Digital eddy current compensation

Eddy current compensation for magnetic field transients arising from electric current transients is obtained by digital computation of the time dependence of the eddy current magnetic effect, reversing the sense thereof to obtain a corrective signal portion, converting both the corrective portion and the basic signal profile to analogue form, summing same and directing the pre-compensated electric current through an inductive element.

FIELD OF THE INVENTION 
The invention is in the field of nuclear magnetic resonance (NMR) 
instrumentation and pertains particularly to the reduction of disturbance 
in data arising from transient currents proximate the sensitive volume of 
an NMR instrument. 
BACKGROUND OF THE INVENTION 
Nuclear magnetic resonance measurement techniques require knowledge and 
control of the spatial and temporal properties of magnetic fields in and 
proximate to the sensitive volume of the instrument. Most modern NMR 
instruments employ transient techniques. When the magnetic field itself 
exhibits transient characteristics there are accompanying parasitic 
consequences of eddy current excitation in conducting structures of the 
apparatus. The eddy currents contribute an increment to the field directed 
in opposition to the transient, with time constants which depend upon the 
structure supporting the eddy current. 
In the prior art it is well known to provide a delay time after a transient 
or to so control the time dependence of the transient as to reduce or 
minimize the effect of the ensuing eddy current. This is of rather limited 
application given other requirements for time dependence and inter-pulse 
delays. It is also known in the prior art to provide for magnetic 
shielding to reduce the coupling of the magnetic field arising from the 
transient current to the surrounding structures wherein the eddy currents 
are induced. Shielding is is no more than partially effective, at best. 
It is also known to compensate the effect of eddy currents by 
pre-compensation, that is, a deliberate distortion of the time dependence 
of the applied transient so as to yield the desired time dependence for 
the resulting field. The prior art is fairly reviewed and summarized by 
Jehenson, et al, J. Mag. Res. V.90, pp. 264-278 (1990); van Vaals, et al, 
J. Mag. Res., vol. 90, pp 52-70 (1990); Morich, et al, IEEE Trans. Mag. 
Imag., vol. 7, pp. 247-254 (1988). 
The desired pulse shape for a field B in the direction p may be designated 
B.sub..rho. (t) and would ideally be supplied by a voltage waveform V(t) 
applied to coils of the appropriate orientation. We shall refer to V(t) as 
the "demand" pulse. In the real world, surrounding conducting structures 
such as nested cryostat shields, reservoir and containment vessel, probe 
shields and the like will have eddy currents induced thereon. These eddy 
currents generate magnetic field elements which are generally opposed to 
the field ideally associated with the demand pulse, as well as elements 
having diverse orientations. The time dependence of the realized pulse 
B.sub..rho. (t) is distorted relative to the time dependence of the demand 
pulse due to the superposition of the time constants for decay of the eddy 
currents on the various conducting structures. Moreover, as a consequence 
of eddy currents circulating on non-planar conductors, there will be eddy 
current induced transient field components directed along axes other than 
.rho.. 
More than one magnetic field component can be combined as a superposition 
to create spatial variations (gradients) in the resulting field. 
Excitation of a field element along .rho. may produce a desired gradient 
along p or a gradient along some other axis. There exists many 
combinations of desired gradient direction and field direction, and for 
each combination, there is potential for undesired eddy current 
distortion. 
SUMMARY OF THE INVENTION 
It is an object of the invention to produce a controlled transient magnetic 
field with reduced magnetic disturbances attributable to eddy current 
phenomena. 
The object is achieved by pre-compensation of the current pulse to magnetic 
field coils where the pre-compensation is computed from the details of the 
current pulse and the particular design parameters of proximate conducting 
structures.

DETAILED DESCRIPTION OF THE INVENTION 
A specific context for the invention is shown in FIG. 1 which illustrates 
schematically, an NMR apparatus wherein the desired magnetic field at 
points of interest is disturbed by eddy currents on surrounding structure 
induced by current transients. 
A magnet 10 having bore 11 provides a main magnetic field. In order to 
control the magnetic field with precision in time and direction, there are 
provided magnetic field gradient coils (not shown) disposed very close to 
the bore 11. These are driven by gradient power supplies 16, 18 and 20, 
respectively. Additionally, other shimming coils (not shown) and power 
supplies (not shown) may be required for compensating residual undesired 
spatial inhomogeneities in the basic magnetic field. An object for 
analysis (hereafter "sample") is placed within the magnetic field in bore 
11 and the sample is subject to irradiation by rf power, such that the rf 
magnetic field is aligned in a desired orthogonal relationship with the 
magnetic field in the interior of bore 11. This is accomplished through a 
transmitter coil 12 in the interior of bore 11. Resonant signals are 
induced in a receiver coil, proximate the sample within bore 11. The 
transmitter and receiver coils may be the identical structure, or separate 
structures. 
As shown in FIG. 1, rf power is provided from transmitter 24, which may be 
modulated in amplitude or frequency or phase or combination thereof, 
either upon generation or by modulator 26, is amplified by amplifier 31 
and thence directed via multiplexer 27 to the rf transmitter coil 12 
located within bore 11. Transmitter and receiver coils are usually not 
concurrently used as such. The identical coil may be employed for both 
functions if so desired. Thus, a multiplexer 27 is provided to isolate the 
receiver from the transmitter. In the case of separate transmitter and 
receiver coils, element 27, while not precisely a multiplexer, will 
perform a similar isolation function to control receiver operation. 
The modulator 26 is controlled by pulse programmer 29 to provide rf pulses 
of desired amplitude, duration and phase relative to the rf carrier at 
preselected time intervals. The pulse programmer may have hardware and/or 
software attributes. The pulse programmer also controls the gradient power 
supplies 16, 18 and 20, for respective Y, Z and X axes if such gradients 
are required. These gradient power supplies may maintain selected static 
gradients in the respective gradient coils if so desired. 
The transient nuclear resonance waveform is processed by receiver 28 and 
further resolved in phase quadrature through phase detector 30. The phase 
resolved time domain signals from phase detector 30 are presented to 
Fourier transformer 32 for transformation to the frequency domain in 
accordance with specific requirements of the processing. Conversion of the 
analog resonance signal to digital form is commonly carried out on the 
phase resolved signals through analog to digital converter (ADC) 
structures which may be regarded as a component of phase detector 30 for 
convenience. 
It is understood that Fourier transformer 32 may, in practice, act upon a 
stored (in storage unit 34) representation of the phase resolved data. 
This reflects the common practice of averaging a number of time domain 
phase resolved waveforms to enhance the signal-to-noise ratio. The 
transformation function is then applied to the resultant averaged 
waveform. Display device 36 operates on the acquired data to present same 
for inspection. Controller 38, most often comprising one or more 
computers, controls and correlates the operation of the entire apparatus. 
The magnet 10 is ordinarily a superconducting magnet housed within a 
cryostat which includes a number of nested structures having generally 
cylindrical symmetry about the axis of said bore 11. The pulsed excitation 
of gradient coils by respective gradient supplies 16,18 and/or 20 induces 
eddy currents on these structures including the outer housing. The 
transient circulating eddy currents in turn furnish transient magnetic 
field components which produce unwanted perturbations to the desired 
magnetic field distribution. 
It is often the case in modern usage that the signal of selected shape is 
prescribed digitally and formed by passing the digital representation 
through a digital-to-analog converter (DAC). Having the digital 
representation available, straightforward digital operations may be 
employed to obtain the distortion that such signal would be expected to 
generate. For the case of an eddy current contribution following from an 
ideal step function current pulse, the magnetic field resulting from the 
current pulse is smeared into an exponential decaying pulse of time 
constant .tau.. 
A preferred embodiment of the invention is shown in FIG. 2. The discussion 
is in terms of a step function current pulse pre-compensated to yield a 
magnetic field step function pulse of desired shape taking account of 
distortion arising from eddy currents induced in surrounding structure. 
The generality of the invention in respect of other diverse applications 
is not to be regarded as limited to this context. A desired transient 
profile is presented in digital form to a digital to analog converter 102 
and simultaneously to a digital signal processor (DSP) or equivalent 
computational apparatus 104 of known digital structure to compute the 
distortion which is expected to arise for the resulting phenomena. The 
output of DSP 104 is presented to another DAC 106. The output of DAC 106 
is combined with the output of DAC 102 and the result is directed through 
amplifier 110 for excitation of the desired pre-compensated pulse. For the 
case where a magnetic field is excited from a current pulse, the eddy 
current induced on conductor(s) proximate the current pulse carrying 
conductor (for example, a coil) will have the functional properties of an 
exponential opposing the step function, characterized by an amplitude and 
decay time. In this embodiment a synchronizer 112 is optional to assure 
the analogue realizations of the demand pulse and the correction transient 
add properly. This may be accomplished by a gating arrangement by which 
the digital output register of the eddy current calculating module 104 is 
strobed concurrently with an enable pulse to the DAC 102. Synchronicity of 
the resulting analogue signals may be further assured by known techniques 
such as operating upon signal magnitudes of desired relative scale to 
retain analogue synchronism with appropriate attenuation to provide the 
correct relative scale. 
Possibility of loss of synchrony between the demand profile and the 
computed distortion can arise from the delay inherent in the compensating 
calculation while conversion of the digital representation of the demand 
signal initiates. However, the relative operational rate of the signal 
processor 104 and the DAC 102 is of such disparity that the calculational 
delay is negligible. For example, the signal processor 104 (by way of 
example, a Texas Instruments TMS320C32) operates in a repeating loop at 
high repetition rate of about 500 KHz with null input and a precision of 
16 bits. The calculational delay and misphasing error are not noticeable 
until the precision is reduced to 4 bits and the repetition rate is 
reduced to about 1 KHz. In the present (eddy current correction) usage, 
the distortion correction is a monotonic curve representing a sum of 
exponentials. Consequently the translation of such curve along either time 
or amplitude axes is easily tolerated except when the processor 104 is 
delayed excessively relative to DAC 102 and the digital precision is 
allowed degrade to produce excessive amplitude error. 
The multiple inputs shown in FIG. 2 allow for the presentation of demand 
transients of different channels, any of which may require compensatory 
activity in the given channel. 
Compensation for eddy current effects is particular to the structure 
proximate the field point. Eddy current pre-compensation contemplates the 
addition of a "counter-distortion" function to the desired time profile of 
the field transient. The physical distortion function accompanying a 
simple step function signal consists of a sum of decreasing exponential 
functions exhibiting a characteristic set of amplitudes and corresponding 
time constants. These exponentials correspond to conducting structural 
members, not all of which may be visible. In order to establish a set of 
exponential functions from which to determine quantitative 
pre-compensating parameters, a step function demand pulse is applied and 
the resulting response is measured. The difference in the normalized time 
dependence is then fit to a sum of exponentials to extract the amplitude 
and corresponding time constant for each such exponential. A corresponding 
set of increasing exponential functions, added to the desired signal 
cancels with the physical effect to yield the pre-compensated signal 
profile. 
For the case of eddy current pre-compensation the corrective waveform is 
the result of a recursive calculation carried out by the computational 
module 104 as illustrated schematically in FIG. 3 (where a single time 
constant disturbance is treated). The calculation is of the form 
EQU y(n)=.beta.y(n-1)+.alpha..delta.(n) 
where .alpha. and .beta. are empirically determined parameters derived from 
the strength of the coupling of the eddy current field contribution and 
its time dependence, respectively, to the field point. The quantity 
.delta.(n) is simply the difference in the ordinates of consecutively 
sampled points for a constant sampling rate as obtained at block 152. 
EQU .delta.(n)=y(n)-y(n-1) (Equ. 1) 
Thus, a desired field time dependence (or "demand") is specified from a 
list 
##EQU1## 
read in turn by computational module 104 (block 150) from which there is 
computed a corrected signal 
##EQU2## 
The processing of the demand represented by the list w(i) is carried out 
in a loop at a high rate, for example, 250 KHz. Steps 150, 154, 158 and 
160 represent simple input rearrangement of variables and output as shown. 
The quantities .delta. (obtained at block 152) and the corrected discrete 
signal amplitude is computed at block 156 for the corresponding abscissa 
which is determined by the processing rate of the combination of the 
computational module and the DAC. The latter is independently controlled 
from a clocked pulse. The clock rate determines the time scale for the 
pulse as realized in the conductors which effectuate the pre-corrected 
transient magnetic field pulse. An asynchronous relationship between the 
loop rate of the computational module 104 and the DAC clocking rate is 
satisfactory when the loop rate is very fast (typical factor of 8-10, for 
example) in relation to the DAC clock rate. (The pulse width is ultimately 
the criterion for any relationship of these rates. So long as the loop 
rate is fast in comparison to any other frequency limiting components, the 
loop rate will be satisfactory.) As these rates become comparable, a 
synchronous relationship as suggested in the dotted line arrangement 112 
of FIG. 2, preserves the integrity of the correction. 
For the case of a step function one has 
EQU w(n)=0 for n&lt;0 
EQU w(n)=1 for n.gtoreq.0 
Thus by equation 1 
EQU u(0)=.alpha. 
and for 
##EQU3## 
For the present case .beta.=exp (-T/.rho.) where .rho. is the empirically 
determined eddy current induced field decay constant and T is a selected 
time interval establishing the selected DAC update rate. The quantities 
.beta. and .alpha. are constants. 
Performance of the invention is illustrated below for a simple case of the 
excitation of the magnetic field gradient .differential.H.sub.z 
/.differential.Z. In order to investigate the operation of the present 
invention, a typical superconducting NMR magnet was employed with an NMR 
sample at the center of the sensitive volume and a second sample offset in 
the direction of the gradient to be corrected. As a rule, a gradient pulse 
is applied to the sensitive volume of the magnet symmetrically about the 
center: that is, the field component arising from the contribution of the 
applied gradient is a spatial function and this function passes through 
zero at the center. The sample disposed at the center substantially 
measures the field arising from the spatially uniform polarizing field at 
the region of minimal gradient. The offset sample serves to measure the 
field at the offset position and thus the difference in resonance 
frequency of the two samples produces a measure of the actual magnetic 
field gradient. The eddy currents modulate the magnetic field as a 
function of time over the duration of the transient and this is observed 
by acquiring free induction decay waveforms arising from the displaced 
samples as a function of delay between excitation and acquisition. 
For the particular magnet in which these experiments were carried out, it 
could be determined that there was a time dependence experienced in the 
magnetic field for the Z direction (polarizing axis) which can be 
expressed as 
EQU Z(t)=0.044 exp(-t/270)-0.114 exp(-t/75)+0.013 exp(-t/4) 
where the coefficients represent relationship to the amplitude of the 
applied current pulse (the demand pulse) and the times are in 
milliseconds. The three time constants are interpreted to represent the 
eddy currents sustained on the outer bore of the cryostat container 
surrounding the NMR probe and on major internal structures within the 
cryostat. Other magnetic field axes and gradient directions, when applied, 
effect the field along Z and gradients, and vice versa. The amplitudes 
measure the intensity of the resulting transient magnetic field due to the 
eddy current circulating on the respective structure. The time constants 
measure the exponential decay characteristics. These parameters are 
obtained experimentally by observation of the waveform resulting from a 
standard step function excitation, as above explained. The parameter set, 
thus obtained, is then utilized by the computational module 104 during 
operation. 
FIG. 4a shows the frequency shift offset recorded without any compensation. 
At FIG. 4b pre-compensation of a long (270 ms.) time constant is applied. 
The effect of the short time constants (4 and 75 ms.) is evident close to 
the time origin. FIG. 4c is the result of application of pre-compensation 
of the short time constants absent compensation of the long time constant. 
FIG. 4d pre-compensates both the long and the short time constants with a 
resulting sharp step function in magnetic field along the selected 
direction. 
In common arrangements, the magnetic field pulses are gradient pulses, i.e. 
having a desired spatial dependence. In the above example, the field is 
oriented in the Z direction and the magnitude varies as a function of Z, 
e.g., it has a Z gradient. From basic electromagnetic theory, together 
with the details of the specific geometry of conductors on which eddy 
currents are induced and propagate, it is apparent that the applied 
magnetic field pulse will be accompanied by undesirable components of 
diverse direction and spatial variation. In the practice of NMR, most 
often, the magnetic field is oriented along a single (principal) axis and 
gradient fields may be applied along any selected one of three orthogonal 
axes. To obtain a gradient along some oblique direction, multiple 
concurrent gradients may be simultaneously applied. By the principle of 
superposition, it is only necessary to consider each axis separately, for 
purposes of general analysis as well as for the physical realization of 
the invention. 
Where the undesirable effect of an eddy current is a gradient along the 
same direction as the applied gradient, the effect is frequently the 
greatest and the example discussed above is of this class. Undesirable 
gradients orthogonal to an applied gradient also arise from eddy currents 
and are similarly pre-compensated. The computed distortion is simply 
inverted and the pre-compensation merely nulls the undesirable eddy 
current driven gradient. Yet a third type of parasitic effect may arise 
from a gradient applied in any direction; this is a shift in the magnitude 
of the magnetic field. The correction to be applied in this latter case is 
a spatially constant magnetic increment. 
The digitally represented demand signal and the digitally computed 
correction could be combined by digital methods within DSP 204 and 
converted at DAC 206 as illustrated in FIG. 5, but such an arrangement 
suffers several burdens. Most significant is the limit to dynamic range 
occasioned by the finite width of the digital instrumentation. The 
summation of the two analog signals is commonly realized with a relatively 
large dynamic range and is preferred for the practice of the invention. By 
contrast with the embodiment of FIG. 5, the separate DAC arrangement of 
FIG. 2 allows independent dynamic range for both the demand pulse and the 
correction. 
In another embodiment, the digital demand is not provided separately as a 
list of digital words, but is internally generated within the 
computational module 104. In this embodiment, the computational module 104 
receives a parameter establishing the type of pulse and such parameters as 
required for that type of pulse, e.g., pulse width, amplitude (as for 
example specifying a rectangular pulse) and the desired demand is created 
together with the eddy current corrections. 
The pre-compensation arrangement of the present invention has more general 
application then the eddy current compensation here discussed. In any open 
loop system where a digital representation of a desired excitation has an 
a priori calculable distortion effect upon a physical system, e.g., a 
transducer, the invention may be applied to prepare the required 
pre-compensation and synthesize the appropriate waveform. It is only 
necessary that the undesirable responses of the physical system are known 
or can be measured via canonical experiments and where the signal to be 
applied may be operated upon to obtain the compensatory waveform. Digital 
audio systems are an example of another such context of application. Such 
system includes audio output including a speaker having undesirable 
response characteristics. Instead of driving the speaker with the original 
digital data, a calculated pre-compensating component is computed and 
combined with the original digital data to produce a signal to drive the 
speaker, thereby improving and /or extending the range of satisfactory 
operation. For such application the computational module produces a 
sinusoidal corrective function. Recursion techniques to achieve such 
dependence are known to those of skill in the art. 
Whereas the invention is here illustrated and described with reference to 
embodiments presently contemplated as the best mode of carrying out such 
invention in actual practice, it is to be understood that various changes 
may be made in adapting the invention to different embodiments without 
departing from the broader inventive concepts disclosed herein and 
comprehended by the following claims.