Supplementary Information
Magnetic Imaging: a New Tool for UK National Nuclear Security
Brendan J. Darrer1, Joe C. Watson2, Paul Bartlett1, Ferruccio Renzoni1
1
Department of Physics & Astronomy, University College London,
Gower Street, London, WC1E 6BT, United Kingdom
2
Novel Detection Concepts, National Nuclear Security Programme,
Atomic Weapons Establishment, Aldermaston, Reading, RG7 4PR, United Kingdom
Experimental set-up
The imaging system is sketched in Figure 1(a). It operates by applying an alternating magnetic field over the object
using two coils of radius 13.45 cm arranged in the Helmholtz configuration. Such an arrangement produces a field
approximately uniform over the object, positioned in between the driver coil pair. An amplifier drives the coils using
the reference oscillator of a dual-phase lock-in amplifier at frequencies between 200 and 500 Hz, as an input.
Position-resolved measurements of the total magnetic field, which includes the primary field generated by the driver
and the secondary field produced from the object, are taken using a planar sensor-array of 20 × 20 ferrite-cored coils
(Fig. 1(b)). These coils, which have a diameter equalling (6.9  0.03) mm and inductance equalling (680 ± 10%) H,
are uniformly arranged on a 20 × 20 grid with inter-coil spacing of 12.74 mm. This array is positioned between the
object and one of the Helmholtz coils. Each sensor coil on the array measures the oscillating magnetic field at its
position, consisting of the sum of the primary and secondary magnetic fields. A 400-channel analogue multiplexer
selects individual coils for interrogation. A dual-phase lock-in amplifier measures the amplitude and phase of the
e.m.f.’s, due to the eddy currents, that are induced by the magnetic field. The output from every sensor coil on the
array is independently measured in sequences lasting between 1 and 20 minutes.
Figure 1 (a) Schematic of the experimental set-up; (b) Picture of the 20  20 sensor-coil array used for image capture.
Characterisation of the imaging system
To initially characterise and calibrate our imaging system we performed two series of measurements, with results as in
figure 2. For both sets of measurements the Helmholtz coils were driven at 500 Hz, with field amplitude at the level of
the sensor coils, of 0.11 mT RMS. For the first series of measurements, magnetic images of different diameter disks
ranging from 1.5 cm to 15 cm were taken, where disks were either centred on a single array sensor, or between four
sensors. This demonstrated variations in image size with the position of the disk relative to the array sensors. To
determine the effects of different metallic conductivities (σ), images of disks manufactured from copper (σ = 5.96×107
S/m at 20 °C) and aluminium (σ = 3.5×107 at 20 °C) were captured. Disk profiles were derived from the resultant
magnetic images, formed using a modified Canny-edge-detection algorithm, thereby allowing the derivation of disk
diameters directly from images. As presented in figure 2(a), for disks sufficiently larger than the spacing between
sensors, disk diameter measurements via the magnetic image exhibited a linear dependence with true diameter, and
demonstrated independence between the exact relative-position of an object with respect to sensor array positions. The
resolution of the imaging system, which was defined as the least diameter of the disks that gave an edge-detected
diameter distinguishable from disks of smaller size, was determined from these measurements and found to be
approximately 30 mm. This defined that the limit of resolution was essentially determined by the finite array spacing
between sensor coils.
Figure 2. Canny-edge-detected diameter against true diameter as measured for Copper (Cu) and Aluminium (Al) disks of 2 mm
thickness. Red and blue data set is for the disks centred between four sensors and the black and green data sets for the disks
centred on one sensor. The solid line represents the linear fit to all the data with values of diameter larger than 50 mm.