is substantially orthogonal to the surface of the sample, B' = B + B^ , B is the primary magnetic field, and B^ is the compensatory magnetic field.

6. The method of any of claims 4 to 5, wherein the compensatory magnetic field includes a component in a first direction substantially parallel to the surface of the sample, and preferably substantially orthogonal to an insensitive axis of the atomic magnetometer, to reduce the effect of components of the primary magnetic field in the first direction.

7. The method of claim 6, wherein By' = 0, wherein By' is a component of S' in the first direction, B' = B + , B is the primary magnetic field, and B^ is the compensatory magnetic field.

8. The method of any preceding claim, wherein reducing the effect on an atomic magnetometer of components of the primary and secondary magnetic fields in a direction substantially orthogonal to a surface of a sample includes:

aligning an insensitive axis of the atomic magnetometer with a direction substantially orthogonal to the surface of the sample.

9. The method of claim 8, wherein the atomic magnetometer includes a bias magnetic field, the method including aligning the bias magnetic field with a direction substantially orthogonal to the surface of the sample.

10. The method of claim 8 or 9, including providing a compensatory magnetic field at the atomic magnetometer including a component in a first direction substantially parallel to the surface of the sample, the compensatory magnetic field reducing the effect of components of the primary magnetic field in the first direction.

11. The method of claim 10, wherein By' = 0, wherein By' is a component of S' in the first direction, B' = B + B^ , B is the primary magnetic field, and B^ is the compensatory magnetic field.

12. The method of claim 10 or 11, wherein the compensatory magnetic field includes a component in a second direction substantially parallel to the surface of the sample, the second direction being substantially orthogonal to the first direction, the compensatory magnetic field reducing the effect of components of the primary magnetic field in the second direction.

13. The method of claim 12, wherein Bx' = 0, wherein Bx' is a component of B7 in the second direction, B7 = B + B^ , B is the primary magnetic field, and B^ is the compensatory magnetic field.

14. A system for detecting a material response, including:

15. The system of claim 14, wherein the magnetic field source is configured to be disposed in a non-overlapping relationship with the sample.

16. The system of any of claims 14 to 15, including a computer including a receiver to receive a signal originating from the atomic magnetometer and representing a detection of the secondary magnetic field, the computer being configured to determine changes in conductivity and/or permeability of the sample in response to detection of the secondary magnetic field.

17. The system of any of claims 14 to 16, including a compensatory magnetic field source for providing a compensatory magnetic field at the atomic magnetometer including a component in the primary direction.

18. The system of claim 17, wherein the compensatory magnetic field source includes a coil arrangement.

19. The system of any of claims 14 to 18, wherein the atomic magnetometer has an insensitive axis arranged in the primary direction.

20. The system of claim 19, wherein the atomic magnetometer includes a bias magnetic field source configured to provide a bias magnetic field in the primary direction.

21. The system of any of claims 14 to 20, including a compensatory magnetic field source for providing a compensatory magnetic field at the atomic magnetometer including a component in a first direction substantially orthogonal to the primary direction to reduce the effect of components of the primary magnetic field in the first direction.

22. The system of claim 21, wherein the compensatory magnetic field source is for providing a compensatory magnetic field at the atomic magnetometer including a component in a second direction substantially orthogonal to the primary direction to reduce the effect of components of the primary magnetic field in the second direction, the second direction being substantially orthogonal to the first direction.

23. A method of detecting a material response, including:

24. The method of claim 23, wherein a frequency of oscillation of the primary magnetic field is fixed.

25. The method of any of claims 23 to 24, wherein a frequency of modulation of the bias magnetic field is less, preferably by an order of magnitude, than a frequency of oscillation of the primary magnetic field.

26. The method of any of claims 23 to 25, including demodulating a signal, provided by the atomic magnetometer in response to detection of the secondary magnetic field, to determine an amplitude and/or a phase.

ΊΊ. The method of any of claims 23 to 26, including demodulating a signal, provided by the atomic magnetometer in response to detection of the secondary magnetic field, with reference to a frequency of oscillation of the primary magnetic field, to provide a partially demodulated signal.

28. The method of claim 27, including demodulating the partially demodulated signal with reference to a frequency of modulation of the bias magnetic field to determine an amplitude and/or phase of a signal provided by the atomic magnetometer in response to detection of the secondary magnetic field.

29. A system for detecting a material response, including:

a modulator for modulating the bias magnetic field.

30. The system of claim 29, including a primary magnetic field source for providing an oscillating primary magnetic field.

31. The system of any of claim 29 to 30, including a demodulator arrangement for determining an amplitude and/or phase of a signal, provided by the atomic magnetometer in response to detection of the secondary magnetic field.

32. The system of claim 31, wherein the demodulator arrangement includes a receiver for receiving a signal provided by the atomic magnetometer in response to detection of the secondary magnetic field and is configured to demodulate the signal with reference to a frequency of oscillation of a or the primary magnetic field to provide a partially demodulated signal.

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33. The system of claim 32, wherein the demodulator arrangement includes a receiver for receiving a modulation signal from the modulator and is configured to demodulate the partially demodulated signal with reference to the modulation signal to allow determination of an amplitude and/or phase of the partially demodulated signal.

34. The system of any of claim 29 to 33, wherein the bias magnetic field source includes a coil arrangement.