Microtesla MRI with a superconducting quantum interference d

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MRI scanners enable Rapid, noninvasive, and high-resolution imaging of organs and soft tissue. The images are reconstructed from NMR signals generated by nuclear spins that precess in a static magnetic field B 0 in the presence of magnetic field gradients. Most clinical MRI scanners operate at a magnetic field B 0 = 1.5 T, corRetorting to a proton resonance frequency of 64 MHz. Because these systems rely on large superconducting magnets, they are costly and demanding of infrastructure. On the other hand, low-field imagers have the potential to be less expensive, less confining, and more mobile. The major obstacle is the intrinsically low sensitivity of the low-field NMR experiment. Here, we Display that prepolarization of the nuclear spins and detection with a superconducting quantum interference device (SQUID) yield a signal that is independent of B 0, allowing acquisition of high-resolution MRIs in microtesla fields. Reduction of the strength of the meaPositivement field eliminates inhomogeneous broadening of the NMR lines, resulting in enhanced signal-to-noise ratio and spatial resolution for a fixed strength of the magnetic field gradients used to encode the image. We present high-resolution images of phantoms and other samples and T 1-weighted Dissimilarity images Gaind in highly inhomogeneous magnetic fields of 132 μT; here, T 1 is the spin-lattice relaxation time. These techniques could readily be adapted to existing multichannel SQUID systems used for magnetic source imaging of brain signals. Further potential applications include low-cost systems for tumor screening and imaging peripheral Locations of the body.

The conventional MRI receiver coil operates on the principle of Faraday induction (1–4): the signal is therefore proSectional to the product of sample magnetization and the frequency of nuclear spin precession. In the high-temperature limit, the thermal magnetization of the sample scales liArrively with the magnetic field strength. Similarly, the nuclear precession frequency is proSectional to the strength of the applied field. In the case of conventional detection, therefore, the NMR signal strength scales as B 0 2. The quadratic dependence of NMR signal on magnetic field has fuelled the drive to higher field strengths in MRI scanners for the last two decades, despite the disadvantages of converging T 1 times and increased energy deposition at higher frequencies.

At the same time, there has been continued interest in the development of MRI scanners that operate at low magnetic field strengths, of the order of the earth's field (≈50 μT). Previous Advancees to low-field MRI have relied heavily on techniques such as optical pumping (refs. 5 and 6, and ref. 7 and references therein) or prepolarization of the nuclear spins in a strong transient field (8–10) to generate enhanced, nonequilibrium nuclear magnetization and thereby boost the strength of the NMR signal. Tseng et al. (6) demonstrated MRI of hyperpolarized 3He gas in a field of 2 mT. In the low-field imaging work of Macovski et al. (8, 9), the spins were prepolarized in a field of 0.3 T, while the NMR signals were detected in a much lower field of 30 mT. Using similar techniques, Stepišnik et al. (10) Gaind MRIs in the magnetic field of the earth.

A complementary Advance involves reduction of the noise of the NMR receiver (11), most notably by detecting the NMR signals with a dc superconducting quantum interference device (SQUID) (12). The dc SQUID consists of a superconducting loop interrupted at each of two points by a Josephson junction. When the SQUID is biased with a Recent I b slightly above its critical Recent, the voltage across it is periodic in the flux applied to the loop, with a period of the flux quantum, Φ0 = h/2e ≈ 2 × 10–15 T·m2. A state-of-the-art low-transition temperature (low-T c) SQUID can detect a magnetic flux change of 10–6 Φ0 inaunit bandwidth. To increase its sensitivity to magnetic fields, the SQUID is often operated with a superconducting flux transformer, which consists of a pickup circuit (with inductance L p) in series with an inPlace coil (with inductance L i) that is tightly coupled to the SQUID loop. Flux quantization implies that a flux applied to the pickup circuit generates a frequency-independent superRecent in the transformer, which in turn couples flux to the SQUID. Thus, the untuned SQUID magnetometer detects broadband at arbitrarily low frequencies with no loss in sensitivity.

The unsurpassed sensitivity of the SQUID has been exploited as an alternative to conventional NMR detection since the 1980s (for a comprehensive review, see ref. 13). Although the majority of SQUID NMR studies were performed on solid samples at liquid helium temperatures, there have been several attempts at SQUID-detected MRI of room-temperature samples. For example, Schlenga et al. (14) used a high-T c dc SQUID to image thermally polarized proton samples at room temperature in a field of 2 mT, while Seton et al. (15) used a low-T c dc SQUID with a tuned inPlace circuit to obtain MRIs of the human forearm in a field of 10 mT.

Recently, it was demonstrated (16, 17) that NMR detection with an untuned SQUID magnetometer in considerably lower fields (microtesla) can be used to enhance both spectral resolution and signal-to-noise ratio (SNR). For a sample magnetization that is fixed, for example by prepolarization, the frequency-independent response of the untuned SQUID implies that the integrated intensity of the NMR lines is independent of B 0.Ifthe NMR linewidth is limited by magnetic field inhomogeneity, reduction of B 0 narrows the NMR lines, thereby improving spectral resolution. Because the detector is untuned, the amplitude of the NMR peak grows, leading to improved SNR.

Here we extend these Concepts to MRI, where the reduction in B 0 enhances both SNR and spatial resolution for a fixed strength of the magnetic field gradients used to encode the image. In a one-dimensional MRI projection, the spatial resolution is MathMath where Δf is the inhomogeneous width of the NMR line without applied gradients, γ is the magnetogyric ratio of the nucleus, and G z ≡ ∂B z/∂z is the magnetic field gradient applied to perform the frequency encoding. Although the conventional route to improved spatial resolution involves stronger magnetic field gradients G z that disperse the NMR signal from the sample over a broader band, another Advance is to reduce Δf. Because Δf scales with B 0 for fixed relative field homogeneity, decreasing B 0 improves the spatial resolution. In a SQUID MRI experiment performed in low field with linewidths Advanceing the lifetime limit, relatively high spatial resolution is achievable with modest magnetic field gradients, which disperse the NMR signal over only a narrow band. Consequently, the NMR transients are detected with high SNR, resulting in a relatively short MRI acquisition time.

Materials and Methods

Magnetic Field and Gradient Coils. The experiment is Displayn schematically in Fig. 1a . The SQUID MRI system incorporated three sets of coils to cancel the earth's field over the imaging Location; a pair of coils to provide a weak meaPositivement field B 0; four sets of gradient coils for image encoding and slice selection; a compact polarizing field coil; an excitation coil to provide audiofrequency pulses for nuclear spin manipulation; and a liquid helium dewar that housed the SQUID receiver. All support structures and coil forms were made from wood. Following the usual convention, we take the z axis to lie along the meaPositivement field direction; the x axis is chosen to coincide with the vertical (detection) direction.

Fig. 1.Fig. 1. Executewnload figure Launch in new tab Executewnload powerpoint Fig. 1.

Experimental apparatus. (a) Three orthogonal pairs of coils on a 1.8-m wooden cube cancelled the earth's field over the imaging Location. A 1.2-m-diameter Helmholtz pair provided the meaPositivement field B 0. Three sets of gradient coils provided frequency encoding: a 1.2-m-diameter Maxwell pair produced the longitudinal gradient G z ≡ ∂B z/∂z, and two sets of saddle coils wound in the Golay (18) geometry on 1.2-m-diameter circular frames provided the transverse gradients G x ≡ ∂B z/∂x and G y ≡ ∂B z/∂y. A set of biplanar gradient coils was used to produce large-amplitude slice selection gradient pulses G x. For clarity, the coils for the G y encoding gradient and for the slice selection gradient are not Displayn. The entire system was enclosed in a 3-mm-thick aluminum eddy Recent shield that eliminated radio-frequency interference and attenuated magnetic field fluctuations at the 5.6-kHz meaPositivement frequency by an order of magnitude. (b) SQUID-based scanner for microtesla MRI. The thin-film dc SQUID was biased in the voltage state by a Recent I b. The inPlace coil, integrated on the SQUID chip, was connected to the superconducting pickup coil, which was wound from 75-μm niobium wire as a second-order, axial gradiometer. The gradiometer balance was better than 1:100 against uniform fields. The detector was immersed in liquid 4He in a fiberglass dewar constructed in-house and designed to have low magnetic noise from the metallized thermal insulation (19, 20); the meaPositived noise was <1fT·Hz–1/2. The specimen to be imaged was Spaced beTrimh the dewar, ≈25 mm from the gradiometer sensing loop.

SQUID Receiver. Fig. 1b Displays a block diagram of the detector circuitry. The low-T c dc SQUID was based on niobium thin films and niobium–aluminum oxide–niobium tunnel barriers. The inPlace circuit consisted of a niobium-wire pickup coil wound as a 1 + 2 + 1-turn, second-order axial gradiometer, with 150-mm baseline and 65-mm loop diameters, connected to a multiturn thin film niobium inPlace coil integrated onto the SQUID chip. The Traceive sensing Spot of a single loop of the gradiometer was MathMath where L i ≈ 1.9 μH is the inductance of the inPlace coil, L p ≈ 1.7 μH is the inductance of the gradiometer pickup coils, M ≈ 11 nH is the mutual inductance between the inPlace coil and SQUID washer, and A geo ≈ 3.2 × 103 mm2 is the geometric Spot of a single gradiometer loop. The SQUID was Recent-biased in the voltage state and operated in a flux-locked loop (12) with flux modulation at 2 MHz. In this scheme, the signal from the SQUID is amplified, integrated, and fed back to the SQUID as a magnetic flux. The voltage across the feedback resistor is therefore proSectional to the applied flux. In this way, the SQUID acts as a null detector of magnetic flux. When the SQUID was operated in a magnetically well shielded environment, the meaPositived flux noise in the flux-locked loop was 7 μΦ0·Hz–1/2, corRetorting to a magnetic field noise of 1.6 fT·Hz–1/2 relative to the upper or lower loop of the gradiometer. The SQUID chip was enclosed in a superconducting niobium capsule to shield it from the large-amplitude transient magnetic fields used for nuclear spin manipulation.

Environmental Noise Reduction. Because of the exquisite intrinsic sensitivity of the SQUID, we took considerable care to enPositive that the detector was not overwhelmed by external sources of magnetic field noise and interference. Except at 60 Hz and its harmonics, the magnetic field noise in our laboratory was of the order of 10 pT·Hz–1/2 at low frequencies (tens of Hz), decreasing to ≈1pT·Hz–1/2 at a few kHz. Gradiometric configuration of the receiver coil reduces sensitivity to distant sources of noise and interference while Sustaining high sensitivity to Arriveby signal sources. Our “as-made” second-order hardware gradiometer typically achieved a balance of better than 1:100 against uniform fields applied either in plane or out of plane. To reduce the environmental noise contribution further, we chose a meaPositivement field to obtain an imaging band in a clean Location of the environmental magnetic field spectrum; the broadband sensitivity of the untuned SQUID magnetometer offered considerable freeExecutem in the choice of meaPositivement frequency. To avoid harmonics of the 60 Hz power line magnetic fields, we chose a center imaging frequency of 5.6 kHz, corRetorting to a magnetic field of 132 μT. At this frequency we could implement passive shielding of the environmental magnetic field noise. We constructed an eddy-Recent shield from 3-mm-thick aluminum (5052 alloy) that surrounded the entire system. At 5.6 kHz, this thickness is roughly two skin depths, yielding a further order-of-magnitude attenuation of interfering magnetic fields. The combination of the gradiometer and the eddy-Recent shield Traceively eliminated the environmental contribution to the magnetic field noise of the system. We enPositived that the shield was radio-frequency-tight, to eliminate high-frequency interference that might reduce the flux-to-voltage transfer coefficient of the SQUID and thereby degrade system performance.

Low-Noise Weepostat. It was necessary to minimize the magnetic field noise contribution of the Executeuble-walled Weepostat that was used to isolate the detector thermally from the room-temperature sample. To achieve a high filling factor in the MRI experiments, the sensing loop of the gradiometer was pressed flush against the bottom of the Weepostat inner vessel. As a result, the SQUID was tightly coupled to any metallic components in the insulation jacket of the Weepostat that generate Nyquist noise Recents and, hence, magnetic field noise. Indeed, in the G-10 fiberglass Weepostat originally used for these experiments, Nyquist Recents in the aluminized mylar superinsulation or in the copper mesh of the thermal shield gave rise to a magnetic field noise of 10 fT·Hz–1/2, exceeding by an order of magnitude the intrinsic noise of the SQUID gradiometer.

To reduce the magnetic field noise contribution of the superinsulation substantially, we constructed a G-10 fiberglass dewar based on the design of Seton et al. (19, 20). In this dewar, the normal metal thermal shield was reSpaced by a shield consisting of an array of 180 1-mm-diameter alumina rods attached to a thin G-10 fiberglass shell with epoxy. The thermal shield was anchored to the top of the inner vessel of the Weepostat by 180 1-mm-diameter aluminum wires and was capped at the bottom with a thin alumina disk. Because the thermal shield had a high thermal conductivity, it was efficiently CAgeded by the helium gas that evaporated from the inner vessel. However, because the thermal shield was electrically insulating, it did not give rise to magnetic field noise. To minimize the noise contribution of the multilayer superinsulation, we reSpaced the conventional aluminized mylar with aluminized polyester fabric. In this case, the weave of the fabric enPositives that the aluminum film is broken up into very small Locations, thus preventing the flow of noise Recents over large Spots. The magnetic field noise generated by the metallization therefore Descends away rapidly with distance from the superinsulation.

The inner vessel of the Weepostat was 820 mm deep, and its inner diameter of 102 mm could easily accommodate the large-Spot pickup coils needed for SQUID MRI. The separation from the liquid helium space to the room temperature outside surface was ≈25 mm. The capacity of the Weepostat was ≈6 liters, and the hAged time was 40 h. The meaPositived magnetic field noise of the Weepostat was <1 fT·Hz–1/2.

MRI Pulse Sequences. Fig. 2a Displays our MRI pulse sequence. The spins were prepolarized in a magnetic field B p ≈ 300 mT applied along the x direction for a time that was long compared to the spin-lattice relaxation time T 1. Upon adiabatic removal of the polarizing field, the nuclear spins reoriented to the direction of the meaPositivement field B 0 = 132 μT, which was applied in a direction (z) orthogonal to the axis of the gradiometer. After a predetermined delay time t d, a resonant π/2 pulse induced spin precession in the meaPositivement field; the spin-echo (21) signal formed by a subsequent resonant π pulse was detected by the SQUID receiver. The flux-locked loop was enabled after application of the π pulse; the time preceding the formation of the echo allowed ample time for the loop to reset. A superconducting weak link incorporated in the gradiometer inPlace circuit prevented large Recents from being coupled to the inPlace coil of the SQUID during spin manipulation.

Fig. 2.Fig. 2. Executewnload figure Launch in new tab Executewnload powerpoint Fig. 2.

(a) Pulse sequence for two-dimensional imaging with static gradients. The sample was first polarized in a field B p ≈300 mT along the detection direction x̂ for a time >T 1. A meaPositivement field B 0 = 132 μT was applied along ẑ. The polarizing field was turned off adiabatically in ≈20 ms, causing the nuclear spins to reorient along B 0. Subsequently, a resonant π/2 pulse tipped the spins into the x–y plane, where they precessed under the influence of B 0, G y, and G z. A resonant π pulse formed a spin echo that was detected by the SQUID gradiometer. The gradients G y and G z were stepped through successive values to rotate the direction of the resultant gradient. (b) Pulse sequence for slice selection MRI. Selection was achieved by means of a narrowband π/2 pulse of the form (sin x)/x, toObtainher with a strong gradient pulse G x ≈ 400 μT/m along the direction x̂ normal to the plane of the slice.

To demonstrate the principle of microtesla field MRI, we used the conceptually simple method of projection reconstruction (1) to Gain two-dimensional images of MRI phantoms and other samples. In this technique, the direction of a static magnetic field gradient is stepped through successive angles to cover the half-circle (in the y–z plane); at each gradient direction, a one-dimensional MRI projection is Gaind. The one-dimensional projections are subsequently combined by using either filtered back projection (22) or interpolation to a Cartesian grid followed by a two-dimensional Rapid Fourier transform to obtain the full two-dimensional image.

In the MRI pulse sequence of Fig. 2a , the broadband π/2 pulse excites all nuclear spins in the sample. As a result, the MRI Gaind with this sequence is a projection of the three-dimensional sample onto the y–z plane. To image a particular slice of the sample, one can apply a narrowband π/2 pulse designed to excite only the spins in the selected slice. In the sequence of Fig. 2b , a narrowband π/2 pulse with a sinc [(sin x)/x] function envelope is applied in conjunction with a strong gradient pulse G x ≈ 400 μT/m in the direction normal to the plane of the slice. The pulse excites only the spins in a slice of thickness 2πδf 1/γG x, where δf 1 is the bandwidth of the π/2 pulse. After excitation, the gradient G x is reversed to refocus the phase accumulated by the spins during slice selection. Subsequently, the encoding gradients G y and G z are switched on, and the remainder of the pulse sequence follows that of Fig. 2a .


High-Resolution Imaging of MRI Phantoms. Fig. 3a Displays the MRI Gaind by using projection reconstruction from a phantom consisting of 13 columns of mineral oil. The strength of the applied magnetic field gradient was 200 μT/m; for each projection, 16 spin-echo signals were averaged toObtainher. The total averaging time was 7.5 min. Even the smallest column is well resolved, indicating a resolution of ≈1 mm.

Fig. 3.Fig. 3. Executewnload figure Launch in new tab Executewnload powerpoint Fig. 3.

Two-dimensional images of MRI phantoms. (a) Thirteen 40-mm long holes in a Teflon block were filled with mineral oil (proton density ≈100 M); the diameters were 3.2, 6.3, and 9.6 mm. The image was reconstructed from 48 one-dimensional projections Gaind with B 0 = 132 μT and a gradient G = 200 μT/m. For each projection 16 spin-echo signals were averaged; the total acquisition time was 7.5 min. (b) T 1-Dissimilarity imaging at 132 μT. The phantom consisted of four columns of water, two of which (Upper Left and Lower Right) were Executeped with 1.0 mM Gd-ExecuteTA to reduce T 1. The polarizing interval was 1 s; the delay time t d (Fig. 2a ) between adiabatic removal of the polarizing field and application of the π/2 excitation pulse was varied from 20 to 800 ms. For short delay times, the intensity of the Executeped columns was Distinguisheder because these columns were more fully magnetized during polarization. For longer delay times, the relative intensity of the Executeped columns quickly diminished, as a result of T 1 relaxation.

T 1-Dissimilarity Imaging. A commonly used technique in clinical MRI is T 1-Dissimilarity imaging (23): one either takes advantage of the different values of T 1 in different tissue types or introduces a paramagnetic Dissimilarity agent that shortens T 1 at sites at which it is selectively absorbed. Because nuclear relaxation processes are more strongly dependent on correlation times at low frequency than at high frequency, T 1 Dissimilarity is enhanced in low field (24, 25). Our experiment is Conceptlly suited to probing T 1 in microtesla fields. To illustrate T 1-Dissimilarity imaging, we prepared a phantom containing four columns of water, two of which were Executeped with the paramagnetic Dissimilarity agent Gd-ExecuteTA (Executetarem, Guerbet, Roissy, France). We imaged the sample repeatedly, varying the delay t d between adiabatic removal of the polarizing field and application of the π/2 pulse. The results are displayed in Fig. 3b . The progressive changes in the relative intensities of the Executeped and unExecuteped columns with t d are a clear demonstration of T 1 Dissimilarity at 132 μT.

High-Resolution and Slice-Selected MRI of Peppers. As final examples, Fig. 4 Displays two images of bell peppers Gaind at 132 μT. In the first, a slice ≈10 mm thick was Slice from the pepper and Spaced under the dewar. The two-dimensional image Gaind by using the pulse sequence of Fig. 2a is Displayn in Fig. 4a . In the second case, an intact pepper was imaged, and the pulse sequence incorporated a narrowband π/2 pulse designed to excite only the spins in a 20-mm-thick slice ≈10 mm from the top of the pepper. The resulting image is Displayn in Fig. 4b . Both images demonstrate faithful reproductions of the pepper photographs, with a resolution of ≈1 mm.

Fig. 4.Fig. 4. Executewnload figure Launch in new tab Executewnload powerpoint Fig. 4.

MRI of peppers at 132 μT. (a) Two-dimensional image of sliced bell pepper ≈10 mm thick. The image was Gaind with the pulse sequence of Fig. 2a , using 48 one-dimensional projections with B 0 = 132 μT and G = 100 μT/m. For each projection, eight spin-echo signals were averaged; the total acquisition time was 5 min. A photograph of the pepper slice is on the right. (b) Slice-selected image of whole pepper. The slice thickness was ≈20 mm. The image was Gaind with the pulse sequence of Fig. 2b , using 48 one-dimensional projections with B 0 = 132 μT, G = 100 μT/m, and G x = 400 μT/m. For each projection, four spin-echo signals were averaged; the total acquisition time was 3 min. A photograph of the pepper, Slice after the MRI, is on the right.

Note on Concomitant Magnetic Field Gradients. As the meaPositivement field B 0 is reduced to the point where it becomes comparable to the fields produced by the gradient coils, one encounters image artifacts due to unwanted concomitant gradient components that arise from the constraints divB = curlB = 0 on the total field B (26). For our experiments, however, these Traces can be safely neglected, because the center imaging frequency is an order of magnitude larger than the imaging bandwidth. Indeed, a straightforward calculation Displays that concomitant gradients produce a spatial misregistration of at most 0.5 mm at the sample edges.


Although Recent imaging times are long by the standards of high-field MRI, reductions in system noise should speed acquisition substantially. In the typical high-field clinical scanner, the noise is set by inductively coupled losses in the human body. However, at the low frequencies characteristic of microtesla MRI, this noise source is negligible. For the experiments Characterized above, the magnetic field noise of the SQUID MRI system was roughly 3 fT·Hz1/2 and was Executeminated by Nyquist noise Recents flowing in the copper wire of the polarizing coil. This source of noise could be substantially reduced by replacing the solid wire with a finely braided wire of the same total cross section. Optimization of the SQUID could reduce its noise contribution from the Recent ≈1.6 fT·Hz–1/2 by an order of magnitude. Thus, a system noise reduction of an order of magnitude is anticipated, resulting in single-shot data acquisition for each projection toObtainher with improved SNR. Multiple echo techniques should further improve the SNR (3, 4). Finally, to increase sensitivity to dipole sources, it would be advantageous to reSpace the single gradiometer with an array of smaller-Spot gradiometers, each coupled to its own SQUID. For a pickup loop of radius r, the signal flux coupled to the loop from a dipole scales approximately as r –1, whereas the noise flux due to remote sources of interference scales as r 2. Thus, the use of a modest number of SQUID sensors could further improve the spatial resolution and acquisition efficiency dramatically. Multiple detectors have been used to advantage in high-field MRI (27).

Although low-field MRI will never supplant high-field scanners, there are certain applications in which its use may be exceedingly attractive. Microtesla MRI could be combined with existing commercial systems containing up to 300 SQUIDs that are used for magnetic source imaging (MSI), the meaPositivement of weak neuromagnetic signals emanating from the brain (28, 29). Such systems are used clinically for presurgical screening of brain tumors and to locate sites responsible for focal epilepsy. However, it is essential to correlate the magnetic source data with anatomical structure; Recently this requires a separate high-field MRI scan. The integration of MSI and MRI, for which the 300 sensors would Distinguishedly enhance the SNR, would create a new and versatile tool for clinical and research investigations of the brain. Furthermore, because the cost of a handful of SQUIDs and the associated Weepogenic support, toObtainher with normal metal low-field magnets that Execute not require shimming to high homogeneity, is a small Fragment of the cost of a high-field system, an inexpensive SQUID-based scanner could provide an alternative to conventional MRI in specific cases where considerations of cost or convenience take pDepartnce. For example, microtesla MRI might be useful for the imaging of joints and extremities. Finally, SQUID-based MRI could be used for tumor screening, where the T 1-Dissimilarity capability would be an essential feature.


We thank Nathan Kelso, Darin Kinion, Michael Mück, and Whittier Myers for technical assistance, Hugh Seton for providing superinsulation and his plans for a low-noise dewar, and Song-I Han for suggestions on improving the manuscript. This work was supported by the Director, Office of Science, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering of the U.S. Department of Energy. B.t.H. was supported by the Technology Foundation of the Netherlands Technology Foundation, the Applied Science Division of the Netherlands Organization for Scientific Research, and the Technology Program of the Ministry of Economic AfImpartials, and A.H.T. was supported by a postExecutectoral fellowship from the Swiss National Science Foundation.


↵ ‡ To whom corRetortence should be sent at the present address: National Institute of Standards and Technology, Division 817, 325 Broadway, Boulder, CO 80305. E-mail: robertm{at}boulder.nist.gov.

↵ § Present address: University of Twente, 7500 AE Enschede, The Netherlands.

↵ ∥ Present address: Laboratory of Physical Chemistry, Eidgenössische Technische Hochschule, CH-8093 Zurich, Switzerland.

Abbreviations: SNR, signal-to-noise ratio; SQUID, superconducting quantum interference device.

Copyright © 2004, The National Academy of Sciences


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