Chapter 5: Multi-Squid Devices and Their Applications

CHAPTER 5

MULTI-SQUID DEVICES AND THEIR APPLICATIONS BY

Risto ILMONIEMI and Jukka KNUUTILA Low Temperature Laboratory, Helsinki University of Technology, 02150 Espoo, Finland

and

Tapani RYHANEN and Heikki SEPPA Electrical Engineering Laboratory, Technical Research Centre of Finland and Laboratory of Metrology, Helsinki University of Technology, 02150 Espoo, Finland

Progress in Low Temperature Physics, Volume X I 1 Edited by D.F. Brewer @ Elsevier Science Publishers B. V., 1989 27 1

Contents I . introduction . . . . . . . . . . . . . . . . . . . . . ................................... ..... 2 . SQUIDS . . . . . . . . . .......................... ............................. 2.1. Single-junction (rf) SQUlDs . . . . . . . . . . 2.1.1. General . . . ........................................... ......... 2.1.2. Rf SQUID in the hysteretic mode . . . . . . . . . . . . . . . . . 2.1.3. Discussion . . . . . . . . . 2.2. Double-junction (dc) SQUlDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1. Operation . . . . . . . . . . . . . . . ................................. 2.2.2. Problems with practical devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3. The state of the art . . ................................... 2.3. Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Applications: biomagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Measurement techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3.1 .1. Magnetically shielded rooms . . . . . . . 3.1.2. Gradiometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Neuromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1. Origin of neuromagnetic fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2. Spontaneous activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3. Evoked fields . . . . . . . . . . . . . . . . . . . . . . . ...................... 3.2.4. Clinical aspects of MEG . . . . . . . . . . . . . ...................... 3.3. Cardiac studies ........................................ 3.4. Other hiomagnet ........................................ 3.5. Multichannel neuromagnetorneters . . . . . . . . . . ..................... 3.5.1. Optimization of multichannel neuromagnetometers . . . . . . . . . . . . . . . . . . 3.5.2. Existing multichannel systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.3. Planar gradiometer arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.4. Use of multichannel magnetometers . . . . . . . . . . . . . . . 4 . Other multi-SQUID applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Geomagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Physical experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1. Accelerometers and displacement sensors . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2. Monopole detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ......... References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

212

213 213 214 214 216 219 280 280 284 286 289 292 293 293 295 296 291 298 299 300 302 303 304 305 310 319 323 326 326 328 329 329 332 333

1. Introduction

The Superconducting Quantum Interference Device (SQUID) offers unrivalled sensitivity for the measurement of low-frequency magnetic fields. Recent developments in the fabrication technology and electronics have made it possible to construct reliable low-noise SQUIDs. Consequently, magnetometers with many SQUIDs have become feasible in many applications and the number of SQUIDs is no longer limited by the difficulty of their use. Further reduction of SQUID noise is no more necessarily needed, since the noise limit in the state-of-the-art multi-SQUIDS seems to be determined by dewar materials, environmental low-frrequency noise, and other sources external to the SQUIDs. Additional recent interest in SQUID applications is caused by the possibility of fabricating them from the new high- T, materials. In this review', we start with an overview of the operation of rf and dc SQUIDs, stressing, in particular, the theoretical understanding of complete SQUID circuits. This is necessary for the design of practical devices. Main attention is focused to the operation of the dc SQUID and to recent progress in realizing practical dc-SQUID structures with flux-coupling circuits. A more thorough discussion of SQUID circuits is presented in a companion paper (Ryhanen et al. 1989). So far the largest field of application for SQUID arrays is biomagnetism, the study of magnetic fields originating in biological organisms. The subfield currently attracting most interest is neuromagnetism, where these techniques are applied to investigations of the central nervous system. A potentially important clinical use of SQUIDs in the future is in magnetocardiography (MCG), the recording of heart activity via magnetic measurements. We will give a brief overview of biomagnetic measurement techniques, illustrating them with several examples. Principles of SQUID magnetometers and their application to biomagnetism are discussed. Existing biomagnetic multiSQUID systems and some plans for future instruments are described. In addition, applications of SQUIDs in geomagnetism and in some physical experiments are briefly discussed. 2. SQUIDs

This chapter is a brief review of Superconducting Quantum Interference Devices (SQUIDs), which are formed by interrupting a superconducting 273

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ring by one or two Josephson junctions (Lounasmaa 1974, Tinkham 1975, Barone and Paterno 1982, Likharev 1986, van Duzer and Turner 1981). SQUI Ds have been studied intensively both theoretically and experimentally since the introduction of the double-junction interferometer (dc SQUID) by Jaklevic et al. (1964, 1965) and, in particular, since the invention of the rf SQUID by Silver and Zimmerman (1967). Both rf and dc SQUIDs are common in multichannel applications. In spite of the outstanding properties of SQUIDs as magnetic flux sensors, their impact outside research laboratories has remained modest. Imprudent operation of SQUIDs often leads to unexpected problems that discourage their use. Evidently, the complicated dynamics, caused by the strong nonlinearity and the lack of natural damping, is one of the main reasons for difficulties in practical applications. However, as this paper will show, these problems can be overcome. When discussing the suitability of a particular SQUID in a multichannel system, all the necessary circuits should be included in the analysis. In other words, the contributions to noise of preamplifiers, coupling circuits, postdetection filters, etc. should be as important objects of theoretical and experimental study as the SQUID itself. For example, theory predicts a flux noise of about Q,/& for a typical rf SQUID and about lo-"@,,/& for a dc SQUID; @,=2.07x10 "Wb is the magnetic flux quantum. However, in a practical measurement setup such figures are seldom reached. Excess noise is usually caused by the preamplifier in rf SQUIDs and by parasitic elements in the input circuits of dc SQUIDs. 2.1. SINGLE-JUNCTION (RF) SQUIDS 2.1.1. General

In an rf SQUID the low-frequency external flux in the SQUID ring is read out by superposing on it a high-frequency bias flux and monitoring the amplitude of the rf voltage by a preamplifier matched to the SQUID with a resonant tank circuit (fig. 1). The Josephson junction is typically described by the resistively-shunted-junction (RSJ) model, which consists of an ideal Josephson junction, a resistance R, and a capacitance C. The supercurrent passing through the ideal junction is related to the quantum phase difference across the junction cp by I, = I, sin cp where I , is the critical current of the junction. In a single-junction superconducting loop, cp = -27r( @+ n @ J / @,). If an external flux @a is applied to a SQUID loop with inductance L, the total flux Q = Qa+ LI, in the loop obeys the equation 2 ~ @Q,/

+ pL sin( 2 n Q l Q,,) = 2a@,/

Q, ,

(2.1)

k---Jq, MULTI-SQUID DEVICES

Tank circuit

275

SQUID

x

Josephson

junction 1,sinlp

Fig. 1 . A single-junction SQUID coupled to a resonant tank circuit. If BL= ZTLI,/#~>1 the SQUID is hysteretic, if BL< 1 it is nonhysteretic and called an inductive SQUID; I, is the critical current of the junction, Go is the magnetic flux quantum 2.07 x lo-'' Wb.

where p L = 2rLI,/ @, is the normalized inductance. The dynamics of the single-junction SQUID depends fundamentally on p L ; its influence on the @-@a characteristics is illustrated in fig. 2. When I , is not high enough to screen the ring, i.e., when p L < 1, @(@a) is single-valued; the SQUID is then nonhysteretic. Otherwise, .@( @a) is multivalued and the SQUID is hysteretic. The SQUID in the regime p L< 1 is called a nonhysteretic SQUID, an inductive SQUID, or simply an L-SQUID; its characteristics depend strongly on the parameters of the SQUID ring and the tank circuit. Consequently, the L-SQUID is rarely seen in practical applications. In contrast, the dynamics of the hysteretic SQUID is much less sensitive to parameter

Fig. 2. The total flux @ in the SQUID ring as a function of the applied flux @a for BL< 1 and for pL> 1. When BL> 1. the SQUID is hysteretic and transitions occur at @ = @== *((n + f ) @,, + LIJ.

R. ILMONIEMI ET AL.

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variations; therefore, it is preferred in most applications, including multichannel magnetometers.

2.1.2. Rf SQUID in the hysteretic mode Operation of the $SQUID in the dissipative regime A consequence of high B L is that the total flux through the SQUID loop becomes a multivalued function of the applied flux. In this mode, the flux may jump by about one flux quantum as depicted by arrows in fig. 2 . Sinusoidal flux excitation of sufficient amplitude causes the SQUID to traverse hysteresis loops; the flux transitions involve dissipation of energy that is proportional to the area of the hysteresis loop. Rf SQUIDS are thoroughly discussed in the literature (Zimmerman et al. 1970, Mercereau 1970, Nisenoff 1970, Giffard et al. 1972, Clarke 1973, Jackel and Buhrman 1975, chapter 3 of the companion paper: Ryhanen et al. 1989); only a brief review will be presented here. The peak voltage across the tank circuit depends on the amount of flux needed to excite flux jumps. The points for flux transitions can be approximated by @,= * ( ( n LI,) (see fig. 2 ) . Before a transition, depending on the branch where the system is, the amplitude of the tank circuit voltage approaches one of two critical values:

+a)@,,+

eT

where up is the pump frequency; the mutual inductance M between the SQUID ring and the tank circuit coil L, is proportional to the coupling constant k = M/&. Because of energy transferto the SQUID, the voltage in the tank circ?it periodically drops, rising up again until the next transition takes place at V,. For fixed rf excitation, a peak detector draws a triangular pattern with period @, as a function of dja as shown in fig. 3 . The energy AE absorbed in one complete cycle is approximately the area of the loop in the @- Q a plane divided by the loop inductance (Zimmerman et al. 1970, Jackel and Buhrman 1975); for high P L ,

c,,

ec2

as seen from fig. 2. Although and depend on the dc flux threading the SQUID loop (eqs. ( 2 . 2 ) and ( 2 . 3 ) ) , A E appears insensitive to the point of operation. Consequently, the effective impedance of the tank circuit must depend on the point of operation; the rf SQUID acts as a flux-dependent

MULTI-SQUID DEVICES

1

I

-2 a0

I

I

I

277

1

I

I

1

I

- a0

0

a0

200

Fig. 3. Ideal triangular flux-voltage characteristic of the hysteretic rf SQUID with periodicity of one flux quantum.

resistor. Suppose @a = @0/2: as long as the energy fed into the t?nk circuit during each rf cycle does not exceed A,: :he peak voltage V, remains unchanged, resulting in a plateau in the V,I, characteristics. An increase of power creates another plateau until an energy 2AE is fed into the system during every rf cycle. Correspondingly, at Qa = Go the first plateau ends when the energy 2AE is exceeded. Realistic staircase patterns, corresponding to the cases @ . = ( n + f ) @ , , and Q a = nQ0, are plotted in fig. 4. When k2QT> r / 2 , where QT is the quality factor of the tank circuit (Giffard et a]. 1972, Jackel and Buhrman 1975), the plateaus overlap and proper adjustment of the rf bias current implies a perfect triangular pattern as in fig. 3. Noise in the hysteretic rfSQUID Thermal noise causes flyctuations in the points of flux transitions, tilting the plateaus of the jdVT characteristics (see fig. 4) and increasing the equivalent flux noise. As shown by Kurkijarvi (1972), the uncertainty in the flux jumps decreases when the frequency of the sinusoidal excitation is increased. Kurkijarvi and Webb (1972) derived an expression for the equivalent flux noise and showed that the slope a of the plateaus in the staircase pattern is related to the intrinsic energy sensitivity E (Jackel and Buhrman 1975):

where

E

is associated with the equivalent flux noise @,, in the SQUID loop

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218

Fig. 4. The current-voltage characteristics of a hysteretic rf SQUID in the presence of thermal noise, for even and odd multiples of @,,0/2 of the externally applied flux 0".itf indicates the point of operation producing the triangular response illustrated in fig. 3. Q, is the quality factor of the tank circuit.

as The intrinsic flux noise increases the noise temperature of the tank circuit. If noise from the preamplifier and the tank circuit is included as well, the experimentally determined value of a,a e x pcan , be used to estimate the equivalent input energy sensitivity (Jackel and Buhrman 1975): r

(2.7) where Ti @X/kgL is called the intrinsic tank circuit temperature; TT denotes the equivalent noise temperature of the tank circuit, and TAis the noise temperature of the preamplifier. Equation (2.7) is derived by assuming that the impedance of the loaded tank circuit equals the optimal impedance of the preamplifier (section 2.3) and that k2QT- 7r. Since the energy dissipation caused by the hysteretic loop is related to Ti simply by f k , T , a A E , the size of the loop should be as small as possible but sufficient to assure proper operation. TT is often determined by the preamplifier; thus T,, T,= TT and careful design of the preamplifier becomes imperative for a low-noise magnetometer. If wp = 27r x 20 MHz, L = 1 nH, and PL = 3, eqs. (2.5) and (2.7) predict that a 20.1 and T,= 300 K. Neglecting the tank circuit and the amplifier, an equivalent flux noise as low as (@:)"' = 1.8 x lo-' @,I& should be achievable, but without a cooled preamplifier this is impossible in practice. L-

L-

MULTI-SQUID DEVICES

279

A weak magnetic coupling results in a low flux-to-voltage conversion efficiency if it is not compensated for by a high Q-value of the tank circuit. On the other hand, tight coupling causes uncertainty in the flux transitions induced by tank circuit and preamplifier noise. Optimal choices of the mutual inductance and particularly of the product k2QT are discussed in detail by Jackel and Buhrman (1975). They argue that the best performance is obtained when k2QT exceeds unity. The same conclusion was drawn by Simmonds and Parker (1971) on the basis of computer simulations. Moreover, Ehnholm (1977) derived a small-signal model for an rf SQUID with complete input and output circuits and was able to show that the choice k2QT= 1 is a solid foundation for SQUID design.

Rf SQUIDS at high frequencies The sensitivity of rf SQUIDs can, in principle, be improved by increasing the pump frequency up,but the benefit is partly cancelled by the resulting higher preamplifier noise. When wp = w, = R / L,where w, is the characteristic frequency of the SQUID loop, the original absorption loop begins to deform, manifesting itself as a change in the tank circuit impedance. The flux sensitivity diminishes and the rf SQUID begins to resemble an LSQUID. Buhrman and Jackel (1977) concluded that proper adjustment of the SQUID parameters provides a low-noise rf SQUID even when w p > w , . High wp is tempting not only because it reduces the noise but also because it increases the signal bandwidth. It is, however, evident that a SQUID cannot reach the classical noise limit of the resistive loop, i.e., the thermal energy ( i k B T )divided by the noise bandwidth (aw,). SQUIDs operated at w,> w , have been studied both experimentally and theoretically by many authors (Kamper and Simmonds 1972, Kanter and Vernon 1977, Buhrman and Jackel 1977, Hollenhorst and Giffard 1979, Long et al. 1979, Seppa 1983, Vendik et al. 1983, Kuzmin et al. 1985, Likharev 1986). In principle, the high-frequency or microwave SQUID is suitable for multichannel applications since it can be made to a high-gain, low-noise magnetometer with a large signal bandwidth. The lack of reliable thin-film devices, the high cost of the electronics, and the existence of the dc SQUID, however, do not make it very tempting for applications where several channels are needed.

2. I .3. Discussion It is very important to keep in mind that a well-behaved rf SQUID can be constructed only by damping the junction properly. Incomplete damping may lead to multiple transitions and thus to excess noise. If the shunt

280

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resistance R is adjusted so that the Stewart-McCumber parameter pc= 2 a R ’ C f c / @” remains less than 0.7 (Ketoja et al. 1984a), the I V characteristics of the junction is nonhysteretic and considered well damped. The choice Pc< 1 ensures stable operation of the rf SQUID as discussed by Jackel and Buhrman (1975). Unfortunately, the extra resonances or the parasitic capacitance introduced by a tightly coupled signal coil may substantially decrease the effective damping; this will be discussed in more detail in connection with the dc SQUlD (section 2.2.2). The rf SQUID is based fundamentally on the hysteresis loop traversed as a result of the rf excitation. Energy dissipations reduce the dynamic Q-value of the tank circuit, broadening the signal bandwidth and also making the SQUlD characteristics predictable. The latter consequence is especially important in multichannel applications. With low bias frequencies, the flux-to-voltage conversion efficiency remains moderate and careful design of the preamplifier becomes one of the most important issues in the development of low-noise rf SQUID systems. The intrinsic flux noise can be reached by cooling the first amplifier stage; this is a suitable method in some applications, but hardly in multichannel systems because of increased helium boil-off. Recent developments show that dc SQUIDs are replacing hysteretic rf SQUIDs at least in multichannel magnetometer applications. It seems, however, that the discovery of high- T, materials makes the hysteretic rf SQUlD interesting again. 2.2. DOUBLE-JUNCTION(DC) SQUlDs 2.2.1. Operation

Much lower noise levels than with rf SQUlDs have been obtained with dc SQUlDs (Clarke 1966, Clarke and Fulton 1969, Clarke et al. 1976, Tesche and Clarke 1977, Ketchen 1981). An ideal dc SQUlD is a superconducting loop that has two identical Josephson junctions with critical current I, (fig. 5 ) . In principle, the dc SQUlD can be operated by measuring either the average voltage as a function of the external flux #a with constant bias current f, or by monitoring the current f as a function of @a with constant bias voltage The dc-SQUID loop is in the superconducting state for bias currents below a flux-dependent critical value; at higher currents a voltage over the SQUID appears. The properties of an autonomous dc SQUlD are normally described by two dimensionless parameters P L = 27rLfJ O0 and p, = 2 a R ’ C I J Go,representing the normalized loop inductance and the damping of the junctions, respectively (see also sections 2.1.1 and 2.1.3). The voltage

MULTI-SQUID DEVICES

28 1

Fig. 5. Equivalent circuit of the dc SQUID. The ideal Josephson junctions are characterized by their critical current I , . Each is shunted by a capacitor C, by a resistor R, and by a thermal noise generator I , . I is the bias current and L is the loop inductance of the SQUID. 8 is the phase difference of the macroscopic wave function of the superconductor over the junction.

and the circulating current oscillate at high frequencies, typically on the order of l-lOGHz, depending on @a and Z, and only the time average of the voltage is monitored. The Iv and O a v characteristics are obtained by integration over the period of one oscillation (Tesche and Clarke 1977, Imry and Marcus 1977, Ben-Jacob and Imry 1981, Ketoja et al. 1984b). In fig. 6 we show the Z v characteristics for p L = n- and pc = 0.3. Figure 7 shows the periodic behavior of the voltage 7 as a function of @ a . A more detailed description of the dynamics is presented in section 4.1.3 of the companion paper (Ryhanen et al. 1989). Higher values of p L and pc create more complex behaviour (Ben-Jacob and Imry 1981, Ben-Jacob et al. 1983, 1985, Ketoja et al. 1984b, 1987, Kurkijarvi 1985). When pc> 0.7, the Z v curves are divided into different voltage branches connected by hysteresis loops, leading to multiple solutions at the same set of parameters (Kulik 1967, Imry and Marcus 1977). Qualitatively, the thermal noise affects the and Zv characteristics by rounding the point where the voltage state emerges. Because of thermal noise, the hysteresis also disappears, or the hysteresis loops are rounded. On the other hand, fluctuations between different states increase the excess noise in the system. If the SQUID loop inductance and the junction capacitance are negligible, i.e., p L< 7r and BE= 0, the total flux in the ring @ = @a, and the dc SQUID behaves like a single Josephson junction with a resistance R / 2 and = 21, cos( n-Qa/ Oo).Integrating V over the an effective critical current Ic,eff period T of the Josephson oscillation, the average voltage for Z Zc,cn is obtained (Tinkham 1975): V d t = Y [ l - ( ~ c o s ~2 ) 1/2 .

v

@=v

v=Lj:

]

7

In comparison with figs. 6 and 7, an increased inductance reduces the

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282

3

2

1/24 1

0

Fig. 6. Current-voltage characteristics of the d c SQUID with PI. = T and f3, =0.3. The solid line is obtained when the external flux CDo = @"/2, the dashed line when @, = @,,/4, and the dash-dotted line when CDa = 0. The straight diagonal line is the resistive curve of the SQUID, V = R1/2.

-

,--.

I

0.8-

00--.

,/--'\\

, /

\

\\

'

L.'

\ '' . 4 '

I-

\

-

\ 'i

-U

Fig. 7. Voltage as a function of external flux of a dc SQUID with pL = n and p, = 0.3. The dash-dotted line is obtained when the bias current i = 1 / 2 4 = 0.8, the solid line when i = 1.0, and the dashed line when i = 1.2.

MULTI-SQUID DEVICES

283

modulation depth of the effective critical current AZc.c,; for @ a = 00/2, a voltageless state of supercurrent exists. Because thermal noise rounding was neglected in eq. (2.8), the approximate characteristics do not yet indicate the point of operation maximizing the transfer function 3 P/3@,. Differentiating eq. (2.8), one obtains an estimate at the practical point of operation in the flux-locked-loop mode: TRZ,

-@,=@,,0/4,1=2Ic

d @ O *

In a similar way, the dynamic resistance is (2.10)

To release the assumption pL=O,we note on the basis of RSJ-model simulation of fig. 6 that AZc,effi/3L = IT) = 0.5 x AZc,err(jlL= 0) = I,. Thus a V/a@,a AZ,,, is reduced approximately by a factor of 2 for BL= IT. Using PL = 2rLZ,/ Q0 = IT, we obtain R

z@.=@00/4.1=21,

zL'

(2.1 1 )

The equivalent spectral density of the voltage noise power is

(;:I2

Sv = 4kBT - L 2 / (2 R ) + 4k0 TRdyn+ 4kBTARdyn,

(2.12)

where the first term is the contribution of the fluctuations of the circulating current generated by thermal noise of shunt resistors, the second term represents thermal noise across the SQUID ring, and TA is the noise temperature of the amplifier. Applying approximations (2.10) and (2.1 l ) , the energy resolution (2.6) becomes (2.13)

In comparison to the rf SQUID, eq. (2.7), we note that the energy resolution of a dc SQUID depends on the characteristic frequency o,= R/ L, which is normally much higher than the pump frequencies in rf SQUID magnetometers. Since, in addition, TA tends to increase with frequency, the dc SQUID appears superior. Neglecting amplifier noise and setting PL/ r = PC= 1, we find E = 1 2 k 0 T m . For practical reasons, Bc must be set below 1 (Knuutila et al. 1988); in a dc SQUID with C = 1 p F and L =0.2 nH the shunt resistance is about 5 R implying o,= 27r x 4 GHz. The noise temperature of a state-of-the-art

R. ILMONIEMI ET AL.

284

0’04 0.02

0

t 0

I

I

0.5

HYSTERETIC JUNCTIONS1.5

1.0

2.0

2.5

1 3.0

Bc

-

Fig. 8. Dimensionless energy resolution E = J L / C O ; ~ Cas a function of / 3 c = 2 ~ R 2 C I c / @ , The solid line depicts the approximation (2.13), where the junction capacitance C and the loop inductance L are fixed, BL = n,and /3, is varied by changing R. The dashed vertical line refers to the critical value of p, for hysteresis. The squares are from hybrid computer simulations (de Waal et al. 1984). the circles from numerical simulations (Ryhanen et al. 1989).

amplifier can be as low as 2 K (section 2.3); its contribution is therefore negligible. According to eqs. (2.6) and (2.13), the flux noise in our example O0/&. However, the presence of the coupling ciris ( CD;)~’*= 1.4 x cuits deteriorates the performance (section 2.2.2). The sensitivity of the dc SQUID has been studied by computer simulations (Tesche and Clarke 1977, Bruines et al. 1982, de Waal et al. 1984). The optimized energy resolution was found to be nearly independent of p L and pc for.rr
2.2.2. Problems with practical devices In rf SQUIDS the coupling between the SQUID and the flux transformer circuit has normally been kept relatively loose. In SQUID magnetometers

MULTI-SQUID DEVICES

285

a good coupling between the SQUID loop and the signal coil is tempting because the energy resolution at the output of the device E , , ~ = e l k : , where E is given by eq. (2.13) and k, is the coupling constant (see eqs. (3.1) and (3.2)). In practical devices, this leads to the use of planar gradiometers discussed in section 3.5.3. Several studies (Ketchen et al. 1978, Jaycox and Ketchen 1981, Tesche 1982, Carelli and Foglietti 1982, Tesche et al. 1985, Muhlfelder et al. 1985, Enpuku et al. 1985a, de Waal and Klapwijk 1982, Knuutila et al. 1987a) indicate problems in coupling the dc SQUID to the flux-coupling circuit. Figure 9 illustrates a dc SQUID and its signal coil. The SQUID loop is represented by a thin square washer, with the junctions shown as projecting edges of the plate; the signal coil is shown as a two-turn stripline over the dc SQUID. The signal coil introduces stray capacitance across the junctions, and the signal-coil turns are capacitively connected mainly via the SQUID plate and at crossings of the signal coil stripline. High-Q resonators are created, as shown in fig. 10. The most prominent new feature introduced by the signal coil is the increased parasitic capacitance C,, appearing across the junctions (Tesche 1982, Enpuku et al. 1985a). Evidently, C, is roughly proportional to the number of turns in the signal coil; its effect becomes significant when it approaches C. If C,> C, the dynamics is completely determined by the stray capacitance, because of noise; the voltage-to-flux transfer ratio deteriorates and new sources of noise are introduced. Another important feature in the dynamics is caused by the parasitic capacitance C, in the signal coil. Resonances in the signal coil are far below the operation frequency and do not manifest themselves in the SQUID characteristics as CURRENT NODES

m

--I

DC SQUID

4

+ LOW FREQUENCIES HIGH FREQUENCIES

---

PARAS1 TIC CAPASITANCE

JOSEPHSON JUNCTIONS

Fig. 9. Simplified dc SQUID with its signal coil. The rectangular washer is the SQUID ring; the stripline over the washer is the signal coil. The tunnel junctions are illustrated as black layers interrupting the ring.

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Josephson junctions Fig. 10. Model of a dc SQUID with its signal coil. C, is the parasitic capacitance created by the signal coil, and C, is the stray capacitance in this coil. R, damps parasitic oscillations in the SQUID (Enpuku et al. 1985a), and R , and C, are for damping the signal coil oscillations (Seppa and Ryhanen 1987).

voltage plateaus. Thermal noise can, however, activate these resonances as shown by computer simulations (Seppa and Ryhanen 1987) and by experiments (Knuutila et al. 1987a). The dc-SQUID loop itself forms a A/2 transmission line. The Q-value of the oscillations of this resonator is, however, quite low, unless the signal coil prevents the SQUID from radiating energy into the surrounding space. Increased loop size moves the resonance frequencies near the Josephson oscillations. This is hazardous for proper operation of a dc SQUID, causing voltage plateaus in the Zv characteristics (Muhlfelder et al. 1985, Seppa and Ryhanen 1987, Knuutila et al. 1988). Another resonance is created by the spiral transmission line formed between the SQUID and the stripline. If the signal coil is long, i.e., there are many turns for tight coupling at low frequencies, the resonance is well below the Josephson frequency and the coupling at high frequencies becomes looser, which makes the device more independent of its surroundings. On the other hand, the demand for lower C , favors a short signal coil, and thus the h / 2 resonance of the signal coil has a tendency to be near the operating frequency. Thus, a compromise is necessary. 2.2.3. The state of the art

The desire for maximal coupling efficiency for the external flux favors a large loop area, i.e., a high SQUID inductance, especially at low frequencies, whereas maximum energy sensitivity calls for a small device with a small junction capacitance. Studies of autonomous dc SQUIDS have shown that it is possible to increase slightly the values of BL and / I c from their optima without severe deterioration of performance. In practice, however, increasing the dimensions of the d c SQUID has not been promising.

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Capacitive shunting of the Josephson junctions has been suggested (Paik et al. 1981, Tesche 1982, Tesche et al. 1985). In this structure, the loop inductance is divided into two parts: a small loop of inductance L on the junction side and a large loop of inductance L, on the signal coil side, enabling good coupling. High-frequency Josephson oscillations sense only the small loop, and the effective size of the dc SQUID is small. The parasitic capacitance over the junctions is in parallel with a larger shunting capacitance and thus its effect is negligible. The characteristics appear, however, double-valued, hysteretic and noisy, owing to the frequency-dependent inductance of the dc-SQUID loop. At higher bias currents, where the characteristics are smoother, the noise is mainly thermal; the flux-to-voltage transfer function is, however, much smaller than at low bias currents. The energy resolution turns out to be proportional to L,, and thus the doubleloop dc SQUID is noisier than an optimally adjusted conventional dc SQUID. Enpuku et al. (1985a,b, 1986, Enpuku and Yoshida 1986) have investigated thoroughly the effect of the damping resistance R, (see fig. 10). The main idea of these studies is to increase the SQUID loop inductance in order to secure better coupling to the flux transformer. The increased inductance enhances the current oscillations, and the effect of the internal and external resonances becomes stronger. If the resistive shunting is assumed to wipe out the beating resonance of the SQUID, the damping resistor must be set to R P = W . The damping resistor creates extra flux noise, limiting the energy resolution to E 3 2kBTL/R, = 2 k B T m , which is still determined by the loop inductance, and thus increased L deteriorates the performance. A structure analogous with the capacitively shunted dc SQUID is obtained by dividing the loop inductively into two parts (Ketchen et al. 1978, de Waal and Klapwijk 1982, Koch 1985). In this solution the large loop Le couples the flux while the smaller loop forms the dc SQUID. The is the flux threading flux in the smaller loop is Gi = (L/Lp)@,, where the large loop. The effectkflux noise of the smaller loop is @fn = 4kBTL2/ R, and the energy resolution (2.6) is (2.14) The advantage of this structure is that the parasitic capacitance across the junctions is avoided, which means that LC-resonances at low frequencies do not arise. However, as seen from eq. (2.14), the energy resolution remains modest and the large loop size may bring the transmission-line resonances down to Josephson frequencies.

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Following the idea of the fractional-turn SQUID, originally reported by Zimmerman (1971) for rf SQUIDs, Carelli and Foglietti (l982,1983a, 1985) have constructed multi-loop dc SQUIDs. The structure developed by them suffers from transmission-line resonances that are seen as voltage plateaus of the measured characteristics. This is not surprising considering the large size of the SQUID. The multi-loop structure is suitable for rf SQUIDs because the pump frequency is far below the transmission-line resonances, whereas in dc SQUIDs the Josephson frequencies are near these resonances. The result is good coupling, but there are problems in obtaining smooth characteristics, and hysteresis may cause excess noise. An efficient scheme to couple the low-inductance dc SQUID to a signal source was developed by Muhlfelder et al. (1983). This matching-transformer solution has proved to be excellent for several reasons (Seppa and Ryhanen 1987, Knuutila et al. 1988): (1) The number of turns over the dc SQUID is small; as a result, parasitic capacitances are small and transmission-line resonances are easier to control. (2) Good coupling between the high-inductance signal coil (1-2 pH) and the low-inductance SQUID loop (10-100pH) can be achieved. (3) The effect of parasitic resonances in the transformers can be controlled in the external circuit (see fig. 10). Recently, the design and fabrication of the first completely optimized dc SQUID was published (Knuutila et al. 1988). All resonances were damped or eliminated, and the device was designed to be independent of its surroundings. The problem of bringing the flux to the SQUID was solved by using an intermediate coupling transformer. The dimensions of the SQUID were optimized to obtain the lowest noise level allowed by the available fabrication technology. The energy resolution was limited by two values determined by the fabrication process: the junction capacitance C and'the stray inductance ofthe SQUID loop. The disadvantage is that the realization of the complete structure requires a total of 10 mask layers, complicating the fabrication. Comparison of different dc SQUIDs reveals that the devices are limited by the inductance of the flux-coupling loop. Whatever efforts are made in order to obtain better energy resolution, one is always limited by until the quantum noise limit is reached (see Likharev 1986). Best results have been obtained with low-p, junctions and by damping the signal-coil resonances, or by using relatively moderate values for all the SQUID dimensions in order to prevent the different resonances from interfering with the dynamics of the dc SQUID. The complicated structures needed in dcSQUID devices make the use of high-T, materials difficult, and it is surely going to take a long time before reliable, low-noise high- T, dc-SQUID systems can be produced.

a

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2.3. ELECTRONICS

General When a SQUID is used to monitor a low-frequency magnetic field, current, or voltage, a flux-modulation technique is almost invariably used (Forgacs and Warnick 1967). Usually a square-wave modulation, correspondi'ng to ad2 peak-to-peak, is applied on the SQUID and the output signal is detected by a demodulator circuit. This technique is applicable to any SQUID and it helps to eliminate some sources of low-frequency noise such as thermal EMFs, changes in the critical current of the junctions; drifts in SQUID-circuit parameters, and l/f noise from amplifiers. A further improvement is attained by feeding the detected signal through a resistor back to the SQUID ring. The high-gain feedback loop tends to maintain a constant flux in the SQUID loop, and thus the voltage drop across the feedback resistor is proportional to the external flux. In addition, the ambiguous SQUID response is removed and the output voltage becomes independent of variations in amplifier gain. In general, a well-designed lock-in electronics does not increase the flux noise in the system, but in SQUIDs with multi-valued V@ characteristics some loss in sensitivity may result. Because of the periodicity of the SQUID response, the feedback electronics can lock the intrinsic flux at any of many values. A strong external signal may kick the system from one stable point of operation to another, causing a sudden change in the output voltage. Evidently, the higher the feedback gain, the better the system is for preventing the external flux from entering the SQUID loop. The open loop gain is mainly limited by the filters necessary for stabilizing the feedback loop. In rf SQUIDs the modulation frequency must be less than the bandwidth of the tank circuit, and it is often limited by the bandwidth of the components in the lock-in circuit. In dc SQUIDs the utmost modulation frequency is set by the amplifier noise which tends to grow with increasing frequency. SQUID electronics operated in the lock-in mode is extensively discussed by Giffard et al. (1972) and Giffard (1980); only the most important features will be mentioned here. Usually the feedback loop contains an integrator in a form of a PI (proportional-plus-integrating) controller that provides a feedback gain G(ja)=jwmOd/u In. this construction the maximum rate of flux change but an overall loop stability (slew rate) is limited to the order of is easily attained. Electronics providing a higher slew rate can be constructed but these devices are not very stable against change of loop parameters (Giffard 1980). Anyway, under quiet conditions, such as inside a magnetically shielded room, a conventional PI controller is sufficient to ensure proper operation. In multichannel applications the electronics should

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contain a special unit to automatically reset the SQUIDs after a loss of lock-in. Although the low-frequency readout circuits are very similar, the rest of the electronics may differ essentially for rf and dc SQUIDs. We next discuss special features of both SQUIDs. Rf SQUID in the hysteretic mode Energy dissipation in the rf SQUID loop affects the tank circuit impedance and thus the signal bandwidth. On the other hand, the dynamic impedance is related to the dissipation of the unloaded tank circuit and thus also to the input impedance of the preamplifier. Therefore, the optimization of noise characteristics leads to the condition R,,, = a R T , where a is the slope of the staircase pattern (see fig. 2), Rop,is the optimal input impedance of the preamplifier, and RT is the effective tank-circuit resistance. If R T is limited by the input impedance of the amplifier, the above condition will be fulfilled only in a narrow frequency band. This problem is aggravated with cooled preamplifiers (Ahola et al. 1979). The low output impedance of the hysteretic rf SQUID can be utilized by increasing the flux-modulation frequency and thus by constructing a device with a high slew rate. The electronics of a typical rf SQUID is shown in fig. 11. The rf level is adjusted by the variable capacitor C,, and the tank circuit is tuned by the room temperature capacitor C , . The square-wave oscillator providing the flux modulation also controls the PSD circuit (phase-sensitive detector). The main design principles for obtaining a low-noise rf SQUID are a very careful design of the preamplifier, the elimination of all dissipative elements P Y

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Fig. 11. Block diagram of the electronics for a hysteretic rf SQUID biased via the tank circuit by a radio-frequency (rf) drive and modulated by a square-wave audiofrequency ( a n signal; the amplified rf signal is monitored by the diode detector. The output of the phase-sensitivedetector ( E D )is fed back to the tank circuit and thus into the SQUID ring through the PI controller and the feedback resistor R,. The rfdrive level is adjusted by the tunable capacitance C, and the resonant frequency by the capacitor C,.

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from the cooled tank circuit, which is coupled to the room temperature via a coaxial cable, and choosing the feedback resistor to prevent the increase of the effective temperature of the resonant circuit. Dc SQUID A matching circuit is required to monitor the voltage over a dc SQUID with a low-noise JFET amplifier, which has an optimal input impedance of a few kilo-ohms: the SQUID impedance is typically only a few ohms. The modulation frequency must be high enough to avoid l/f noise from the preamplifier but low enough to exclude input current noise which increases drastically with increasing frequency. Many switching transistors with large gate areas provide excellent noise characteristics for reasonable source impedances and are thus suitable. The low output impedance of dc SQUIDS can be increased by feeding the signal through a cooled inductor into a capacitor, set in parallel with the preamplifier or by using an ordinary tuned transformer (with or without ferrite core) in a helium bath (Clarke et al. 1975a,b, 1976, Danilov et al. 1977). The tuned transformer is recommended since the increase of the output capacitance reduces the bandwidth of the reactive transforming circuit. Wellstood et al. (1984) improved the slew rate by placing another transformer at room temperature and increasing the modulation frequency up to 500 kHz. One practical construction for the dc SQUID readout circuit is illustrated in fig. 12 (Knuutila et al. 1988). The signal from the SQUID is fed through the cooled resonant transformer into the preamplifier consisting of two FETs in parallel (Toshiba SK146). The demodulator circuit contains, in

I

INSIDE SHIELDED ROOM

I

OUTSIDE SHIELDED ROOM

Fig. 12. Block diagram of the dc SQUID electronics based on phase-sensitive detection (Knuutila et al. 1988).

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addition to the switching circuit, also an integrator and a sample-and-hold circuit, which can be used to attenuate effectively the modulation frequency and its harmonics, without introducing a phase shift at signal frequencies. The output of the demodulator is fed via the PI controller and the transconductance amplifier back to the modulation coil. The electronics is operated at 100 kHz, and the cooled input circuits are designed to transform a 10 R SQUID impedance to 4 kR, which is the optimal input impedance of the amplifier stage including two Toshiba SK146 FETs. The noise temperature of the amplifier was found to be 2 K at 100 kHz. A digital-to-analog converter is used for automatic zeroing of the output voltage after flux jumps. It has been found that l/f noise in dc SQUIDs can be reduced by reversing the bias current synchronously with flux modulation. This technique requires complicated electronics and is thus not tempting in devices where the simultaneous operation of many SQUIDs is required. One elegant solution, with effective reduction of low-frequency noise, is discussed by Foglietti et al. (1986).

3. Applications: biomagnetism In biomagnetism, the magnetic field produced by biological events is recorded. The field can be measured non-invasively without any physical contact to the subject; therefore, the technique is well-suited for the study of activity in the human body. Biomagnetic fields are produced by three main mechanisms. First, active electrical currents in the brain, the heart, muscles, or in other parts of the body give rise to fields that convey information about the functions of these organs. Second, magnetized contaminants or foreign objects in the body produce steady fields, which may reveal the amount and distribution of the contaminants or the locations of magnetic objects. Third, diamagnetic or paramagnetic tissues modify externally applied fields; a technique has been developed to determine the content of iron in the liver using this effect. Typical amplitudes and spectral densities of biomagnetic fields and noise sources of various origins are shown in fig. 13. The external magnetic disturbances are several orders of magnitude larger than biomagnetic fields. To illustrate this, consider a flux transformer coil parallel to the earth’s 5 0 p T magnetic field. Tilting the coil by only 0.0002 seconds of arc will change the field sensed by it by 50fT. If the diameter of the coil were 20 mm, this rotation would correspond to a movement of the wire by only 0.01 nm, i.e., by a fraction of an atomic radius! Since many biomagnetic fields of interest are of the order of tens of femtotesla, it is evident that successful measurements require a careful elimination of vibrations of the magnetometer and shielding against external disturbances.

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Fig. 13. Peak amplitudes (the arrows on the left) and spectral densities of various biornagnetic and other fields. The laboratory noise level is adapted from Kelhi et al. (1982). the geomagnetic noise from Fraser-Smith and Buxton (1975). the brain noise from Knuutila and Hamalainen (1988).

3.1. MEASUREMENT TECHNIQUES

3.1.1. Magnetically shielded rooms

The most straightforward and reliable way of reducing the effect of external magnetic disturbances is t o perform the measurements in a magnetically quiet space. Several shielded rooms have been constructed for this purpose. An effective shielded enclosure was first built at the Massachusetts Institute of Technology by Cohen (1970). This room has three ferromagnetic layers and two layers of aluminium in the form of a rhombicuboctahedron, a polyhedron of 26 faces. A shielding factor of 66 dB at very low frequencies was obtained when active shielding and so-called shaking were used to enhance the shielding factor. Shaking is performed by applying a strong continuous 60 Hz field on the ferromagnetic layers so as to increase the effective permeability at other frequencies. At the Low Temperature Laboratory of the Helsinki University of Technology a cubic shield with inner dimension of 2.4 m was built in 1980 (Kelha et al. 1982). This room (see fig. 18) has three layers of mu-metal, sandwiched between aluminium plates; it attenuates external fields by 90-1 10 dB above the frequency of 1 Hz. 10-20dB of additional shielding below 10 Hz is obtained with active shielding, which is based on measurement of the

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external magnetic field and its compensation in a volume that contains the shielded room. A very heavy shield, consisting of 6 layers of mu-metal and one layer of copper, was built at the Physikalisch-Technische Bundesanstalt in Berlin (Mager 1981). Although this room has much thicker walls, its shielding factor is comparable to that of the Helsinki room in the frequency range 1-100 Hz (Emi et al. 1981). The reason is, evidently, that eddy-current shielding is not effective in the six layers of the Berlin room, whereas in Helsinki the aluminium plates in each layer were welded together at their edges to form closed shells for effective eddy-current flow. Recently, several shielded rooms for biomagnetic use have been constructed commercially by Vacuumschmelze'; these enclosures have two ferromagnetic layers and inner dimensions of 3 x 4 x 2.4 m'. The shielding factor varies from about 50 dB at 1 Hz to about 80 dB at 100 Hz. The Vacuumschmelze room is a compromise between performance and price; with suitable second-order gradiometers (see section 3.1.2) it offers a sufficiently quiet space for practically all types of biomagnetic measurements. Less expensive shielded rooms can be built from thick aluminium plates; Zimmerman (1977) constructed such an eddy-current cubic shield with inner dimensions of 2 m. Several similar rooms have been built later (Malmivuo et al. 1981, Stroink et al. 1981, Nicolas et al. 1983, Vvedensky et al. 1985b). The wall thickness in these rooms is about 5 cm; the shielding factor is proportional to frequency, being about 50 dB at 50 Hz. Magnetically shielded rooms are easily made tight against rf fields. One might think that this would facilitate the design and operation of SQUID magnetometers because of reduced demands on the radio-frequency insensitivity of the instruments. However, in many practical situations, at least in a research laboratory, it is difficult to avoid radio-frequency fields inside the shielded room. Some experiments and, in particular, preparations for experiments are easiest to perform when the door of the room is open. Since the room acts as a resonance cavity, strong rf fields may occupy its interior. Even with the doors closed, cables to the stimulus equipment, EEG leads, and other wires act as antennae, bringing external rf fields inside. It is, therefore, essential that the SQUID system operates even in the presence of rf fields. The ultimate noise level in magnetically shielded rooms is determined by Johnson noise in the conducting walls. The effect of this noise source is most significant in eddy-current shields (Varpula and Poutanen 1984); it can be reduced by mu-metal sheets (Maniewski et al. 1985).

' Vacuumschmelze GmbH, Griiner Weg 37,6450 Hanau, West Germany.

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3.1.2. Gradiometers

In addition to or instead of shielded rooms, external magnetic disturbances may be partly cancelled with gradiometric coil configurations. A simple tirst-order gradiometer, where two oppositely wound coaxial coils are connected in series with the signal coil, is shown in fig. 14c. This arrangement is insensitive to a homogeneous magnetic field, because it imposes the same flux on the lower (pickup) and the upper (compensation) coils. On the other hand, the first-order gradiometer is effective in measuring magnetic fields produced by nearby sources. If the pickup coil is close to.the head and if the distance between the two coils (the baseline) is at least 4-5 cm, the magnetic field produced by the brain is sensed essentially by the lower coil only. Other possibilities of arranging the first-order gradiometer are shown in figs. 14b, d and e. In fig. 14d, an asymmetric first-order gradiometer is illustrated; its main advantage is that the compensation coil inductance is reduced; therefore, a better sensitivity is obtained than with a symmetrical gradiometer. In fig. 14e, the pickup coil and the compensation coil are connected in parallel instead of in series so as to reduce the inductance of the detection coil by a factor of four from the configuration in fig. 14c. This parallel connection is easier to match to a SQUID signal coil with a small inductance; the disadvantage is that homogeneous magnetic fields give rise to shielding currents in the detection coil that couple to neighbouring

t

Fig. 14. Different types of flux transformers. (a) Simple magnetometer that measures the flux threading the loop. (b) Planar 2-D gradiometer that is sensitive to the difference of flux in the two loops. (c) Symmetrical gradiometer; the difference of the field between the two coils, connected in series, is measured. (d) Asymmetric gradiometer; the homogeneous magnetic field sensed by the pickup coil is compensated for by a single large turn in the upper coil. (e) Symmetrical gradiometer, in which the pickup and compensation coils are connected in parallel. (f) Symmetrical second-order gradiometer.

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gradiometer channels. In fig. 14b, a planar off -diagonal, so-called double-D gradiometer is shown. To obtain insensitivity to homogeneous fields, one has to make the turns-area products of the pickup and compensation coils equal. In wirewound gradiometers, an initial balance of a few percent is typical; it can be improved by adjusting the effective areas of the coils with movable superconducting tabs. Three balancing tabs are needed to balance all three field components; a final balance of about 1-10 ppm can be achieved. One must remember that even after careful balancing at low frequencies, the balance at rf frequencies is not guaranteed. Therefore, it is important to have good rf shielding surrounding the pickup coils on an rf shunt across the signal coil; an R C shunt is appropriate (Ilmoniemi et al. 1984, Seppa and Ryhanen 1987). Figure 14f shows a configuration where two gradiometers are connected together in opposition so that the detection coil is insensitive to both homogeneous fields and to uniform field gradients. This arrangement further improves the cancellation of magnetic fields produced by distant noise sources; successful experiments with second-order gradiometers have been performed in unshielded environments. A disadvantage of gradiometers of high order is that the signal energy coupled to the SQUID is reduced. Although superconducting tabs are suitable for balancing single-channel instruments, their use is too complicated with multichannel devices. In New York University a system was adopted where balancing was done electronically, as described in more detail in section 3.5.2. 3.2. NEUROMAGNETISM At present, neuromagnetism, the study of magnetic fields that originate in the human brain, is the branch attracting most attention in biomagnetism. Magnetoencephalography (MEG) is closely related to electroencephalography (EEG): both are produced by the same cerebral events; a great advantage of MEG is that the local irregularities of the skull and the scalp do not essentially affect the magnetic field whereas they have a major effect on the electric field. The current that gives rise to the magnetic field is confined by the poorly conducting skull to flow within the cranial cavity. As a result, the determination of locations of sources from the measured electric potential or magnetic field distribution is more accurate in MEG than in EEG. Another advantage of MEG is that no electrode leads need be attached to the head. This facilitates the preparation of experiments especially in multichannel measurements; putting on, say, 32 EEG electrodes can take about one hour. A fundamentaljustification for the magnetic technique is that MEG and EEG are sensitive to different configurations

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of active currents in the brain; MEG conveys information not contained in EEG signals. A more detailed view on neuromagnetism can be obtained from several recent reviews (Hari and Ilmoniemi 1986, Romani and Narici 1986, Kaufman and Williamson 1987, Williamson and Kaufman 1987). 3.2.1. Origin of neuromagnetic fields

Interpretation of MEG signals requires an understanding of the origin of the neuromagnetic field. It is believed that a major portion of the measured field is produced by currents of neurons whose alignment is approximately perpendicular to the cortical surface. This primary current gives rise to volume currents, and the primary and volume currents together produce the measured magnetic field. In a spherically symmetric conductor, the magnetic field due to the radial primary current is cancelled by the accompanying volume currents. Thus, the externally observable magnetic field is produced by tangential primary currents alone, i.e., mainly by activity in the fissures (Grynszpan and Geselowitz 1973). If a small area of cortex is active, one may model the associated primary current as a dipole. Vector formulae for the magnetic field produced by a dipole in a spherically symmetric volume conductor have been developed (Ilmoniemi et al. 1985, Sarvas 1987). The sphere model for the head is, of course, a severe simplification. However, in studies where the spherical head model was compared with a realistically shaped multilayered head model (Hamalainen and Sarvas 1987), it was found that in regions where the deviation from sphericity is small, e.g. at occipital areas, the sphere model gives correct field values to an accuracy of a few percent, provided that the radius of the sphere is fitted to the local radius of curvature of the skull’s inner surface. In frontotemporal locations, however, the sphere model failed to reproduce the correct field pattern. The realistically shaped head model is, of course, computationally much more demanding than the sphere model, since explicit formulae for the magnetic field are not available. At present, realistically shaped models are too tedious for use in least-squares fitting. A possible solution might be in applying the homogeneous head approximation (Hamalainen and Sarvas 1987), where the skull and the scalp are neglected and the head is replaced by a uniform conductor of the shape of the inner surface of the skull. This is justifiable since only a small amount of the volume current flows in and through the poorly conducting skull, thus giving negligible contribution to the magnetic field measured outside the head. The homogeneous head approximation performs substantially better than the sphere model in nonspherical areas and yet is not computationally as demanding as the three-

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layer model. However, at present only the sphere model is in routine use. Once the forward problem, i.e., the calculation of the magnetic field from a given primary current distribution, is mastered, one must tackle the inverse problem by determining such primary current distributions that can explain the observed field. The simplest source model is the current dipole, which in a spherical conductor geometry is described by five parameters, i.e., three location coordinates and two tangential components of the dipole moment vector. Figure 15 shows the pattern of the radial component of the magnetic field due to a current dipole in a spherically symmetrical conductor. To determine the location of the dipole on the basis of noisy measurements, it is necessary to measure the pattern at points that cover both polarities of the field. Otherwise, small amounts of noise may put the estimated location of the dipole in a totally wrong region. The inverse problem can be solved only if the number of independent measurements is equal or exceeds the number of parameters that are to be calculated. In practice at least twice this number is needed, because the magnetometers are usually not optimally located for the purpose of determining the source parameters from noisy measurements. Further, to evaluate whether the model itself is reasonable, more measurements are required than there are adjustable parameters. 3.2.2. Spontaneous activity Neuromagnetic fields were first measured by Cohen ( 1968) who detected the magnetic alpha rhythm with an induction-coil magnetometer. The

Fig. 15. A calculated isofield contour map of the radial component of the magnetic field due to a current dipole in the brain. The dipole points in the direction of (he arrow; its depth is roughly equal to the distance between the field extrema divided by J2. Solid lines indicate field emerging from the head, dashed lines field entering it. A measured pattern like this can be used for estimating the tangential part of the current dipole vector and its three-dimensional location.

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measurements were carried out in a shielded enclosure and the signals were averaged using a trigger from the EEG. The polarity of the signal was opposite over the left and right hemispheres; this suggested that the primary currents associated with the magnetic alpha rhythm are oriented along the direction of the sagittal midline and located in the occipital area. Subsequent experiments with SQUID magnetometers have confirmed these results (Carelli et al. 1983, Chapman et al. 1984), the major new results being the determination of locations of equivalent sources (Vvedensky et al. 1985a) and the finding that different spindles of alpha waves are generated by different configurations of cortical activity (Ilmoniemi et al. 1988). The latter two studies would not have been possible without multichannel SQUID magnetometers (see section 3.5.2): the signals are not repeatable and, therefore, measurements performed at different times over different locations are not directly comparable.

3.2.3. Evoked fields

In the most common type of neuromagnetic measurements, suitable sensory stimuli are given to the subject and the magnetic field due to the subsequent cerebral activity is measured. Because of noise, including that produced by the background activity of the brain itself, the same stimulus is repeated dozens of times, and the measured signals are averaged. An example of a sequence of magnetic field patterns evoked by an auditory stimulus is shown in fig. 16 ( S a m et al. 1985). The stimulus in this experiment was a 30-ms tone burst of 1000-Hz frequency and of 70-dB amplitude delivered to the left ear. The magnetic field maps are shown at intervals of 20 ms beginning at the time of stimulus onset. There is some evidence of a response 40 ms after the onset of the stimulus; at 100ms the field amplitude is maximal. Dipoles that best explain the measured patterns were determined and are shown as dark arrows in the figure. The sites of the dipoles agree with the known location of the auditory cortex. A number of evoked-field studies have been performed on the auditory as well as other modalities (see, for example, Romani and Williamson 1983, Hari and Kaukoranta 1985, Weinberg et al. 1985, Hari 1989, Atsumi et al. 1988). These studies have amply demonstrated the locating power of M EG and provided new information about the origin of several evoked-field components. Recently, interest has grown among psychologists in using MEG as an indicator of the location of activity changes that are related to mental operations. One of the results in this area is the demonstration that conscious attention has a marked effect on the amplitude of the 100ms deflection of the auditory evoked response at or near the primary auditory cortex (Curtis et al. 1988). Of special relevance appear to be neuromagnetic

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Fig. 16. Magnetic field isocontour maps obtained in response to a 30 ms tone burst of lo00 Hz frequency, delivered to the left ear. The field was measured with three channels simultaneously and the measurement was repeated at a number of locations as shown in the upper left panel. The frames are labeled by the time, in ms, from the onset of the stimulus. In maps obtained after 80 ms, an equivalent dipole is drawn as an arrow; the amplitude Q of the dipole is shown as well as the proportion E of field energy explained by the dipole model. Solid lines indicate field emerging from the head and dotted lines field entering the head. The dots show the locations of magnetometer channels. The difference in field amplitudes between adjacent isocontour lines is 40 IT. Modified from Sams et al. (1985).

studies related to processing of speech sounds (Kaukoranta et al. 1987); the role of speech in communication is unique to the human species. While many other cerebral phenomena are amenable to detailed investigations in animals, language can be studied in humans only. 3.2.4. Clinical aspects of MEG

Clinical applications of MEG are just beginning. One of the reasons for the slow start is that with single-channel instruments, measurement sessions have simply taken too long for being practical for studies of patients. Multichannel instruments will remove this problem and it is expected that several clinically oriented MEG laboratories will start operation in the near future. MEG has obvious merits as a potential diagnostic tool. There are several other methods to probe brain anatomy and functions, but the only noninvasive techniques available for the real-time monitoring of brain activity are

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MEG and EEG. The latter is already in wide clinical routine use, but its capability for locating brain activity is poor, so MEG seems to have unique possibilities. While the EEG is mostly used to detect abnormal wave forms of electrical cerebral activity, the locating power of MEG offers a possibility to characterize the spatiotemporal operation of the brain in a more specific manner. Proper analysis of EEG signals would require detailed knowledge about the conductivity as a function of location in the head, particularly in the scalp and the skull. Although the numerical description of the detailed shape of the skull and the scalp is cumbersome and computational analysis of EEG with the acquired shape information requires a great deal of computer time, it is probable that realistic models for the conductivity distribution of the head will be used increasingly. The spatial accuracy of EEG will thereby improve, but because MEG contains information that is complementary to EEG and because its use involves no tedious attachment of electrodes, MEG will become clinically increasingly attractive, particularly when large magnetometer arrays become available. Epilepsy The first clinically relevant application of MEG was with focal epilepsy, where progress has been made in locating spots in the brain where seizures originate. In cases where drugs are not effective in controlling seizures, the location of the foci is needed for the planning of their surgical removal. Modena et al. (1982) reported simultaneous electric and magnetic recording of epileptic activity from 12 patients with generalized epilepsy and 15 with focal epilepsy; in 9 patients out of the latter group sharply localized magnetic field patterns were observed. Locations of epileptic foci in three dimensions were determined by Barth et al. (1982), who used electrically measured interictal spikes as triggers for averaging, and by Chapman et al. (1983), who applied the relative covariance method (Chapman et al. 1984) in the formation of magnetic field maps for subsequent determination of equivalent dipole parameters. In addition to finding epileptic foci, MEG seems appropriate for establishing patterns of the subsequent spread of the activity as well as for studying the dynamics of non-focal epilepsy. Other clinical applications There is much interest in other clinical applications, especially in the most common disorders of the brain and in disorders that are difficult to diagnose. So far practically nothing has been done with MEG in studies of this type, and it is premature to judge what the chances for success are. However, because of the immense significance of any progress in understanding or diagnostics of brain dysfunction and because of the lack of alternative noninvasive real-time monitors, it seems worthwhile to put effort into this

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area. If the dynamics of the disorders in question will be understood, one will probably also be able to develop diagnostics using MEG, possibly together with EEG. However, because work in this area is just beginning and multichannel instruments will come into widespread use only in the next decade, one should not expect many significant results earlier than in the mid-90s. Another line of development that might lead to clinical applications of MEG is the monitoring of the integrity of sensory pathways. Most of current MEG research is of the evoked-field type, in which stimuli are given to the subject and the neural response is measured. Abnormalities in the pathways can be objectively evaluated using this paradigm. A study along these lines was performed by Peliuone et a]. (1987) who found, on the basis of neuromagnetic measurements, how auditory pathways had been modified in a patient with a cochlear prosthesis. The ability of MEG to determine the location of brain activity has recently attracted interest in its application to the study of effects of drugs on cerebral function. Sinton et al. ( 1986) administered the psychoactive substances diazepam and triazolam to an experimental subject in order to investigate the feasibility of using MEG to monitor central effects of drugs. They found that these substances modify the amplitudes of magnetic deflections at 100 ms and 150 ms after an auditory tone stimulus; the time course of the effect is an indicator of clearance of the drug from the body. In another study, Ribary et al. (1987) investigated the effect of antidepressive drug treatments on MEG response to 40 Hz auditory stimulation. The advantage over EEG in these studies is that one knows that the observed change in activity is at the auditory cortex. This spatial specificity is of importance in testing the location-specific effects of drugs. 3.3. CARDIAC STUDIES A potentially very large area of clinical applications of SQUID magnetometers is in cardiac monitoring and in the diagnosis of various pathological conditions. Magnetocardiography (MCG) is the oldest branch of biomagnetism, but progress towards clinical practice has been slow. A major obstacle is the difficulty of taking into account the complicated conductivity of the heart and its surroundings. The changing blood volume in the heart has a conductivity that differs from that of the heart muscle, and the conductivity of the lungs is much smaller than that of the surrounding tissue. These effects can be taken into account by using multi-compartment conductivity models (Horacek 1973, Cuffin and Geselowitz 1977a,b, Miller and Geselowitz 1978); even these attempts suffer from insufficient knowledge of the conductivity distribution. The conductivities of the different tissues

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are generally well-known, but there is uncertainty about the locations of boundaries between the different compartments. A further complication is the marked anisotropy of the conductivity of the heart muscle. In addition, it is not yet known how much information is contained in MCG that is not conveyed by the ECG (MacAulay et al. 1985). Progress in MCG has been made, for example; in the diagnostic evaluation of the conduction system: extra conduction pathways, which are excited in the Wolff -Parkinson-White syndrome, have been found to give rise to magnetic field patterns that make it possible to find their location (Fenici et al. 1985, Katila et al. 1988). Estimation of locations of active tissue has been attempted also for arrhythmias and so-called late fields, which are created by the circular activation of the heart muscle in pathological tissue. A recent area of interest is the study of so-called micropotentials that have been found to correlate with the risk of sudden heart failure (Montonen et al. 1988). At present, the uncertainty in locating pathological tissue or function in the heart on the basis of MCG measurements is at best of the order of 2 cm (Ern6 1985, Katila et al. 1987); improved accuracy can be expected with better conductivity models, which, for example, take into account the anisotropy of the heart muscle. With advances in the analysis of MCG signals and with the projected availability of multichannel systems suitable for hospitals, one may expect increased clinical use of this methodology. In MCG, no electrodes need be attached to the body like in ECG; the convenience of the magnetic measurement is valuable in this context. One must bear in mind that the patients in question are often in an unstable condition. It is therefore important to complete the study quickly so that the state of the patient does not change during the field mapping. Many channels are also necessary for capturing possible one-time events. Standard MCG is done without an attempt to determine source locations. Its widespread acceptance into hospitals to essentially just replace ECG would require an inexpensive multichannel system for field measurement over the chest. A large-area array is necessary and it seems that one must wait for the high- T, superconductors to help bring down the cost of refrigeration. On the other hand, even with present magnetometer technology, further progress in conductivity models would make MCG attractive for preoperative determination of pathological sources. Also here, a multichannel system is needed. 3.4. OTHERBIOMAGNETIC APPLICATIONS

Dust contamination in the lungs can be assessed by measuring its remanent field after magnetization. Metal dust usually contains iron, oxidized to

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magnetite or hematite. Magnetopneumography offers a non-invasive determination of the inhaled dust load among steel workers, welders etc. (Cohen 1973, P.-L. Kalliomaki et al. 1983) but also a means for studying lung functioning as small amounts of these particles serve as a tracer (Brain et al. 1985). To avoid complicated models, the sensitivity of the measuring system should be roughly constant over the chest. A straightforward method would be to use both a uniform magnetizing field and a detector with a uniform sensitivity pattern. However, it is impractical to make detector coils large enough to fulfill this criterion; instead, the field is measured at several points with smaller coils. Usually, this is accomplished by moving the subject with respect to the sensor (K.Kalliomaki et al. 1983). For lung measurements, SQUID sensors are not absolutely necessary; good results have been obtained with flux-gate sensors. Detecting excessive accumulation of iron in the liver, which is an intermediate storage of iron in the body, has significance in the diagnosis of the diseases hemochromatosis and thalassemia. Assessment of the iron overload of the liver has been traditionally carried out using biopsy, which is not totally free of risk and causes discomfort to the patient. The magnetic susceptibility of the liver provides a quantitative, noninvasive measure of hepatic iron concentration. An external field is applied and the distortion in the field caused by the liver is then sensed with a SQUID magnetometer. The liver gives a paramagnetic response to the applied field, whereas the surrounding body tissue is diamagnetic with a susceptibility close to that of water. The diamagnetic background normally outweighs the paramagnetic signal of the liver; hence a reference measurement is necessary. Usually this is accomplished by moving the sensor with respect to the body. Typical resolution of the method is of the order of 100 ppm of iron in the tissue; therefore, iron deficiency cannot be measured accurately and the method is best suited for detecting iron overload (Farrell 1983, Farrell et al. 1983). The biomagnetic technique has also been applied to studies of steady magnetic fields caused by dc currents in the human body. These currents can be due to an injury or they may be produced by normal electrophysiology of an organ; noninvasive in vivo information may thus be obtained (Cohen 1983, Grimes et al. 1983). In addition, biogenic fernmagnetism naturally occurring in some organisms has been studied (Kirschvink 1983). NEUROMAGNETOMETERS 3.5. MULTICHANNEL

Until fairly recently, all biomagnetic measurements were carried out using single-channel magnetometers, with their pickup and compensation coils

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wound of superconducting wire on three-dimensional coil formers. The optimization of the coil parameters, i.e., the coil diameter and length, the number of turns, and the baseline of the gradiometer, for good sensitivity and discrimination against external disturbances has been discussed by several authors (Romani et al. 1982, Vrba et al. 1982, Duret and Karp 1983, 1984, Farrell and Zanzucchi 1983, Ilmoniemi et al. 1984). Besides maximizing the field sensitivity, the spatial distribution of the biomagnetic signal and of the disturbances must be taken into account in the design. Since locating current sources is one of the main objectives of biomagnetic studies, multichannel devices designed to map the spatial pattern of the magnetic field are very desirable. Such instruments not only make the measurements faster but also give more reliable data. So far, devices have been designed for brain measurements; multichannel systems for cardiac measurements may emerge in the near future. In this section we shall mainly consider magnetometers intended for neuromagnetic research. After discussing the design of these devices, with remarks about the applicability of the methods to other biomagnetic studies, we present existing biomagnetic multichannel systems. Problems encountered in their construction using conventional solutions and the introduction of integrated SQUID sensors indicate that in the near future multichannel devices may be made using planar technology. We end the section by discussing some specific questions about multichannel devices in biomagnetic research.

3.5.I . Optimization of multichannel neuromagnetometers Because of the large variety of possible source current distributions in the human brain, general criteria for optimality in magnetometer design do not exist. Figures of merit for different configurations can be obtained only by making assumptions about the signal sources and their characteristic field distributions. The ability to separate field patterns caused by sources at different locations and of different strengths requires a good signal-to-noise ratio; maximum sensitivity in every channel is thus desirable. At the same time, one has to find the sensor configuration that gives the best locating accuracy. Unfortunately, these two tasks are not independent. For example, an increase of pickup-coil diameter improves field sensitivity, but sacrifices spatial resolution. In practice, the freedom of the designer is restricted by several constraints: the size of the dewar, the properties of the SQUID sensors, the feasible upper number of channels, the distribution and strength of external noise sources, the characteristics of the cerebral signals.

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The design of flux transformers In optimizing a gradiometer coil, the problem is to maximize the flux (3.1)

coupled to the SQUID loop by the flux transformer circuit. Here L,, L, and L, are the inductances of the pickup, compensation, and signal coils, respectively. L is the SQUID inductance, L, denotes the parasitic inductance of the connecting leads, k, is the coupling coefficient between the signal coil and the SQUID. the difference of fluxes threading the pickup and compensation coils, depends on the field distribution. The field sensitivity of a magnetometer is defined as the locally homogeneous magnetic field at the pickup coil that would produce a signal at the output of the system of equal magnitude with the system noise. If @" is the flux noise in the SQUID, the corresponding field noise level is

where np is the number of turns in the pickup coil and A, is their average area. As far as the SQUID and its signal coil are concerned, the key for high field sensitivity is the energy resolution at the output, E , , ~ = l ~ ; ~ ( @ ; ) / 2 L . However, as the SQUID and its signal coil are usually fixed, only the pickup and compensation coil parameters can be adjusted. Then, the inductancematching condition,

(3.3)

L , = L,+ L,+ L,,

does not generally maximize the sensitivity. Furthermore, as will be discussed later, the diameter and length of the pickup coil are often determined by other considerations and the compensation coil dimensions are fixed by the gradiometric balance condition and by space limitations. The optimum number of turns np in the pickup coil is found by differentiating eq. (3.1), where Qne, is assumed to be proportional to n,, (Ilmoniemi et al. 1984):

a

L,+L,+L,+L,-n,-(L,+L,+L~)=O. (3.4) an, Therefore, the inductance-matching condition, eq. (3.3), maximizes the sensitivity for tightly wound coils only. In general, no simple analytical expression exists for the dependence of the inductance on the number of turns in the pickup coil; thus the optimum number of turns and other coil parameters must be determined numerically. Then, feasible maximum dimensions must be specified as constraints, quite often dictated by the space available in the dewar.

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Enlarging the pickup coil increases field sensitivity but at the same time the loop integrates the field from a larger area; thus the coils can no longer be approximated by point magnetometers. In practice, this effect becomes significant when the coil diameter exceeds the distance to the source (Romani et al. 1982, Duret and Karp 1984). Similarly, an increased length of the coil, i.e., less tight winding, allows more turns without excessive increase of inductance; the sensitivity improves, but because of increased distance from the source the signal becomes weaker. For cortical current dipoles these two effects tend to cancel, leading to a broad maximum in the signal-to-noise vs. coil length curve. For successful numerical analysis of neuromagnetic data it may be necessary to take into account the finite volume of the coils. The first significant correction to point magnetometers, namely the effect of the diagonal second-order derivatives of the field, may be calculated by evaluating the average field at the vertices of a tetrahedron, ( * r / 2 , *r/2, h / 2 h ) , ( * r / 2 , T r / 2 , - h / 2 h ) , located symmetrically around the center of a cylindrical coil of radius r and height h. The base length of the gradiometer should be chosen 1-2 times the typical distance to the sources. This provides adequate rejection of distant noise sources, without significantly attenuating the signal (Vrba et al. 1982, Duret and Karp 1983). One should note, however, that noise from nearby sources such as the dewar, cannot be avoided with gradiometric techniques. With modern SQUIDS, noise from the dewar has turned out to limit the field sensitivity. Thus, further improvement requires the reduction of dewar noise, which is probably dominated by thermal currents in metallic insulation layers. Locating error calculations and simulations A useful figure of merit of multichannel magnetometers is the uncertainty in locating cortical current sources. To estimate this uncertainty, a suitable source current model and a volume conductor model must be chosen. A current dipole in a spherically symmetric volume conductor is appropriate; because of computational limitations, as discussed in section 3.2.1, it is the only model presently used in the least-squares search of cortical sources. The locating ability of the magnetometer may be simulated numerically by adding noise to the calculated field values and by then fitting an equivalent dipole source to the data by means of a least-squares search. Repeated simulations then reveal the average locating error. A more effective way to estimate the error is to directly determine the confidence regions of the least-squares fit (Kaukoranta et al. 1987, Hari et al. 1988). The confidence region in the parameter space may be defined as being the smallest set of parameter values with a given total a posteriori probability.

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Since the field depends in a nonlinear way on the source parameters, the confidence set in the parameter space is tedious to compute exactly (Hamalainen et al. 1987). However, linearization in the vicinity of the least-squares solution makes the problem tractable (Kaukoranta et al. 1986, Sarvas 1987). The resulting confidence region is an m-dimensional hyperellipsoid, where m is the number of model parameters, centered at the estimated value. The half-axes of the ellipsoid are given by the eigenvectors and eigenvalues of the matrix ( J T 2 - ' J ) - ' ,where J is the Jacobian of the function giving the dependence of the field on the model parameters and Z is the covariance matrix of the measurement errors. The confidence intervals for the model parameters are then given by the edges of a rectangular box containing the confidence ellipsoid and having its faces parallel to the coordinate planes. The confidence limits for a current dipole are generally largest in the depth direction and smallest in the direction perpendicular to the dipole in the tangential plane. Their values depend on the signal-to-noise ratio, but also on the depth of the dipole and on the measurement grid. Therefore, the calculated confidence limits can be applied for comparing various magnetometer arrays (Knuutila et al. 1985, 1987b). Other considerations If the spatial frequency content of the signal to be measured is known, the spatial analog of sampling theory can be applied to determine the best spacing for the measurement grid (Romani and Leoni 1985). Field distributions caused by current dipoles in the brain have maximum spatial frequencies between 10 and 30 m-', depending on the depth of the sources. Thus, a suitable grid spacing is 20-30 mm. To apply this criterion, a large area of coverage must be assumed. If .the number of channels is fixed in advance, the optimal channel separation may turn out to be larger than predicted by the spatial-frequency analysis. With a fixed number of channels, it is also instructive to calculate the angles between the lead fields of the channels, as discussed by Ilmoniemi and Knuutila (1984) and by Knuutila et al. (1987b). This angle is a measure of the amount of diferent information conveyed by the channels. In a multichannel magnetometer, compact modular construction is a virtue. When many channels are simultaneously used, the possibility for computer control of the electronics is important. Furthermore, to avoid cross talk between channels, cables must be well shielded or symmetrized; this is also important for the noise immunity of the system. For highsensitivity magnetometers, a robust grounding system is essential. In addition, materials must be carefully chosen; for example, careless cabling to

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room temperature may increase the liquid helium boil-otf rate to an intolerable level; in a 30-channel dc-SQUID system, 90 wires are needed if no special techniques are used. Making dewars for wide-area multichannel magnetometers is problematic, too. Because of considerable variations in head shapes, no dewar bottom can be made optimal for them all; one may use a spherical bottom to approximate the average curvature, but then the maximum area is obviously limited. The fact that some of the channels are rather far from the scalp imposes high demands on the sensitivity of the SQUIDS. In addition, a large sensing area requires thick dewar walls for strength and thus a wide gap between the room temperature surface and the 4.2K interior. High-T, materials may make it possible to get the sensors closer to the head, resulting in increased signal strength. A good combination of high sensitivity and close-to-the-head sensors might be obtained with a hybrid structure, with a high-T, pickup coil and a SQUID at 4.2 K. Design of multichannel systems for other biomagnetic studies The previous discussion was primarily about magnetometers for neuromagnetic research. However, the same general principles can be applied to cardiac studies as well. The main new factors affecting the design are the different conductor geometry and the different source configuration. In the brain, the tissue can be modeled successfully as a homogeneous conductor, whereas in the chest the lungs introduce a major inhomogeneity which must be taken into account. As a result, simple models do not give sufficiently accurate results and computationally tedious finite-element methods must be used. Estimating the locating accuracy of various magnetometer configurations is thus difficult. The body surface of interest is larger in magnetocardiographic than in neuromagnetic studies; typically, the field is measured over the whole chest (for a standardized MCG grid, see Karp 1981). Therefore, a device for clinical use which would cover the entire area at once, requires a very large helium container. The dewar does not need a curved tail, but the gap in the tail should be as small as possible. Also, the optimal interchannel separation is larger in a cardiac multichannel device than in a neuromagnetometer. Although the cardiac signals are two orders of magnitude stronger than the cortical magnetic fields, a very high sensitivity is required for highresolution measurements, which detect possible disorders in the heart’s conduction system. A small signal of interest, superposed on the strong cardiac field, naturally requires electronics with a high slew rate.

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3.5.2. Existing multichannel systems The double-D sensor at M I T The double-D gradiometer of Cohen (1979) was the first multichannel neuromagnetometer. It consisted of two mutually orthogonal off -diagonal gradiometers, shown schematically in fig. 14b, measuring the components a E : / a x and aE,/ay. The diameter of the coils was 2.8 cm and the gradient sensitivity of the 2-D detectors 16 fT/(cm&). In addition to the two 2-D channels, the system has a 2.8 cm diameter coil measuring B,;the sensitivity of this third channel was lOfT/&. In each channel, a commercial rf SQUID was used. Since a 2-D detector is sensitive to currents directly under it, and since the orthogonal channels (see also the discussion in section 3.5.3) measure orthogonal current components, the system was used to display the distribution of currents as a function of surface location. In studies of the magnetic alpha rhythm over the occipital lobe, the currents were found to flow preferably along the direction of the longitudinal fissure (Cohen 1979). The MIT system has recently been augmented with a duplicate assembly of a two-channel 2-D detector and a E, channel in a separate dewar (Kennedy et al. 1988). The four-channel gradiometer in Helsinki A multichannel neuromagnetometer measuring the field at several locations

simultaneously was first used by Ilmoniemi et al. (1984). Their 4-channel first-order gradiometer (4M), developed for use in a magnetically shielded room (see section 3.1.1), consisted of three elliptical pickup coils inside a 30 mm diameter dewar tail and a fourth circular 2 I mm diameter coil 12 mm above the lower coils. The field sensitivities of the channels in this rf-SQUID instrument, obtained with flux noise @ , = 7 x were 22 and 15 fT/JHz in the lower and upper coils, respectively. The compensation coils for all four channels are coaxial; thus the signs of mutual inductances of adjacent and coaxial coils are opposite, reducing the coupling between the lower channels. By suitably adjusting the distance between the individual turns in the compensation coils, the mutual inductances can, in principle, be made arbitrarily small. The fourth pickup coil of 4M was placed above the lower three in order to get additional information from the variation of the field strength as a function of distance from the brain. The magnetic field outside a surface enclosing all the sources is uniquely determined by the values of the normal field component on this surface; however, when the detection coils are constrained to a narrow dewar tail, useful additional information is obtained from a more distant channel. The location of the fourth channel was

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determined by maximizing its sensitivity to source current patterns that are not seen by the lower three channels (Ilmoniemi and Knuutila 1984). An experiment with 4M that would not have been possible with fewer than the four channels was performed by Vvedensky et al. (1985a). They measured the magnetic field produced by the spontaneous human alpha rhythm, concluding that the sources of alpha bursts on the left and right sides of the occipital lobe could be active separately. The analysis was based on normalized gradients that were obtained by dividing the gradient calculated from signals in the lower three channels by the amplitude in the fourth channel. Near a field extremum, to a first approximation, these gradients point toward the extremum and their amplitudes are proportional to the distance. The four-channel magnetometer was in use from mid-1983 to the end of 1986; most experiments were of the evoked-field type, and usually, only the three lower channels were used (see, for example, Hari et al. 1987, Huttunen et al. 1987, Kaukoranta et al. 1987, Makela and Hari 1987).

The five-channel installation in New York

A 5-channel dc-SQUID system was installed at New York University (NYU)

in 1984 by BTi' (.Williamson et al. 1985). The Neuromagnetism Laboratory of NYU is situated in Manhattan; it may be the noisiest location where MEG is recorded. Each detection coil is a symmetrical second-order gradiometer, with 15 mm diameter and a 40 mm baseline. The pickup coils lie on a spherical surface of 10 cm radius, four of them at the comers and one slightly above the center of a 28 by 28 mm square; the axis of each coil passes through the center of the sphere. The dewar is moved in a special scanner; with the subject's head in its center, each channel is approximately radial and the probe can be quickly repositioned, the dewar moving on a spherical surface around the head. A novel attempt was made in New York to tackle the external noise problem: in addition to the five signal channels, the system has four SQUID channels far away from the head that measures the three magnetic field components and the axial derivative of the radial component. These compensation channels are insensitive to brain sources but sensitive to distant noise sources. When the compensation signals are suitably weighted and added to each signal channel, rejection of external noise is improved by about 20 dB. Still, the noise level could not be reduced sufficiently for some experiments, although many successful measurements were performed with this system (see, for example Pelizzone et al. 1985, Kaufman and Williamson 1987). A magnetically shielded room was installed at NYU by Vacuum-

'

Biomagnetic Technologies, Inc., 4174 Sorrento Valley Blvd., San Diego, California 92121, USA.

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schmelze in 1987 (see section 3.1.1); the electronic balancing system may not be necessary any more. An exciting addition to the five-channel system is a pair of so-called CryoSQUIDs (Buchanan et al. 1988). Each consists of a standard BTi second-order SQUID gradiometer in a dewar kept cold by a commercial Gifford- McMahon cooler and a helium Joule-Thomson refrigerator. A noise level of 25 f l / a was obtained while operating the cryocooler. The obvious advantage with this closed-cycle system is that helium refills are avoided; in addition, the CryoSQUlD has been designed to operate in virtually any orientation, even upside down. If reliable cryocoolers suitable for high-sensitivity magnetic measurements will become available, SQUID systems might find more acceptance in hospitals and in applications or locations where the supply of liquid helium is limited.

The four-channel sysfem in Rome The rf-SQUID system in Rome (Romani et al. 1985) has four parallel and symmetrical, second-order gradiometers with a baseline of 53 mm; the coils are 15 mm in diameter and they are located at the corners of a 21 by 21 mm square. The system is designed to operate in an unshielded environment. The permanent balancing of the gradiometers is done separately for each channel before the final assembly of the system. Thermal cycling deteriorated the original balance only by a factor of 2-3. The noise level obtained in the wooden hut at the lstituto di Elettronica dello Stato Solido in Kome is 40-50ff/& (Romani et al. 1985). A number of successful studies with this system have been reported (see, for example, Romani and Narici 1986). Particular attention has been paid to positioning the probe accurately: two optic fibers emitting narrow light beams have been attached to the bottom of the dewar; this helps locating the probe with respect to a predetermined grid on the subject's head; an accuracy of about two millimeters is achieved. Commercial seven-channel gradiometers A 7-channel second-order gradiometer system with dc SQUIDS is commercially available from BTi. The arrangement is similar to that of the 5-channel system in New York;the main difference is just that the four detection coils surrounding the center coil are replaced by six. Several of these units are now in use; a pair, named Gemini, has been installed at the NYU Medical Center in Manhattan (see fig. 17) and is operated in a Vacuumschmelze shielded room. There the emphasis is in clinical studies, but the system was first used to investigate the alpha rhythm (Ilmoniemi et al. 1988). This is the first multichannel system allowing measurements over both hemispheres simultaneously; it is suitable for studies in which interhemispheric correlation or the transfer of signals is investigated. A novel feature of the system

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Fig. 17. The Gemini system of two seven-channel gradiometers (Biomagnetic Technologies, Inc.) in the magnetically shielded room of the New York University Medical Center. One transmitter coil of the probe position indicator system (see section 3.5.4) is seen on the subject’s head; the receiver coils are mounted on the dewars.

is an automated probe-positioning indicator (see section 3.5.4). As of December 1987, BTi had installed their 7-channel MEG system at 9 sites. A special version of this instrument with 2.7cm channel separation and flat-bottomed dewar was installed at the University of California in Los Angeles (Sutherling and Barth 1987). Another commercially available 7-channel second-order gradiometer is manufactured by Shimadzu Corporation3. This instrument has 25 mm diameter pickup coils at a mutual separation of 37.5 mm in a flat-bottomed dewar, connected to rf SQUIDS. The quoted noise level is less than 100 fT/&.

The seven-channel device in Helsinki A sensitive 7-channel first-order dc-SQUID gradiometer, covering a spherical cap area of 93 mm in diameter, was put into use at the Helsinki University of Technology in 1986, in collaboration with the IBM Corporation (Knuutila et al. 1987b). The experimental setup is shown in fig. 18.

’ Shimadzu Corp., Nakagyo-ku, Nishinokyo-Kuwabara-cho 1, Kyoto 604, Japan.

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Fig. 18. The magnetically shielded room of the Low Temperature Laboratory of the Helsinki University of Technology; the 7-channel first-order gradiometer (Knuutila et al. 1987b) is seen through the open door. The electronics of the magnetometer is on the left part of the top row on the instrument rack in the tf-shielded cabinet; most of the rack is occupied by a commercial 32-channel E E G amplifier.

The coils of the device (see fig. 19) are located at the vertices and slightly above the center of a regular hexagon, and the coil system is placed inside a dewar having a curved, tilted bottom4. The inner diameter of the tail section is 140 mm, and the radius of curvature of the spherical cap is 125 mm, with its symmetry axis slanted 30" from vertical; the isolation gap at the tip of the dewar, when cold, is less than 15 mm. The pickup-coil diameter is 20 mm, length 7 mm, and the number of turns is six; the compensation coils have 4 turns, a diameter of 24.5 mm, and a length of 15 mm. The baseline of the gradiometers is 60 mm. The design of this device aims at very high sensitivity and coverage of a large area. The instrument enables both quick, coarse mappings without The dewar was made by C T F Systems. Inc.. Port Coquitlam, British Columbia, Canada V3C I M9.

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Preamplifiers Top flange Thermal radiation shields Support tube Impedance matching transformers SQUIDS Dewar Gradiometer coils

Fig. 19. The Helsinki 7-channel gradiometer.

moving the dewar and more detailed field distribution measurements by recording successively at different dewar positions. The system was designed for use inside a magnetically shielded room (Kelha et al. 1982) so that first-order gradiometers without precise balancing can be used. The coil configuration in this instrument was selected on the basis of calculations discussed in section 3.5.1. The locating uncertainty decreases with increasing interchannel distance within the fixed inner space of the dewar; the pickup-coil dimensions were selected to give maximum sensitivity without significant deterioration of the spatial resolution due to the integrating effect. The d c SQUIDS in the 7-channel device were developed by the IBM mainly (Tesche et al. 1985). The sensitivity of each channel is 5 ff/&, limited by thermal noise from radiation shields in the dewar, and the l/f noise is very low with the comer point at a few tenths of hertz. The intrinsic noise of the complete magnetometer, measured inside a superconducting shield, is only 1-2ff/&, corresponding to a flux noise of 3-6x Having the SQUID noise clearly below dewar noise is advantageous: small excursions from the optimal operation point of the SQUID do not appreciably increase the noise level of the system. In the construction, particular care was exercised to eliminate excess noise from resonances in the flux transformers and to ensure insensitivity to rf fields (see section 2.2.2). Each flux transformer is shunted with a capacitor and a resistor to lower the Q-value of signal-coil resonances. All cables are carefully shielded and properly grounded to minimize interchan-

@,/a.

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nel interference. Since the channel separation in this instrument is relatively large, coupling between the channels via the pickup coils is only a negligible 0.7%. The electronics was made compact and modular to simplify its use in a multichannel instrument (see section 2.3). The preamplifiers, with optimum source impedances of a few kilo-ohms, are carefully matched to the dcSQUID impedances of only a few ohms. Besides impedance transformation, a reasonably high bandwidth is needed at the same time, suggesting the use of a cooled resonant transformer. The high sensitivity of the 7-channel instrument was necessary in a study of the middle-latency (about 30-60 ms after the stimulus onset) deflections in the auditory evoked response following short noise bursts (Pelizzone et al. 1987).These deflections are very weak, only 40-50 fT. The corresponding deflections have been studied electrically, but without certainty about the source location; both subcortical and cortical sources have been suggested. The successful field mapping suggested a source at supratemporal auditory cortex, slightly anterior to the source of the main auditory response at l00ms after the stimulus onset. A state-of-the-art display of auditory responses recorded with the 7-channel system is shown in fig. 20. Another example is given in fig. 21, where traces of alpha rhythm, recorded in real time with the Helsinki 7-channel instrument are shown. The traces were recorded over the occipital lobe with the subject having his eyes closed. Comparison of multichannel neuromagnetometers The key parameters of the multichannel magnetometers discussed above have been summarized in table 1. The noise levels reported in the table depend on the particular installation and on testing conditions and are not directly comparable. Besides these existing instruments, several other projects of constructing multichannel instruments based on wire-wound gradiometers with more than 10 channels have been started (Becker et al. 1987, Knuutila et al. 1985, 1987c; CTF, Inc.; BTi, Inc.). Vector magnetometers In addition to SQUID instruments for mapping one component of the field pattern, vector magnetometers have been introduced, the first of them by Shirae et al. (1981). In their device, three rf SQUIDS are connected to first-order gradiometer coils with a baseline of 11 cm. The sensors share a common tank circuit, an rf preamplifier and a detector, but use different audio modulation frequencies. The signals of the individual channels are then separated by phase-sensitive detection. This approach resulted, however, in a high noise level, 1 pT/(cm&). Later, frequency multiplexing was applied in a six-SQUID system (Furukawa et al. 1986) having a

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stimuli

- left eor _ _ _riaht ear

1st

2;

NlOOm

step 20 f T

NlOO m'

step 20 f T

Fig. 20. Responses evoked by left-ear (solid lines) and right-ear (dashed) sound stimuli as recorded with the Helsinki 7-channel SQUID magnetometer. The stimulus begins with bandlimited white noise (marked black on the time axis) and ends with a 250 Hz square wave (vertical-line shading). The passband is 0.05-45 Hz; 120 responses were averaged to get these traces. The locations of the seven first-order gradiometers are shown as circles on the head profile. On the right, magnetic field isocontour maps are shown for the deflections that occur approximately 100 ms after the beginning of the noise burst (N100m) and after the transition from noise to square wave (N100m'). The separation between the isocontour lines is 20 ff. These maps, although from the same subject, do not include data from traces shown on the left (Joutsiniemi 1988).

*L ~

-_

ptuVMflbpw~ -

Fig. 21. Alpha rhythm recorded with the Helsinki 7-channel magnetometer over the occipital lobe of a subject with his eyes closed; the bandwidth was 0.05-40 Hz.Note the polarity reversal between, for example, Channels 1 and 4 at the time instant marked with a vertical bar.

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Table 1 Comparison of multichannel magnetometers. llmoniemi Williamson et al. et al. (1984) (1985) Channels Pickup diam. [mm] Gradiometer order Baseline [mm] Channel sep. [mm] Noise [ I T l G ]

5

4 20/12",2Ih

15

1 60 16' 22d. 15'

2 40 20 20

Romani et al.

BTi Corp.

Shimadzu Cop.

(1985)

4 I5 2 53 21 50

Knuutila et al. (1987b)

7

I

I

15 2 40 20 20

25 2 35 37.5

20

(100

1 60 36.5 5

Axes of the elliptical lower coils. Diameter of the upper circular coil. ' Distance between the centers of the coils, located at the vertices of a regular tetrahedron. Lower coils. Upper coil.

second-order vector gradiometer plus a vector magnetometer for monitoring noise fields; the signals from these reference channels were used for electronic balancing. The vector gradiometer of Seppanen et al. (1983) had square coils with 27 mm side length and two turns separated by 15.6 mm in each; the baseline was 12 cm. The detection coils were connected to rf SQUIDs operated at 20-30 MHz; the resulting sensitivity was 28 fT/&. Time-division multiplexing of the SQUID readout is used in the vector gradiometer of Lekkala and Malmivuo (1984), which consists of three first-order asymmetric gradiometers with pickup-coil diameters of 28 mm and compensation coils of 48.5 mm diameter. The outputs of the rf SQUIDs are fed to separate preamplifiers, then multiplexed for the main amplifier using phase-sensitive detection. The output of the lock-in amplifier is then routed to sample-and-hold circuits and integrators, separate for each channel. There thus exist three separate parallel feedback loops. The noise level of the device, 85-105 fT/&, is 2.5 times that obtained in nonmultiplexed mode. Multiplexing of the SQUIDs is not recommended, because aliasing associated with the sampling of the different channels increases the noise level. Although the input signal to the magnetometer may be filtered to avoid aliasing, intrinsic SQUID noise and the wide-band noise in the preamplifier and in the tank circuit remain; their contributions to the noise at the output will increase at least by the square root of the number of multiplexed channels. In principle, multiplexing the detection coils would not increase the noise level, provided that the switching frequency would

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be high enough and the switching would not involve additional noise mechanisms. Multiplexing in multichannel dc-SQUID magnetometers has been proposed also by Shirae et al. (1988). In their scheme the SQUIDs are connected in series, and the sum voltage is read out using an extra dc-SQUID. Each channel is modulated with a different frequency, and the signals are separated by lock-in detection.

Multichannel susceptometers Measurements of the magnetic susceptibility of the human liver and of the remanent field of contaminated lungs have been carried out using singlechannel devices; the patient and the magnetometer are moved with respect to each other. At most 2-3 SQUIDs are used simultaneously, as in the susceptometer of Farrell et al. (1983), which had two second-order gradiometers, or in the forthcoming 3-SQUID liver measurement system made by Dornier Systems GmbH (Ludwig and Sawatzki 1986). 3.5.3. Planar gradiometer arrays At present, seven channels in a hexagonal array seems to be the de facto standard for MEG instrumentation; most of the devices are second-order gradiometers. The 7-channel instruments are only one step towards magnetometers with enough channels to cover the whole area of interest. Only then routine clinical studies become feasible. Several plans for devices having 20-30 or even 100 SQUIDs have been put forward. However, the construction of multiple-SQUID systems is not just multiplication of previous designs; many new problems are introduced (Knuutila et al. 1985). The use of 20-30 conventional, wire-wound axial gradiometers leads to a bulky, elaborate, and expensive construction. In addition, the conical space required by axial gradiometers aggravates space problems in dewar design. Axial gradiometers, measuring the radial component of the field, have been popular because .of the easy intuitive interpretation of the results. Since the baseline is usually longer than the distance to the source, the signal measured by the gradiometer is well approximated by the field at the pickup coil; the effect of the compensation coil is merely to cancel uniform fields. However, other components and derivatives of the magnetic field are, in principle, not more difficultto analyze and should thus not be rejected a priori. With magnetometers the construction would be simpler and there would be no problems in the interpretation of data; in practice, however, simple magnetometers are not feasible, even inside shielded rooms: mechanical vibrations of the dewar in the remanent magnetic field and nearby noise sources such as the heart may disturb the measurement.

3 20

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To avoid problems of wire-wound gradiometers, there has been growing interest in the use of planar integrated sensors (Knuutila et al. 1985, ErnC and Romani 1985, Carelli and Leoni 1986). The compact structure and excellent dimensional precision, allowing a good intrinsic balance, are the main advantages of thin-film gradiometers. The first integrated gradiometer was reported by Ketchen et al. (1978). In their design, the SQUID loop shares a common conductor with a larger field-collecting loop, thus forming an inductively shunted dc-SQUID structure as discussed in section 2.2.3. The flux coupling to the SQUID is poor, because of the mismatch between the pickup loop inductance and the inductance of the SQUID. For a pair of 24x 16 m m coils, connected in parallel, the gradient sensitivity was 20 fT/(cm&). Later, several other integrated first- and second-order gradiometers, with the pickup loop an integral part of the SQUID loop itself, were introduced (de Waal and Klapwijk 1982, van Nieuwenhuyzen and de Waal 1985, Carelli and Foglietti 1983b); their performance was similar to that reported by Ketchen et al. ( 1978). Integrated magnetometers have been discussed in several review articles (Donaldson et al. 1985, Ketchen 1985, 1987). The best results with integrated gradiometers have been achieved by connecting the pickup loop to the SQUID via a signal coil (see Jaycox and Ketchen 1981), which allows a good signal coupling and the necessary inductance matching (see also section 2.2.2). The first such fully-integrated magnetometer, built for geomagnetic applications, was reported by Wellstood et al. (1984); their device had a pickup-coil area of 47 mm’, a n a t h e sensitivity of this instrument was 5 fT/& above 10 Hz and 20 f T /JHz at 1 Hz. Quite recently, new devices based on the same signal coupling principle have been reported by groups working at Karlsruhe University (Drung et al. 1987), at the Electrotechnical Laboratory in Japan (Nakanishi et al. 1987), and at the Helsinki University of Technology (Knuutila et al. 1987~). The Karlsruhe device (see fig. 22) is a first-order gradiometer with coil areas of only 4 mm’ and a baseline of 3.7 mm; its gradient sensitivity is 3 8 f T / ( c m m ) . A 1-bit D/A converter is on the same chip for a digital feedback readout scheme (Drung 1986). The integrated magnetometer of ETL, s h E n in fig. 23, uses a square-loop area of 64 mm’; its sensitivity is 11 1T/JHz. A twelve-channel device, measuring all three field components at four different locations is currently under construction (M. Nakanishi, personal communication). The structure of the integrated sensor of the Helsinki group is shown schematically in fig. 24. It consists of two orthogonal off-diagonal gradiometers in a rectangular figure-8 configuration, measuring a B , / a x and aE,/ay. The pickup-coil size is 28x28mm2; the baseline is 14mm. The signals are coupled via intermediate transformers to two dc SQUIDS,located

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Fig. 22. The Karlsruhe integrated gradiometer (Drung et al. 1987).

Bonding

8 x 8 mm2

JJ

DC SOUID

Input coil

LOOP

Fig. 23. The integrated magnetometer of the Electrotechnical Laboratory in Japan (Nakanishi et al. 1987).

/

/ ,

/

/

\ \

\ \

Pickup coil

Prim. Intermediate transformer

Input coil

Fig. 24. Schematic structure of the integrated SQUID gradiometer of the Helsinki group (Knuutila et al. 1988). See text for details.

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on separate 6 x 9 mm2 chips. The three chips are mounted together on a fiber-glass holder to form a single two-channel module. The intermediate transformer allows a small SQUID with only a few signal coil turns on top of it; this results in a low intrinsic SQUID noise and reduced parasitic capacitances. Yet it is possible to match the small-inductance SQUID to a practical-sized coil; in addition, the control of resonances is easier (Knuutila et al. 1988). This separate-chip construction, with inductive coupling, allows flexibility for changing the pickup coil design, because it is not necessary to redesign the whole SQUID when the pickup coil is changed. The intermediate transformer and the SQUID have two oppositely wound coils to avoid spurious signals caused by homogeneous fields. The gradient sensitivity of this sensor, measured in a fiber-glass dewar, is about 4.5 fT/(cmJHz) at frequencies above 3 Hz. The sensor has been designed for use in a 32-channel device measuring the gradient of the radial field component at 16 locations (see fig. 25). Uncertainties in locating cortical current dipoles with off-diagonal gradiometers have been calculated for planar arrays (Ern6 and Romani 1985, Knuutila et al. 1985, Carelli and Leoni 1986). It was found that the locating accuracy of first-order planar gradiometers is essentially the same as that of axial first-order gradiometers; the higher-order gradiometers investigated in the first and last references were in some cases better than second-order axial gradiometers. The short baseline of off -diagonal sensors may make them better than conventional axial gradiometers for measurements in noisy environments. In addition, the spatial sensitivity pattern of off-diagonal gradiometers is narrower. These sensors thus collect the brain’s background activity from a restricted area near the sources of interest. The “field patterns” measured by off-diagonal gradiometers are morphologically different from those of axial gradiometers. For example, the 2-D gradiometer (Cohen 1979) gives the maximum response directly over the source, the direction of the current being perpendicular to the direction of the gradient. This is shown in fig. 26 for a current dipole.

Fig. 25. W e planned configuration of the 32-channel planar gradiometer at the Helsinki University of Technology. Each square module consists of two orthogonal off-diagonal gradiometers connected to planar SQUIDS (see fig. 24).

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I

I

-100

I

- 50

I 0

I

50

323

I 100

d (mm)

Fig. 26. The off-diagonal gradient a B z / a x of a 10 nAm tangential cerebral dipole as a function of position on a spherical surface of 125 mm radius. The distance from the gradiometer pickup coil to the scalp is 15 mm, and the dipole is 40 (solid line), 30 (dashed line), and 20 m m (dash-dotted line) below the scalp, respectively.

It is seen that the response is well localized, the 50% width of the peak being 35-55 mm for dipoles 20-40 mm below the scalp. The spatial frequencies at which the amplitudes of the spectral components have dropped under lo%, are 20 and 30 m-', respectively. Therefore the size of the sensors should be less than 30 mm and the grid spacing ideally no more than 30 mm. 3.5.4. Use of multichannel magnetometers

Calibration and Dewar position indication Shielding currents in superconducting flux transformers distort the magnetic field; an individual channel does not sense the original external field. If the inductances of flux transformers and their mutual inductances are known, a correction can be calculated easily.' Assume that there are n channels and that the mutual inductances are described by an n x n matrix M. Let further 9' = (@I . . . @k)T, where T means the transpose, be the net fluxes measured by the flux transformers and let @ be the undistorted applied flux. Then,

@=(z+ML-')9',

(3.5)

' Note that the effective inductance of a flux transformer coil is affected by feedback.

R. ILMONIEMI ET AL.

324

-

where L = diag( L , . . L , ) is a diagonal matrix containing the total inductances of the flux transformers and I is the identity matrix. In practice, one measures the output voltages V = (V, . . * Vn)T, which are related to @' via calibration coefficients K, . . K,. Since in MEG measurements the field distribution generally differs from that used in the calibration, the effects of coupling also differ. Consequently, the calibrations K, cannot be simply calculated from @,/ V,, where now the applied flux CP is calculated from the geometry of the experimental setup. Instead, the true calibration @:/ V, is obtained from eq. (3.5). Of the n( n - 1)/2 independent mutual inductances between n channels, often only the nearest neighbours need to be taken into account. Nevertheless, the situation becomes complicated if the mutual inductances cannot be measured directly. The best way is then to calibrate the device with a phantom whose field distribution resembles that generated by the brain, thus taking the interchannel interference corrections into account during the calibration of coefficients. An elegant alternative solution to these problems has been presented by ter Brake et al. (1986). In their method, flux feedback is applied to the flux transformer rather than to the SQUID. Now, the feedback keeps the transformer effectively currentless, thus eliminating cross talk between the detection coils. In locating cortical sources on the basis of externally measured magnetic fields, the accuracy with which the position of the magnetometer can be determined affects the results in an essential way. In single-channel measurements, the uncertainty in the location of the field point may be considered as a source of extra random noise. A Gaussian distributed positioning error, with a standard deviation of 5 mm, may cause an uncertainty of up to 20% in the magnitude of the measured field and, correspondingly, an error in the position of the current dipole as determined on the basis of the experimental field values (Romani et al. 1985). In multichannel devices this difficulty is, in principle, simpler to solve because the relative positions of the different channels are accurately known. However, the problem is fully resolved only when the device has enough channels to record the whole field pattern of interest at the same time; even then the position and orientation of the dewar with respect to some fixed points on the head must be known. Traditionally, the magnetometer has been positioned with some alignment marks on the dewar and on the subject's head. The shape of the skull may also be digitized to provide 3-D information. When the multichannel magnetometer covers an extended area, however, the dewar bottom is quite large and its accurate positioning becomes difficult. The accurate location and orientation of the dewar with respect to the head can be determined by measuring the magnetic field produced by

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current in small coils attached to the head (Knuutila et al. 1985, 1987b, Ern6 et al. 1987). This approach was taken with the seven-channel magnetometer in Helsinki with three small coils, mounted on a thin fiber-glass plate. The plate is attached to the subject's head at some point in the measurement area, the dewar is positioned, the coils are energized separately, and the resulting field is measured. The location and orientation of the magnetometer are found by a least-squares fit of magnetic dipoles to the test data; the dewar location can be determined with rms error of about 1 mm. The method provides direct information on the locations of the measuring sensors themselves and does not rely on knowing the relative position of the magnetometer with respect to the dewar. BTi uses three orthogonal coils in the receiver and in the transmitter, attached to the dewar and to a stretch band on the head, respectively. From the measured mutual inductances the position and the orientation of the magnetometer can be found. The locations of the head coils are first found by a reference measurement: the three-dimensional coordinates of landmarks on the head are determined by touching them with a pointer having a similar orthogonal-coil transmitter. The probe position. indicator system is shown in a measurement situation in fig. 17.

Correlated noise The background activity of the brain produces magnetic fields that are not relevant to the experiment; this so-called subject noise limits the signal-tonoise ratio in experiments made with the best SQUID magnetometers. In contrast to instrumental noise, the subject noise is correlated between the different channels; this correlation can be taken into account in the analysis to reduce the effects of subject noise. If the noise source is different from the signal source, the two can be separated in multichannel recordings. The spectral density of the subject noise is typically 20-40 fT/& below about 20 Hz,decreasing towards higher frequencies (Maniewski et al. 1985, Knuutila and Hamalainen 1988). An example of the field spectrum measured over the head for one subject is shown in fig. 27. The contribution of instrumental noise is negligible at low frequencies. Since the subject noise' is often not time-locked to the stimulus, its effect can be reduced by signal averaging. The normalized coherence functions show substantial correlation even in channels located 73 mm apart; the correlation extends up to 5060 Hz. The observed long-range correlation has important practical consequences for the analysis of evoked responses. Multiple, simultaneously measured data can be used to estimate the covariance matrix for the field errors at different sites. This matrix can then be used for advantage in the least-squares search of the equivalent current dipole (Sarvas 1987). Its effect is to reduce the variance of the maximum-likelihood estimate, which can be considered

R. ILMONIEMI ET AL.

3 26 80

@. t5

60

-

40

-

>

t

$ W

n

FREQUENCY (Hz)

FREQUENCY ( H Z )

Fig. 27. (a) Subject noise measured with the Helsinki 7-channel gradiometer. The upper trace was recorded over the left temporal lobe with the subject having his eyes open; the bottom trace shows the corresponding noise spectrum without a subject. (b) Coherence for channels 36.5 mm (solid line) and 73 mm (dashed line) apart, recorded at the left postero-temporal lobe, with the subject having his eyes open. The dash-dotted bottom curve shows the coherence without a subject (Knuutila and Hamalainen 1988).

as the change in the volume of the five-dimensional hyperellipsoid describing the confidence limits of the maximum-likelihood estimate. In the study of Knuutila and Hamalainen (1988), an example is calculated; it was shown that this reduction is significant, demonstrating the advantages of simultaneously measured multiple recordings in obtaining more accurate estimates for the source parameters. 4. Other multi-SQUID applications 4.1.

G EO MA G N ETI S M

In addition to biomagnetism, multiple-SQUID systems are used in geomagnetism. The main advantages of SQUID magnetometers are low noise even with compact detection coils, a large dynamic range, a wide frequency band that starts from dc, and selectivity to specific field or field gradient components, allowing vector measurements. However, the need of liquid helium may cause problems at remote observation sites that are often necessary in geomagnetic studies; large dewars are needed to allow long maintenancefree operation. Small, closed-cycle cryocoolers would be most welcome; they must be battery operated and must not cause magnetic or mechanical disturbances in the measuring system, which has to operate in the open without shielding. The sensitivity of SQUIDS to rf interference and mechanical vibrations complicates their field use. Besides, the high cost of

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adequate multi-SQUID systems is perhaps the main factor limiting their use in geological research and surveying. The SQUID sensors for geophysical applications must have a very large dynamic range. The signals of interest are often only small variations superposed on large field fluctuations not relevant to the particular event under study. The slew rate must be high, even in the frequency range of several tens of kHz, to ensure operation without losing the flux lock. In addition, since the signals of interest extend to very low frequencies, low l/f noise and stable operation, free from flux jumps and drifts, are required. A compact integrated magnetometer with a high slew rate, .intended specifically to geomagnetic studies, has been introduced by Wellstood et al. (1984). In geomagnetic studies, usually all three components of the magnetic field are measured, and thus three SQUIDs are required. Measurements of the magnetic field gradient tensor may also be performed to detect possible anomalies; a gradiometer gives a strong signal when the sensor is moved over the boundary of the anomalous region. In magnetotelluric studies, the magnetic field and the electric field on the ground, caused by incident electromagnetic waves, are measured simultaneously. These waves, typically from 0.1 mHz to 100 Hz, are generated by ionospheric and thunderstorm activity. From the measured electric and magnetic field components as functions of frequency, the impedance tensor Z ( w ) can be determined. The analysis must usually be restricted to simple models such as plane waves and one- or two-dimensional structure of the ground. Because of noise, the estimates of the impendance tensor are, however, unreliable. To overcome this problem, a second measurement is carried out simultaneously at a site several kilometers away and transmitted to the first site by radiotelemetry. Since the noise sources at the two sites are uncorrelated, an unbiased estimate is obtained (Gamble et al. 1979). Correlation techniques can also be applied to improve the estimates, when an artificial variable-frequency electromagnetic source is used in magnetotellurics (Wilt et al. 1983). In addition to the distant reference signal, a phase reference signal is transmitted to the measurement station for lock-in detection. In this case, the reference measurement site senses mainly naturally-occurring geomagnetic fluctuations, which in this controlled-source paradigm constitute noise; this background noise scales roughly as l/f below about 1 Hz, easily outweighing the signal. Measuring the remanent magnetization or magnetic susceptibility of rock samples was perhaps the first application of SQUIDs to geological studies. In paleomagnetism one investigates the history of the earth’s magnetic field; another important area of interest is the identification of magnetic phases in samples. In both cases, a dewar with room temperature access to the

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measurement volume is needed; the devices have a coil to generate a magnetizing field and pickup coils to measure the remanent field components in the axial and transverse directions. Use of SQUID magnetometers in geophysics has been reviewed in detail by Clarke (1983). Several applications have been proposed and some feasibility studies made, although no full-scale tests have been carried out. Yet, for example, stress changes in the ground prior to earthquakes give rise to observable changes in the local magnetic field. The changes of the field are due to the piezomagnetic effect when the domains are reoriented under pressure. I n an experimental feasibility study, the gradients due to seismic waves were found to be typically on the order of 1 pT/m and thus easily detectable with a SQUID (Czipott and Podney 1987). Such a system requires an array of vector magnetometers with telemetry and data acquisition and processing capabilities; the high cost, however, limits the popularity of the method. The measurement of the magnetic field vector could also be applied to locate artificially induced fractures in the ground. These are made by injecting high-pressure propellant into a borehole; such fractures enhance oil or gas flow to a collecting borehole in weakly permeable rock regions. Similarly, in geothermal power plants water is pumped into the ground and high-pressure steam is collected via another borehole. If a magnetic tracer fluid is injected in the fractures, the resulting magnetic anomaly can be detected on the ground with SQUID magnetometers. In addition to measurement of the earth's magnetic field, SQUIDs are used in gravimeters to detect gravitational anomalies (see section 4.2.1). Geomagnetic magnetometers have been made commercially by BTi, CTF, and Cryogenic Consultants, Ltd.6 4.2. PHYSICAL EXPERIMENTS

SQUIDs have many applications in metrology and in various physical experiments where high sensitivity is required. Many of these rather nonstandard applications have been reviewed in detail by Cabrera (1978) and Fairbank (1982), and more recently by Odehnal (1985). Usually such measurement setups contain only a single SQUID; since we are discussing systems with multiple SQUIDs, we consider only a few specific examples where simultaneous recordings are important. In these experimental systems multiple SQUIDs are used mainly to measure different components of the magnetic field. Normally, no mapping

'Cryogenic Consultants, Ltd., Metrostore Building, 23 1 T h e Vale, London W3 7QS.

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of the field pattern is necessary; in some cases a simultaneous reference reading outside the experimental cell is needed. In many of the physics applications, SQUIDs are used to detect very small changes, usually requiring ultra-low-noise sensors. 4.2.I . Accelerometers and displacement sensors

SQUIDs can also detect very small displacements and accelerations. Devices of this type are based on a superconducting proof mass, suspended by springs or by magnetic levitation to allow free movement with respect to a superconducting coil. The inductance of the coil becomes very sensitive to its distance from the proof mass; the measurement coil is connected to a second, auxiliary superconducting coil, and a circulating current is persisted in the circuit. Changes in the inductance are then sensed by measuring the flux changes in the auxiliary coil (see fig. 28). In practical devices, the test mass is usually a superconducting diaphragm, and the coils are flat, as in the original work of Paik (1976). The design may then include several proof masses and coil sets connected to different SQUIDs. This enables the simultaneous measurement of sum and difference phases, different gravitational gradient tensor components, angular accelerations etc. The devices can be applied for detecting anomalies and for measuring the gradient tensor to improve inertial navigation (see, for example, Paik et al. 1978, Colquhoun et al. 1985); sensitivities better than s-* HZ-’’~can be achieved. These instruments have been used for sensing the movements of gravitational wave antennae (see, for example, Kos et al. 1977; McAshan et al. 1981) and for measuring transmitter movements in Mossbauer spectroscopy with subatomic precision of the order of m/& (Ikonen et al. 1983). Besides this inductance-modulated technique, piezoelectric and capacitive sensing with SQUIDs as pre-

Proof mass

--

Detector coil

Auxiliary coil

Pickup

coil

I

Input

coil

Fig. 28. Schematic illustration of a superconducting accelerometer. A current I is persisted in the detector coil - auxiliary coil loop; changes of the detector coil inductance due to movement of the superconducting proof mass cause in the auxiliary coil a flux change, which is sensed by the SQUID.

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amplifiers have been used in gravitational wave antennae as well (Kos 1978, Cosmelli et al. 1987). 4.2.2. Monopole detectors

Superconducting detectors connected to SQUIDS have been applied in the search for magnetic monopoles predicted by grand unification theories. These particles are predicted to be very massive, too heavy to be produced at accelerators, and extremely penetrating. A magnetic monopole passing through a superconducting loop changes the flux threading the ring by 2Q0, providing a means of detection that is independent of the particle mass or velocity. These detectors should have as large an area as possible to enhance the probability for the passage of a monopole; then, however, the ambient field variations have to be carefully eliminated since an event in a detector, having an effective area of 1 m2 for example, would correspond to a 4fT field change. SQUID sensors with stable operation and freedom from flux trapping are thus required. So far, only one candidate event has been reported (Cabrera 1982). The apparatus consisted of a four-turn 5 cm diameter coil connected to an rf SQUID; it was surrounded by a 20cm diameter superconducting shield and a mu-metal cylinder, providing an ambient field as low as 5 pT and an 180 dB shielding factor for external magnetic fields. Ideally, a monopole traversing the four turns would give rise to a current of 8@,/L. in the loop for coupling to the SQUID, where L is the total inductance of the coil. However, a monopole traversing the superconducting shield will leave doubly quantized vortices at the intersections of its trajectory with the walls. This change in trapped flux reduces the observed signal; the reduction becomes a significant fraction of 2Q0 when the detector dimensions are close to those of the shield. In addition, the degree of degradation is dependent on the trajectory of the monopole, which creates a spread of magnitudes for possible signals instead of a single well-defined value. On the other hand, a small transient is found even from near-miss events. Later, the Stanford group reported a three-channel monopole detector having orthogonal coils with an area of 71 cm2 and a corresponding equivalent near-miss area of 476cm2 (Cabrera et al. 1983). Reliability in detection is based on a coincidence technique: a monopole passing through the detector should be seen in all loops. In a period of 150 days, however, no candidates for monopole events were found. The requirement of eliminating the effect of ambient magnetic field variations severely restricts the cross-sectional area of the sensor. However, the variations in the external field and the effects of the surrounding superconducting shield can be suppressed by twisting the coils to a

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0

1x1

33 1

2x2

h g . 29. Schematic illustration of the structure of two-dimensional planar gradiometers. The order of the gradiometer is given below the coils, and the clockwise and counterclockwise windings are indicated by pluses and minuses. The dashed lines show adjacent wires that can be left out.

gradiometric configuration. A monopole passing through only one of the loops still gives a full signal. Design of planar high-order gradiometers has been discussed by Tesche et al. (1983). Generally, an ( N + 1) x ( N+ 1) rectangular two-dimensional array is obtained by taking four N x N units with adjacent blocks oriented oppositely; a zeroth-order sensor is a simple loop (see fig. 29). An N x N array is insensitive to gradients of order P < 2N. In superconducting structures, adjacent loops having the same polarity may be joined. The construction may also be extended to polar and cylindrical geometries. Planar gradiometric sensors provide adequate rejection of external disturbance in ambient fields of the order of 1 FT (Tesche et al. 1983, Incandela et al. 1984). The latter device had two identical 60 cm diameter sensors. To be able to differentiate between real events and spurious signals even better, multiple planar detectors that cover the surface of a certain volume have been built. The six-channel device of IBM (Chi et al. 1984, Bermon et al. 1985) has independent fifth-order sensors on the sides of a 15 x 15 x 60 cm3 rectangular parallelepiped, providing a total area of 0.4 m2. A monopole passing through the volume causes signal in two and only two of the six coils; this kind of coincidence detection provides rejection also to events that might excite all of the detection coils in other geometries, as in the closely spaced set of parallel plates. Quite recently, a new dc SQUID detector of the same parallelepiped geometry of dimensions 26 x 26 x 380 cm3 and an effective area of 1 m2 (averaged over the solid angle 4 n ) has been reported (Bermon 1987); the Stanford group has constructed an octagonal-shaped detector with eight independent 17 x 521 cm2 gradiometer coils, having an effective area of 1.25m2, averaged over 4 n solid angle (Huber et al. 1987).

In addition, several anticoincidence detectors such as accelerometers, field sensors, cosmic ray detectors, power line analyzers, and rf monitors have been used. All the devices have been operated several hundreds of

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days; the null results imply an observed upper limit of 1.5 x lo-' m-* sr-2s-' (90% confidence level) for the magnetic monopole flux (Berrnon 1987). This is still three orders of magnitude higher than the theoretically predicted Parker bound (Turner et al. 1982). With the new superconductors operating at liquid nitrogen temperature it might be feasible to fabricate sensor arrays with a total area a few orders of magnitude larger than in the present devices; then the theoretical bound could be achieved during an operation of a couple of years. 5. Conclusions

Recent progress has made it posssible to build arrays of reliable, low-noise SQUIDs. First such systems, although with rather few channels, are already in use in neuromagnetism. It is expected that arrays with more than 20 channels will become available in the near future. In the state-of-the-art biomagnetic systems, SQUID noise is already negligible in comparison with noise from the dewar materials and from the subject itself. Therefore, there is no immediate need for further reduction of SQUID noise. However, reliability and insensitivity to rf interference will probably be improved as a result of further development. Also, the price of SQUIDs and the readout electronics is expected to drop significantly. The new high- T, superconductors offer some hope in eventually reducing the cost of operating SQUIDs, because liquid helium as a coolant could be replaced by liquid nitrogen. There are many problems on the way to practical high-T, SQUIDs, but one should keep in mind that up to 100 times inferior energy resolution than that in present state-of-the-art SQUIDs would be sufficient for neuromagnetometers. One reason for this is that the noise level in present SQUIDS is already significantly below that from other sources. In addition, the pickup coils in liquid nitrogen could be brought closer to the head, where the signals are stronger and the field profile carries more information about cerebral activity. Even if no high-7, SQUIDs will prove practical, detection coils made of these materials could be used to advantage. Simultaneously with improvements in instrumentation and as a result of it, the feasibility of using SQUIDs in fundamental brain research and in clinical applications has been demonstrated. Although the measurement of electric and magnetic fields are the only methods for non-invasive real-time monitoring of brain function, the eventual significance of neuromagnetism can only be speculated upon. MEG seems superior to EEG in that its interpretation is simpler and because the need of attaching electrodes to

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the scalp is avoided. However, because these two methods convey complementary information, they probably will often be used together. We live in a period of rapid change in the use of SQUIDS: the present 7-channel magnetometers will be replaced in a few years by systems with several dozens of SQUIDS. Faster data collection, provided by the possibility to record the whole field pattern at once, enables more complicated exoeriments and studies of patients, and improves the reliability of results. In addition to technical development of instruments, new ways of thinking are needed in the signal analysis and in the inverse problem studies to optimally utilize the measured signals. For the wide acceptance of the biomagnetic technique, it is crucial that clinically relevant results will be obtained. Acknowledgements

We thank Olli V. Lounasmaa for suggestions and criticism; Toivo Katila, for sharing his views on cardiomagnetism; Riitta Hari, Matti Hamalainen, Matti Kajola, and Jyrki Makela for reviewing the manuscript. Financial support of the Academy of Finland and of Telecommunications Laboratories of Posts and Telecommunications of Finland is acknowledged. References Ahola, H., G.J. Ehnholm, P. Ostman and B. Rantala. 1979, J. Low Temp. Phys. 35, 313. Atsumi, K., M. Kotani, S. Veno, T. Katila and S.J. Williamson, eds, 1988, Biomagnetism '87 (Tokyo Denki Univ. Press, Tokyo). Barone, A., and G. Paterno, 1982, Physics and Applications of the Josephson Effect (Wiley, New York). Barth, D.S., W. Sutherling, J. Engel Jr and J. Beatty, 1982, Science 218, 891. Becker, W., V. Diekmann, R. Kaufmann, H.H. Kornhuber and W. Ludwig, 1987, Dornier Post 1, 12. Ben-Jacob, E., and Y. Imry, 1981, J. Appl. Phys. 52,6806. Ben-Jacob, E., D.J. Bergman, Y. Imry,B.J. Matkowsky and Z. Schuss, 1983, J. Appl. Phys. 54, 6533. Ben-Jacob, E., D.J. Bergman. B.J. Matkowsky and Z. Schuss, 1985, in: SQUID '85, Superconducting Quantum Interference Devices and Their Applications, eds H.D. Hahlbohm and H. Liibbig (De Gruyter, Berlin) p. 219. Bermon, S., 1987, IEEE Trans. Magn. MAG-23, 441. Bermon, S., P. Chaudhari, C.C. Chi,C.D.TescheandC.C. Tsuei, 1985, Phys. Rev. Lett.55.1850. Brain, J.D., P. Gehr, P.A. Valberg, S.B. Bloom and I. Nemoto, 1985, in: Biomagnetism: Applications and Theory, eds H. Weinberg, G. Stroink and T. Katila (Pergamon Press, New York) p. 378. Bruines, J.J.P., V.J. de Waal and J.E. Mooij, 1982, J. Low Temp. Phys. 46,383.

334

R. ILMONlEMl ET AL.

Buchanan, US..D. Paulson and S.J. Williamson, 1988, in: Advances in Cryogenic Engineering, Vol. 33. ed. R.W. Fast (Plenum Press, New York) p. 97. Buhrman, R.. a n d L. Jackel, 1977, IEEE Trans. Magn. MAG-13, 879. Cabrera, B., 1978, in: Future Trends in Superconductive Electronics, eds B.S. Deaver Jr, C.M. Falco. J.H. Harris and S.A. Wolf (American Institute of Physics, New York) p. 73. Cabrera, B., 1982, Phys. Rev. Lett. 48, 1378. Cabrera. B., M. Taber. R. Gardner a n d J. Bourg. 1983. Phys. Rev. Lett. 51, 1933. Carelli, P., and V. Foglietti. 1982, J. Appl. Phys. 53, 7592. Carelli. P., and V. Foglietti, 1983a. IEEE Trans. Magn. MAG-19, 299. Carelli, P., and V. Foglietti, 1983b, J. Appl. Phys. 54, 6065. Carelli. P., and V. Foglietti, 1985, IEEE Trans. Magn. MAG-21, 424. Carelli, P., a n d R. Leoni, 1986. J. Appl. Phys. 59, 645. Carelli, P.. V. Foglietti, 1. Modena and G.L. Romani, 1983. Nuovo Cim. D 2, 538. Chapman, R.M.. G.L. Romani. S. Barbanera, R. Leoni, I. Modena, G.B. Ricci and F. Campitelli, 1983, Lett. Nuovo Cimento 38, 549. Chapman, R.M., R.J. Ilmoniemi, S. Barbanera and G.L. Romani, 1984, Electroencephalogr. Clin. Neurophysiol. 58, 569. Chi. C . C . , C.D. Tesche, C.C. Tsuei, P. Chaudhari and S. Rermon, 1984, in: Monopole 83. ed. J.L. Stone (Plenum Press, New York) p. 451. Clarke. J., 1966, Philos. Mag. 13, 115. Clarke. J., 1973. R o c . IEEE 61, 8. Clarke, J.. 1983, IEEE Trans. Magn. MAG-19, 288. Clarke. J., a n d T.A. Fulton. 1969, J. Appl. Phys. 40,4470. Clarke, J., W.M. Goubau a n d M.B. Ketchen, 1975a. IEEE Trans. Magn. MAG-11, 724. Clarke. J . , W.M. Goubau a n d M.B. Ketchen. 1975h. Appl. Phys. Lett. 27, 155. Clarke. J . , W.M. Goubau a n d M.B. Ketchen, 1976, J. Low Temp. Phys. 25, 99. Cohen. D.. 1968, Science 161, 784. Cohen. D.. 1970, Rev. Phys. Appl. 5, 53. Cohen, D., 1973. Science 180, 745. Cohen. D., 1979. in: Proc. 12th Int. Conf. on Medical and Biological Engineering, Jerusalem, p. 15. Cohen, D., 1983, in: Biomagnetism, An Interdisciplinary Approach, eds S.J. Williamson, G.L. Romani, L. Kaufman a n d 1. Modena (Plenum Press, New York) p. 327. Colquhoun. A.B., N.A. Lockerbie and G.B. Donaldson, 1985, in: S Q U I D '85. Superconducting Quantum Interference Devices and Their Applications, eds H.D. Hahlbohm a n d H. Liibbig ( D e Gruyter. Berlin) p. 1191. Cosmelli, C.. P. Carelli, M.G. Castellano a n d V. Foglietti, 1987, IEEE Trans. Magn. MAG-23, 454. Cuffin, R.N., and D.B. Geselowitz, 1977a. IEEE Trans. Biomed. Eng. BME-24,242. Cuffin, B.N., and D.B. Geselowitz, 1977b. Ann. Biomed. Eng. 5, 164. Curtis, S., L. Kaufman a n d S.J. Williamson, 1988, in: Biomagnetism '87. eds K. Atsumi, M. Kotani, S. Ueno, T. Katila and S.J. Williamson (Tokyo Denki Univ. Press, Tokyo) p. 138. Czipott. P.V., and W.N. Podney, 1987, IEEE Trans. Magn. MAG-23, 465. Danilov, V.V., K.K. Likharev, D . V . Sniguiriev and E.S. Soldatov. 1977, IEEE Trans. Magn. MAG-13. 240. d e Waal, V.J., and T.M. Klapwijk, 1982, Appl. Phys. Lett. 41, 669. de Waal. V.J., P. Schrijner and R. Llurba, 1984, J. Low Temp. Phys. 54, 215. Donaldson, G.B.. C.M. Pergrum a n d R.J.P. Bain, 1985, in: S Q U I D '85, Superconducting Quantum Interference Devices a n d Their Applications, eds H.D. Hahlbohm and H. Liibbig ( D e Gruyter, Berlin) p. 729.

MULTI-SQUID DEVICES

335

Drung, D., 1986, Cryogenics 26, 623. Drung, D., E. Crocoll, R. Henvig, A. Kniittel, M. Neuhaus and W. Jutzi, 1987, in: Extended Abstracts of the 1987 Int. Superconductivity Electronics Conf., ISEC '87 (Japan Society of Applied Physics, Tokyo) p. 21. Duret, D., and P. Karp, 1983, Nuovo Cim. D 2, 123. Duret, D., and P. Karp, 1984, J. Appl. Phys. 56, 1762. Ehnholm, G.J., 1977, J. Low Temp. Phys. 29, 1. Enpuku, K., and K. Yoshida, 1986. J. Appl. Phys. 59, 1714. Enpuku, K., K. Sueoka, K. Yoshida and F. hie, 1985a. 1. Appl. Phys. 57, 1691. Enpuku, K., T. Muta, K. Yoshida and F. h e , 1985b, J. Appl. Phys. 58, 1916. Enpuku, K., K. Yoshida and S. Kohjiro, 1986, J. Appl. Phys. 60, 4218. Erne, S.N., 1985, Med. & Biol. Eng. & Comput. 23, Suppl., 1447. Erne, S.N., and G.L. Romani, 1985, in: SQUID '85, Superconducting Quantum Interference Devices and Their Applications, eds H.D. Hahlbohm and H. Liibbig ( D e Gruyter, Berlin) p. 951. Erne, S.N., H.-D. Hahlbohm, H. Scheer and Z. Trontelj, 1981, in: Biomagnetism, eds S.N. Erne, H.-D. Hahlbohm and H. Liibbig (De Gruyter, Berlin) p. 79. Erne, S.N., L. Narici, V. Pizzella and G.L. Romani, 1987, IEEE Trans. Magn. MAG-23, 1319. Fairbank, W.M., 1982, Physica B 109&110, 1404. Farrell, D.E., 1983, in: Biomagnetism, An Interdisciplinary Approach, eds S.J. Williamson, G.L. Romani, L. Kaufman and I. Modena (Plenum Press, New York) p. 483. Farrell, D.E., and P. Zanzucchi, 1983, CRC Crit. Rev. Solid State & Mater. Sci 11, 99. Farrell, D.E., J.H. Tripp, G.M. Brittenham, E.H. Danish, J.W. Harris and A.E. Tracht, 1983, Nuovo Cim. D 2, 582. Fenici, R.R., M. Masselli, L. Lopez and F. Sabetta, 1985, New Trends in Arrhythmias 1, 455. Foglietti, V., W.J. Gallagher, M.B. Ketchen, A.W. Kleinsasser, R.H. Koch, S.I. Raider and R.L. Sandstrom, 1986, Appl. Phys. Lett. 49, 1393. Forgacs, R.L., and A. Wamick, 1967, Rev. Sci. Instrum. 38,214. Fraser-Smith, A.C., and J.L. Buxton, 1975, J. Geophys. Res. 80, 3141. Furukawa, H., M. Katayama, H. Emoto and K. Shirae, 1986, in: Proc. 6th Sensor Symp., ed. S. Kataoka (Institute of Electrical Engineers of Japan, Tsukuba) p. 319. Gamble, T.D., W.M. Goubau and J. Clarke, 1979, Geophysics 44, 959. Giffard, R.P., 1980, in: SQUID '80,Superconducting Quantum Interference Devices and Their Applications, eds H.D. Hahlbohm and H. Liibbig ( D e Gruyter, Berlin) p. 445. Giffard, R.P., R.A. Webb and J.C. Wheatley, 1972, J. Low Temp. Phys. 6, 533. Grimes, D., R. Lennard and S. Swithenby, 1983, Nuovo Cim. D 2, 650. Grynszpan, F., and D.B. Geselowitz, 1973, Biophys. J. 13, 911. Hamalainen, M.S., and J. Sarvas. 1987, IEEE Trans. Biomed. Eng. BME-36, in press. Himalainen, M.S., H. Haario and M.S. Lehtinen, 1987, Inferences about Sources of Neuromagnetic Fields using Bayesian Parameter Estimation, Report No. TKK-F-A620 (Helsinki University of Technology, Otaniemi). Hari, R., 1989, Adv. Audiol. 6 (in press). Hari, R., and R.J. Ilmoniemi, 1986, CRC Crit. Rev. Biomed. Eng. 14, 93. Hari, R., and E. Kaukoranta, 1985, Prog. Neurobiol. 24, 233. Hari, R., M. Peliuone, J.P. Makela, J. Hallstrom, L. Leinonen and O.V. Lounasmaa, 1987, Audiology 26, 3 1. Hari, R., S.-L. Joutsiniemi and J. Sarvas, 1988, Electroencephalogr. & Clin. Neurophysiol. 71. 64.

Hollenhorst, J.N., and R.P. Giffard, 1979, IEEE Trans. Magn. MAG-IS, 474. Horacek, B.M., 1973, IEEE Trans. Magn. MAG-9, 440.

3 36

R. I L M O N l E M l E T AL.

Huber, M.E.,B. Cabrera, M. Tdber and R.D. Gardner, 1987, in: Proc. 18th Int. Low Temp. Phys. Conf. LT-18, Japan, ed. Y. Nagaoka. J. Appl. Phys. 26, Suppl. 26-3, 1687. Huttunen, J., R. Hari and L. Leinonen. 1987, Electroencephalogr. &Clin. Neurophysiol. 66.391. Ikonen, E., P. Karp. T. Katila and K. Riski, 1983, J. Phys. E 16, 875. Ilmoniemi. R.J.. and J. Knuutila, 1984. in: Proc. 10th Int. Cryogenic Engineering Conf. ICEClO, eds H. Collan, P. Berglund and M. Krusius (Butterworths, London) p. 457. Ilmoniemi. R.J., R. Hari and K. Reinikainen, 1984, Electroencephalogr. & Clin. Neurophysiol. 58.467. Ilmoniemi. R.J.. M.S. Hamalainen a n d J. Knuutila, 1985, in: Biomagnetism: Applications and Theory, eds t i . Weinberg, G. Stroink and T. Katila (Pergamon Press, New York) p. 278. Ilmoniemi, R.J., S.J. Williamson a n d W. Hostetler, 1988, in: Biomagnetism '87. eds K. Atsumi, M. Kotani, S. Ueno,T. Katila and S.J. Williamson (Tokyo Denki Univ. Press, Tokyo) p. 182. Imry, Y., and P.M. Marcus, 1977, IEEE Trans. M a p . MAG-13, 868. Incandela, J., M. Campbell, H. Frisch, S. Somalwar, M. Kuchnir and H.R. Gustafson, 1984, Phys. Rev. Lett. 53, 2067. Jackel, L.. and R. Buhrman, 1975, J. Low Temp. Phys. 19, 201. Jaklevic, R.C., J . Lambe, A.H. Silver and J.E. Mercereau, 1964, Phys. Rev. Lett. 12, 159. Jaklevic. R.C., J. Lambe, J.E. Mercereau and A.H. Silver, 1965, Phys. Rev. A 140, 1628. Jaycox, J.M., and M.B. Ketchen, 1981, IEEE Trans. Magn. MAG-17, 400. Joutsinierni, S.-L., 1988, Acta Neurol. Scand. 78, 337. Kalliomaki, K., P.-L. Kalliomaki, K. Aittoniemi and M. Moilanen, 1983, in: Biomagnetism, An Interdisciplinary Approach, eds S.J. Williamson, G.L. Romani, L. Kaufman and I. Modena (Plenum Press, New York) p. 545. Kalliomaki, P.-L., K. Aittoniemi and K. Kalliomaki, 1983, in: Biomagnetism, An Interdisciplinary Approach, eds S.J. Williamson, G.L. Romani, L. Kaufman and I. Modena (Plenum Press, New York) p. 559. Kamper, R.A., a n d M.B. Simmonds, 1972. Appl. Phys. Lett. 20, 270. Kanter, H., a n d F.L. Vernon Jr, 1977, IEEE Trans. Magn. MAG-13, 389. Karp. P., 1981, in: Biomagnetism, eds S.N. E m i , H.-D. Hahlbohm a n d H. Liibbig ( D e Gruyter, Berlin) p. 219. Katila, T.. R. Maniewski, M. Mikijarvi, J. Nenonen and P. Siltanen, 1987, Phys. Med. & Biol. 32, 125. Katila, T., J. Montonen, M. Makijarvi, J. Nenonen. M. Raivio a n d P. Siltanen, 1988, in: Biomagnetism '87. eds K. Atsumi, M. Kotani, S. Ueno, T. Katila and S.J. Williamson (Tokyo Denki Univ. Press, Tokyo) p. 274. Kaufman. L.. a n d S.J. Williamson, 1987, in: Evoked Potentials 111, eds C. Barber and T. Blum (Butterworths, Boston) p. 100. Kaukoranta. E., M.S. Hamalainen, J. Sarvas and R. Hari, 1986, Exp. Brain Res. 63, 60. Kaukoranta, E., R. Hari and O.V. Lounasmaa, 1987, Exp. Brain Res. 69, 19. Kelhi, V.O., J.M. Pukki. R.S. Peltonen, A.A. Penttinen, R.J. llmoniemi and J.J. Heino, 1982, IEEE Trans. Magn. MAG-18, 260. Kennedy, J.G., D. Cohen, B.N. Cuffin, D.L. Schomer, R.J. Gumnit and C.T. Lombroso, 1988, in: Biomagnetism '87, eds K. Atsumi, M. Kotani, S. Ueno, T. Katila and S J . Williamson (Tokyo Denki Univ. Press, Tokyo) p. 214. Ketchen. M.B., 1981, IEEE Trans. Magn. MAG-17, 387. Ketchen, M.B.. 1985, J. Appl. Phys. 58, 4322. Ketchen, M.B.. 1987, IEEE Trans. M a p . MAG-23, 1650. Ketchen, M.B.. W.M. Goubau, J. Clarke and G.B. Donaldson, 1978, J. Appl. Phys. 49. 41 1 1 . Ketoja, J.A., J. Kurkijarvi a n d R.K. Ritala, 1984a. Phys. Lett. A 105. 425. Ketoja. J.A., J. Kurkijarvi and R.K. Ritala, 1984b, Phys. Rev. B 30,3757.

MULTI-SQUID DEVICES

337

Ketoja, J.A., J. Kurkijarvi, T. Ryhanen and H. Seppa, 1987, Phys. Rev, B 35. 404. Kirschvink, J.L., 1983, in: Biomagnetism, An Interdisciplinary Approach, eds S.J. Williamson, G.L. Romani, L. Kaufman and I. Modena (Plenum Press, New York) p. 501. Knuutila, J., and M.S. Hamalainen, 1988, in: Biomagnetism '87, eds K. Atsumi, M. Kotani, S. Ueno, T. Katila and S.J. Williamson (Tokyo Denki Univ. Press, Tokyo) p. 186. Knuutila, J., A.I. Ahonen, M.S. Hamalainen, R.J. llmoniemi and M.J. Kajola, 1985. in: SQUID '85. Superconducting Quantum Interference Devices and Their Applications, eds H.D. Hahlbohm and H. Lubbig (De Gruyter, Berlin) p. 939. Knuutila, J., A.I. Ahonen and C. Tesche, 1987a. J. Low Temp. Phys. 68, 269. Knuutila, J., S. Ahlfors, A.I. Ahonen, J. Hallstrom, M.J. Kajola, O.V. Lounasmaa, V. Vilkman and C. Tesche, 1987b. Rev. Sci. Instrum. 58, 2145. Knuutila, J., M.J. Kajola, R. Mutikainen and J. Salmi, 1 9 8 7 ~ .in: Extended Abstr. 1987 Int. Superconductivity Electronics Conf.. ISEC '87 (Japan Society of Applied Physics, Tokyo) p. 261. Knuutila, J., M.J. Kajola, H. Seppa, R. Mutikainen and J. Salmi, 1988, J. Low Temp. Phys. 71, 369.

Koch, H., 1985, in: SQUID '85, Superconducting Quantum Interference Devices and Their Applications, eds H.D. Hahlbohm and H. Lubbig (De Gruyter, Berlin) p. 773. Kos, J.F., 1978. J. Appl. Phys. 49,955. Kos. J.F., R. Barton and B. Ramadan, 1977, J. Appl. Phys. 48, 3193. Kulik. 1.0..1967, Zh. Eksp. & Teor. Fiz. 37, 157. Kurkijarvi, J., 1972, Phys. Rev. B 6, 832. Kurkijarvi, J., 1985, in: SQUID '85, Superconducting Quantum Interference Devices and Their Applications, eds H.D. Hahlbohm and H. Lubbig (De Gruyter, Berlin) p. 377. Kurkijarvi, J., and W.W. Webb, 1972, in: Roc. 1972 Applied Superconductivity Conf. (IEEE, New York) p. 581. Kuzmin, L.S., K.K. Likharev, V.V. Migulin, E.A. Polunin and N.A. Simonov. 1985, in: SQUID '85, Superconducting Quantum Interference Devices and Their Applications, eds H.D. Hahlbohm and H. Liibbig (De Gruyter, Berlin) p. 1029. Lekkala, J.O., and J. Malmivuo. 1984, J. Phys. E 17, 504. Likharev, K.K., 1986, Dynamics of Josephson Junctions and Circuits (Gordon and Breach, New York). Long, A., T.D. Clark, R.J. Prance and M.G. Richards, 1979, Rev. Sci. Instrum. 50, 1376. Lounasmaa, O.V., 1974, Experimental Principles and Methods Below 1 K (Academic Press, New York). Ludwig, W., and G . Sawatzki, 1986, Dornier Post 1, 22. MacAulay, C.E., G. Stroink and B.M. Horacek, 1985, in: Biomagnetism: Applications and Theory, eds H. Weinberg, G. Stroink and T. Katila (Pergamon Press, New York) p. 115. Mager, A,, 1981, in: Biomagnetism. eds S.N. Erne, H.-D. Hahlbohm and H. Lubbig (De Gruyter, Berlin) p. 51. Makela, J.P., and R. Hari, 1987, Electroencephalogr. & Clin. Neurophysiol. 66. 539. Malmivuo, J., P. Heinonen, M. Tuomola and J. Lekkala, 1981, in: Biomagnetism, eds S.N. Erne, H.-D. Hahlbohm and H. Lubbig (De Gruyter, Berlin) p. 107. Maniewski, R., 1. Derka, T. Katila, T.Ryhanen and M. Seppanen, 1985, Med. & Biol. Eng. & Comput. 23, Suppl., 9. McAshan, M.S., W.M. Fairbank, P.F. Michelson and R.C. Taber, 1981, Physica B 107, 23. Mercereau, J.E., 1970, Rev. Phys. Appl. 5, 13. Miller 111, W.T., and D.B. Geselowitz, 1978, Circ. Res. 43, 301. Modena, I., G.B. Ricci, S. Barbanera, R. Leoni, G.L. Romani and P. Carelli. 1982, Eledroencephalogr. & Clin. Neurophysiol. 54, 622.

R. ILMONIEMI ET AL.

338

Montonen. J., T. Katila, M. Leinio, S. Madekivi, M. Makijarvi, 1. Nenonen and P. Siltanen, 1988, in: Biomagnetisrn '87, eds K. Atsurni, M. Kotani, S. Ueno, T. Katila and S.J. Williamson (Tokyo Denki Univ. Press, Tokyo) p. 278. Muhlfelder. B., W. Johnson a n d M.W. Cromar, 1983, IEEE Trans. Magn. MAG-19, 303. Muhlfelder. B., J.A. Beall, M.W. Cromar, R.H. Ono and W.W. Johnson, 1985, IEEE Trans. Magn. MAG-21, 427. Nakanishi. M., M. Koyanagi, S. Kosaka, A. Shoji, M. Aoyagi, F. Shinoki, H. Nakagawa, S. Takada, N. Kasai, H. Kado and T. Endo, 1987. in: Extended Abstr. 1987 Int. Superconductivity Electronics Conf., ISEC '87 (Japan Society of Applied Physics, Tokyo) p. 265. Nicolas, P., D. Duret, D. Teszner and T. Tuomisto, 1983, Nuovo Cim. D 2, 184. Nisenoff. M., 1970, Rev. Phys. Appl. 5, 21. Odehnal, M., 1985, Sov. J. Low Temp. Phys. 11. 1. Paik, H.J., 1976, J. Appl. Phys. 47, 1168. Paik, H.J., E.R. Mapoles and K.Y. Wang, 1978. in: Future Trends in Superconductive Electronics, eds B.S. Deaver Jr, C.M. Falco, J.H. Harris and S.A. Wolf (American Institute of Physics, New York) p. 166. Paik, H.J., R.H. Mathews and M.G. Castellano, 1981, IEEE Trans. Magn. MAG-17, 404. Pelizzone, M.. S.J. Williamson and L. Kaufman, 1985, in: Biornagnetism: Applications and Theory, eds H. Weinberg, G. Stroink and T. Katila (Pergamon Press, New York) p. 326. Pelizzone, M., R. Hari, J.P. Makela. J. Huttunen, S. Ahlfors and M.S. Hamalainen, 1987, Neurosci. Lett. 82. 303. Ribary, U., H. Weinberg, P. Brickett, R.J. Ancill, S. Holiday, J.S. Kennedy and B. Johnson, 1987, SOC.Neurosci. Abstr. 13, Part 2, 1268. Romani, G.L., and R. Leoni, 1985, in: Biornagnetisrn: Applications and Theory, eds H. Weinberg. G. Stroink and T. Katila (Pergarnon Press, New York) p. 205. Romani, G.L., and L. Narici, 1986, in: Medical Progress through Technology (Nijhoff, Boston) p. 123. Rornani, G.L., and S.J. Williamson, eds, 1983, Proc. 4th Int. Workshop on Biomagnetism, Nuovo Cim. D 2, 121-664. Romani, G.L.. S.J. Williamson and L. Kaufrnan, 1982, Rev. Sci. Instrum. 53, 1815. Rornani, G.L., R. Leoni and C. Salustri, 1985, in: S Q U I D '85, Superconducting Quantum Interference Devices and Their Applications, eds H.-D. Hahlbohm and H. Liibbig (De Gruyter, Berlin) p. 919. Ryhanen, T., H. Seppa, R.J. llrnonierni and J. Knuutila, 1989, J. Low Temp. Phys. 76(5/6), in press. Sarns, M., M.S. Hamilainen, A. Antervo. E. Kaukoranta, K. Reinikainen and R. Hari, 1985, Elenroencephalogr. & Clin. Neurophysiol. 61, 254. Sarvas, J., 1987, Phys. Med. & Biol. 32, 11. Seppa, H., 1983, IEEE Trans. Instrum. & Meas. 32, 253. Seppi, H., and T. Ryhanen, 1987, IEEE Trans. Magn. MAG-23, 1083. Seppanen, M., T. Katila, T. Tuomisto, T. Varpula. D. Duret and P. Karp, 1983, Nuovo Cim. D 2, 166. Shirae, K., H. Furukawa a n d K. Kishida, 1981, Cryogenics 21, 707. Shirae, K., H. Furukawa, M. Katayama and T. Katayarna, 1988, in: Biomagnetisrn '87, eds K. Atsumi, M. Kotani, S. Ueno. T. Katila and S.J. Williamson (Tokyo Denki Univ. Press, Tokyo) p. 470. Silver, A.H., and J.E. Zimmerrnan, 1967, Phys. Rev. 157, 317. Simrnonds, M.B., and W.H. Parker, 1971, J. Appl. Phys. 42, 38. Sinton, C.M., J.R. McCullough, R.J. Ilrnoniemi and P.E. Etienne, 1986, Neuropsychobiology 16. 215.

MULTI-SQUID I>EVICES

339

Stroink, G., B. Brown, B. Blackford and B.M. Horacek, 1981, in: Biomagnetism, eds S.N. Emt, H.D. Hahlbohm and H. Liibbig (De Gruyter, Berlin) p. 113. Sutherling, W., and D.S. Barth, 1987, in: Abstracts of the 6th Int. Conf. on Biomagnetism, Tokyo, August 27-30, 1987, p. 102. ter Brake, H.J.M., F.H. Fleuren, J.A. Ulfman and J. Flokstra. 1986, Cryogenics 26, 667. Tesche, C.D., 1982, J. Low Temp. Phys. 47, 385. Tesche, C.D., and J. Clarke, 1977, J. Low Temp. Phys. 29, 301. Tesche, C.D., C.C. Chi, C.C. Tsuei and P. Chaudhari, 1983, Appl. Phys. Lett. 43, 384. Tesche,C.D., K.H. Brown, A.C. Callegari, M.M.Chen, J.H.Greiner, H.C. Jones, M.B. Ketchen, K.K. Kim, A.W. Kleinsasser, H.A. Notarys, G. Proto, R.H. Wang and T. Yogi, 1985, IEEE Trans. Magn. MAG-21, 1032. Tinkham, M., 1975, Introduction to Superconductivity (McGraw-Hill, New York). Turner, M.S., E.N. Parker and T.J. Bogdan, 1982, Phys. Rev. D 26, 1296. van Duzer, T., and C.W. Turner, 1981, Principles of Superconductive Devices and Circuits (Elsevier, New York). van Nieuwenhuyzen, G.J., and V.J. de Waal, 1985, Appl. Phys. Lett. 46,439. Varpula, T., and T. Poutanen, 1984, J. Appl. Phys. 55, 4015. Vendik, O.G., Yu.N. Gorin and M.G. Stepanova, 1983, Pis'ma v Zh. Tekh. Fiz. (Sov. Tech. Phys.) 9, 1007. Vrba, J., A.A. Fife, M.B. Burbank, H. Weinberg and P. Brickett, 1982, Can. J. Phys. 60, 1060. Vvedensky, V.L., R.J. llmoniemi and M.J. Kajola, 1985a. Med. & Biol. Eng. & Comput. 23, Suppl., 1 I . Vvedensky. V.L., S.P. Naurzakov, V.I. Ozhogin and S.Yu. Shabanov, 1985b. in: Biomagnetism: Applications and Theory, eds H. Weinberg, G. Stroink and T. Katila (Pergamon Press, New York) p. 57. Weinberg, H., G. Stroink and T. Katila, eds, 1985, Biomagnetism: Applications and, Theory (Pergamon Press, New York). Wellstood, F., C. Heiden and J. Clarke, 1984, Rev. Sci. Instrum. 55, 952. Williamson, S.J., and L. Kaufman, 1987, in: Handbook of Electroencephalography and Clinical Neurophysiology, eds AS. Gevins and A. RCmond (Elsevier, Amsterdam) p. 405. Williamson, S.J.. M. Pelizzone, Y. Okada, L. Kaufman, D.B. Crum and J.R. Marsden, 1985. in: Biomagnetism: Applications and Theory, eds H. Weinberg, G. Stroink and T. Katila (Pergamon Press, New York) p. 46. Wilt, M., N.E. Goldstein, M. Stark, J.R. Haught and H.F. Morrison, 1983, Geophysin48,1090. Zimmerman, J.E., 1971, J. Appl. Phys. 42.4483. Zimmerman, J.E., 1977, J. Appl. Phys. 48,702. Zimmerman, J.E., P. Thiene and T. Harding, 1970, J. Appl. Phys. 41, 1572.