## Info

1800 spectra

Linen id 1 h 54 Hz I'hasc increment:

Im aginary 1

(Ai,) •/Vi rV

on

Ji

Freq, increment: 3.3 Hz

Figure 12.4

bottom of the receiver coil (z = -8 mm) and moving in small steps to the top (z = +8 mm), while incrementing the phase as we move up to model the Z1 shim error. The result is shown in Figure 12.4, with five complete cycles of phase error from the bottom of the coil to the top. The real spectrum and the imaginary spectrum, as well as the magnitude

(^J(real2 + imag.2)) spectrum are shown. The phase at any position in the spectrum can be determined by setting the intensity of the real spectrum (relative to the magnitude value) equal to sin $ and the intensity of the imaginary spectrum (relative to magnitude) equal to cos $. The angle $ is the phase.

I(real)/I(imag.) = sin $/cos $ = tan $; $ = arctan[I(real)/I(imag.)]

If the arctan (inverse tangent) function is defined to give values between +90° and -90°, we would have $ moving linearly from -90° to +90° and then suddenly jumping back to -90°, but the software can unravel these discontinuities to generate a smooth field map. A "control" experiment is done with t = 0, and the control field map is subtracted from the field map generated with the delay t.

To calculate the changes in shim settings, we need an accurate "map" of the effect of each shim on the Bo field as a function of the z coordinate. We need to know how many Hz difference in field is created at each level of the sample by changing, say, the Z1 shim by +1 DAC unit (shim units are called "DAC units" because they are integers that drive the digital-to-analog converter to produce an analog current in the shim coil). The shims can be mapped by changing each shim by a significant amount (e.g., 100 DAC units) and remapping the field. By subtracting this field map from the map obtained before changing the shim value, we know exactly what effect is produced for each 100 units of change in that shim setting. Figure 12.5 shows an ideal shim map for shims Zx-Z6; from it we could calculate the change in field at each level for any change in one of these six shim settings. The mathematical problem is then to determine, for any arbitrary map of field inhomogeneity, how much we need to change each of the six shims to generate a function exactly opposite to this inhomogeneity to cancel it out and give us a perfectly homogeneous field. This is a relatively simple fitting problem and the computer can solve it very quickly, automatically

applying the shim changes to the six shim DACs and changing the currents in the shim coils to correct for the inhomogeneity.

Some gradient probes have three gradient coils, oriented in the x, y, and z directions. With a "triple axis" gradient probe and three pulsed-field-gradient amplifiers, one can generate a 3D map of the field inhomogeneity, and using 3D maps of all of the shims, including those involving the x and y axes (e.g., X, Y, XZ, YZ, XZ2, YZ2, XY, X2-Y2, X3, Y3, etc.) corrections can be calculated for all of the shims, not just the Z shims. In a matter of minutes, a spectrometer with 40 shim settings can be shimmed from zero shim current in all 40 coils to nearly perfect homogeneity without using any human skill or judgement. The only thing that is required is a sample with a single, very strong, and dominant peak. For biological samples in 90% H2O, this single peak is the water peak, but the technique has now been extended to samples in deuterated solvents (D2O, CDCl3, etc.) by using the deuterium spectrum. In CDCl3, for example, the deuterium spectrum consists of a single, very stong, and dominant peak: the 2H peak due to the solvent CDCl3. A bit of switching hardware is needed to shut off the lock circuit and apply the same pulse sequence (Fig. 12.1) at the deuterium frequency. Now automatic gradient shimming is routine even for samples in fully deuterated organic solvents.

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