Shaped RF pulses

Many other pulsed NMR experiments are possible, and some are listed in the final sections. Most can be canied out using the standard equipment described above, but some require additions such as highly controllable, pulsed field gradients, shaped RF pulses for (for example) single-frequency irradiations, and the combined use of pulses at several different frequencies. 

The inhomogeneity in Bi, especially when using surface coils, can lead to a spatially dependent population of desired and undesired coherence pathways. Field gradient pulses in combination with shaped RF pulses lead to spatially selective excitation or refocusing and, in such cases, localization can be viewed as a type of coherence pathway selection. The inherent Bi gradients resulting from the inhomogeneous RF fields of surface coils have also been used for water suppression in in vivo experiments. ... 

If our instrument is appropriately equipped, we can use shaped RF pulses to selectively excite resonances. We might wish to do this if using CW, RF is not selective enough. This practice is required in cases where the resonance to be irradiated is near other resonances in the spectrum (not in space) whose irradiation might yield ambiguous results. 

Fig. 1.10 Soft rf pulses (left) in the shape of a sine (sin x/x) function, and their Fourier transforms (right), being equivalent to the excited slice in the presence of a constant magnetic field gradient. The well defined sine function (top) produces an excitation that is a slice...

Fig. 1.11 Typical basic three-dimensional negative intensity directly before the actual imaging sequence with slice selection, frequen- read gradient. The shape of the 180° rf pulse cy encoding and phase encoding in three ortho- is drawn schematically to indicate that a soft gonal directions. The compensating lobe for pulse is used, the read gradient is drawn as a rectangle with...

The shape of any rf pulse can be chosen in such a way that the excitation profile is a rectangular slice. In the light of experimental restrictions, which often require pulses as short as possible, the slice shape will never be perfect. For instance, the commonly used 900 pulse is still acceptable, while a 1800 pulse produces a good profile only if it is used as a refocusing pulse. Sometimes pulses of even smaller flip angles are used which provide a better slice selection (for a discussion of imaging with small flip angles, see Section 1.7). 

The rf transmitter amplifies an rf pulse signal of about 1 mW up to several W or up to several kW. The amplifier should work in a linear mode (class AB) because excitation pulse shape for slice selection must be reproduced. Class AB rf transmitters such as these with blanking gates are widely available commercially. 

Figure 23 Calculation of the shape of the actively compensated pulse can be carried out on the software. (A) shows the real (red line) and the imaginary (green line) component of an example of the target pulse shape t>,(f). Its leading and the trailing edges have a cosine shape with a transition time of 1.25 xs in 50 steps, and the width of the plateau is 5 ps. (B) Laplace transformation B(s) multiplied by the Laplace transformed step function U(s). (C) It was then divided by the Laplace transformation Y(s) of the measured step response y(t) of the proton channel of a 3.2-mm Varian T3 probe tuned at 400.244 MHz to obtain V(s). (D) Finally, inverse Laplace transformation was performed on V(s) to obtain the compensated pulse that results in the RF pulse with the target shape. Time resolution was 25 ns, and o = 20 was used for the Laplace and inverse Laplace transformations.

ST2-PT thus results in a 2D [15N, H]-correlation spectrum that contains only the most slowly relaxing component of the 2D 15N- H multiplet. The data are processed as described by Kay et al. [44] in an echo/antiecho manner. Water saturation is minimized by keeping the water magnetization along the z-axis during the entire experiment, which is achieved by the application of the water-selective 90° rf pulses indicated by curved shapes on the line H. It was reported that on some NMR instruments the phase cycle mentioned above does select the desired multiplet component. On these instruments, the replacements of S, with S, = y, x for the first FID and 9, =... 

Similarly to non-selective experiments, the first operation needed to perform experiments involving selective pulses is the transformation of longitudinal order (Zeeman polarization 1 ) into transverse magnetization or ly). This can be achieved by a selective excitation pulse. The first successful shaped pulse described in the literature is the Gaussian 90° pulse [1]. This analytical function has been chosen because its Fourier transform is also a Gaussian. In a first order approximation, the Fourier transform of a time-domain envelope can be considered to describe the frequency response of the shaped pulse. This amounts to say that the response of the spin system to a radio-frequency (rf) pulse is linear. An exact description of the... 

Figure 7.3 Sampling principles in 2D k space (a) Cylindrical coordinates. The angle of the field-gradient direction with respect to the x axis is given by 6= arctan Gy / Gx, (b) Cartesian coordinates. For rectangular gradient pulse shapes ky = -g Gy t1 and kx = -g Gx t2. Such sampling schemes are applicable to a slice which can be selected when the rf pulse is applied selectively in the presence of a gradient Gz. The areas of k space accessible by the pulse sequences shown are shaded in gray. TX transmitter signal ...

In NQR, composite pulses have been proposed for the compensation of resonance offset [107-111] and RF field inhomogeneity [107,108,112-114], Several reports on pulses of continuously variable shape for use in NQR have also appeared [115-117], Shaped pulses that compensate for RF field inhomogeneity also partially compensate for the powder average effect (Section 2.1.2.). Theoretically, shaped excitation pulses can enhance SNR by up to 15% in powder samples [117]. Combinations of shaped excitation and refocusing pulses may also provide better response from multi-echo pulse sequences [9],... 

RF pulses and timings were identical to those used in the spectral simulation. Overall, Figure 11 demonstrated good agreement between simulations and experimental data. The small deviations between the simulation and the phantom data were likely caused by T2 differences between different GABA proton groups and line shape distortions from eddy currents (not accounted for in the simulations). The calculated increase in GABA intensity (18%) at 3.01 ppm in the difference spectrum for PRESS+4 compared well with observed a 17% increase in phantom spectrum. 

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