IEEE TRANSACTIONS ON MAGNETICS, VOL. 27, NO. 2, MARCH 1991

HIGH-RESOLUTION MAGNETIC MAPPING USING A SQUID MAGNETOMETER ARRAY

Abstract

D.J. Staton, Y.P. Ma, N.G. Sepulveda, and J.P. Wikswo, Jr.

Electromagnetics Laboratory Department of Physics and Astronomy

Vanderbilt University Box 1807, Station B Nashville, TN 37235

A four-channel, high-resolution, Superconducting Quantum Interference Device (SQUID) magnetometer array was used t o map magnetic fields from various samples. Each SQUID has a 3 mm diameter pickup coil located 4.4 mm from the adjacent channel. The spacing between the cryogenic array and the room temperature sample is adjustable from 1.5 mm to 4.0 mm. We mapped the field from a 350 pm diameter hole in an 11 cm x 15 cm x 60 pm copper sheet that was carrying a current of 100 mA. Field shape and strength were compared with predictions from analytical and finite element models, which indicate that this technique should be able to detect an order of magnitude smaller flaws in flat plates. We have demonstrated the ability both t o detect magnetic contamination in a 230 pm deep by 1.1 mm long slot that was electric-discharge-machined into a non-magnetic tube, and t o determine the orientation of the slot with respect t o the tube axis. Slices of pyroclastic rock of thickness as low as 30 pm thick have also been mapped.

Introduction

Conventional SQUID magnetometers have poor spatial resolution, typically having coil diameters on the order of 2.0 cm and dewar walls 1.0 to 2.0 cm in thickness separating the cryogenic coils from room temperature samples. Our SQUID magnetometer', termed MicroSQUID (pSQUID), with 0.3 cm coils and 0.15 to 0.4 cm adjustable spacing to a room temperature sample has much higher spatial resolution and is able t o produce better images due to a decrease in coil diameter and coil-to-sample spacing. Although smaller coils may result in an order of magnitude higher system noise, this is more than offset by the increased field strength resulting from decreased coil-to- sample spacing. Smaller coils also average the field spatially to a lesser degree than do larger coils, thereby increasing spatial resolution.

Mametic Images

The following data demonstrates some of the capabilities of pSQUID in obtaining high-resolution images of magnetic fields. Biological measurements are described elsewhere'. The measurements were all made with pSQUID operating in a double-layer magnetic shield for a low-noise scanning environment3. The samples were scanned beneath the magnetometer by a high-resolution, non-magnetic, motorized x-y stage with 50 mm x 50 mm travel distance and better than 5 pm resolution. All samples were scanned in a plane less than 3.0 mm beneath the SQUID coils.

Holes in Conducting Plates

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Images of the magnetic fields due t o current passed through thin plates containing small, circular holes are shown in Fig. 1. Holes of 350 pm and 1.0 mm in diameter were drilled into the center of 11 cm x 15 cm x 32 pm copper on phenolic printed-circuit boards. A 4 Hz AC current was passed uniformly through the sheets and the field scanned. The amplitude was calculated using a digital AC lock-in amplifier with an effective time constant of 250 ms.

Finite-element and analytical solutions4 are comparable in shape and amplitude with the measured values. The measured peak-to-peak value of 3.2 nT for the 350 pm hole agrees well with the predicted value of 3 nT. For holes of diameter much smaller than the coil-to-sample spacing, analytical expressions predict that the spatial frequency of the field remains constant for decreasing diameter4. This indicates that we can image a hole with a diameter on the order of 30 pm.

Trace Magmetic Contamination

As shown iri Fig. 2, we can detect magnetic contamination in (left) 230 pm deep x 1.1 mm long, and (right) 150 pm deep x 760 pm long slots that were formed in a 1/2 inch diameter, non-magnetic, metallic tube by electric-discharge-machining (EDM). The isocontour plot was used to determine that the left slot was oriented a t an angle of 17 degrees with respect to the tube axis, which is in close agreement with the expected value of 15 degrees.

Remanent Magnetization in Rock and Photocopier Toner

Two planar samples of pyroclastic rocks were scanned 2.8 mm beneath the SQUID coils. "he results are shown in Fig. 3. These rocks have characteristic inclusions with a remanent magnetization that differs from that of the bulk material. Figures 3a and 3b show the images and isofield contours for a 3 mm thick slab, and Figs. 3c and 3d show the corresponding plots for a 30 pm thick section mounted on glass. The thin section presents a more detailed spatial variation than does the slab, demonstrating that thickness and variation in sample composition can blur the image.

A Xerox copy of Fig. 4c was scanned. As shown in Fig. 4, large (20 nT) remanent fields were produced by ferromagnetic material in the photocopier toner. MicroSQUID has sufficient sensitivity t o detect trace amounts of toner particles that appear to the unaided eye as image-free, white regions of paper.

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0018-9464/91x)300-3237$01.00 0 1991 IEEE

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2

2

0 VI m -

1 0

VI D

0 C

-

i j o 0 z

c

z o

-2

- 1

Fig. 1. Maps of the magnetic field produced by a current flowing in an 11 cm x 15 cm x 32 ym thick copper sheet with a circular hole in the center. The current was applied in the direction shown by the arrows. a) The magnetic field produced by scanning when the SQUID coils were 2.5 mm above a 1.0 mm diameter hole, with the plate carrying 85 mA. b) The field map for coils 2.8 mm above a 350 ym hole in a sheet carrying 100 mA. c-d) Isofield contours (400 pT and 200 pT contour intervals, respectively).

1.5

1 .o 0

0

C 0 z

- ij 0.5

0

-0.5

30 E

z 20

10

0 10 20 30 40 50

x, mm

Fig. 2. a) The magnetic field produced by contamination in EDM slots that were (left) 230 ym deep by 1.1 mm long and (right) 150 ym deep x 760 ym long. b) An isofield plot showing how the left slot is not parallel to the tube axis (200 pT contour interval).

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200 1.5

0

0

0 C 0 z

- U 1.0 c

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0

0

0 0

40 40

E E E E

30 30

z z 20 20

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0 10 20 30 40 50

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0 10 20 30 40 50 x, m m x, m m

Fig. 3. The magnetic field map and isofield contours produced by remanent magnetization in a pyroclastic rock. a-b) 3 mm thick-section (20 nT contour interval). c-d) 30 pm thin-section (100 pT contour interval).

10 20 30 40 50 x, m m

Fig. 4. a-b) The magnetic field map and isofield contours produced by the remanent magnetization of ferromagnetic particles in the toner of the Xerox copy of fig 4c). (2.5 nT contour interval).

3240 Discussion References

As demonstrated, MicroSQUID can be used to obtain detailed, high-resolution images of magnetic fields. This is due t o the decreased coil diameter and coil-to-sample spacing. The importance of this spacing to field strength can be illustrated by considering magnetic fields which fall off as l/r, l/rz, or l/r3. Examples of these are a current- carrying wire, a hole in a thin plate carrying uniform current, and a magnetic dipole. When comparing a 1.5 cm t o 0.15 cm dewar thickness, the field strength is increased by a factor of 10, lo2, and lo3, respectively. Typically, decreasing the coil-to-sample spacing is more important than decreasing background noise5.

Acknowledgements

This research has been supported by Air Force Office of Scientific Research Grant 87-0337 and by the Electric Power Research Institute. The purchase of MicroSQUID was funded by Office of Naval Research Grant N0001486G0129, National Institutes of Health Grants R01 NS 19794 and 2507RR7201-8, and by Vanderbilt University. We are indebted to Carlos Trenary, Pat Henry, and Sam Francescon for their help with equipping the Magnetic Imaging Facility, and to Licheng Li for her care in preparing the illustrations. We thank Thomas Moyer for providing the rock samples.

1. D.S. Buchanan, D.B. Crum, D. Cox, and J.P. Wikswo, Jr., "MicroSQUID: A close-spaced four channel magnetometer", Adv. in Biomagnetism, S.J. Williamson, M. Hoke, G. Stroink, and M. Kotani, Eds., Plenum, New York, p. 677-679, 1989.

2. J.P. Wikswo, Jr., J. van Egeraat, Y.P. Ma. N.G. Sepulveda, D.J. Staton, S. Tan, and R.S. Wijesinghe, "Instrumentation and techniques for high-resolution magnetic imaging", to be published in Digital Image Synthesis and Inverse Optics, A.F. Gmitro, P.S. Idell, and I.J. Lattaie, Eds., SPIE Proceedings, vol. 1351.

3. Y.P. Ma and J.P. Wikswo, Jr., "A magnetic shield for wide-bandwidth magnetic measurements for non- destructive testing and biomagnetism", in preparation.

4. N.G. Sepulveda, D.J. Staton, and J.P. Wikswo, Jr., "A mathematical analysis of the magnetic field produced by flaws in two-dimensional current- carrying conductors", in preparation.

B.J. Roth, N.G. Sepulveda, and J.P. Wikswo, Jr., "Using a magnetometer to image a two-dimensional

5.

current distribution", J. Appl. Phvs., vol. 65, pp. 361- 372, 1989.