Composite pulses

Figure 1.41 Applying the first incorrectly adjusted 90° pulse (actually, 85° pulse) bends the z-magentization vector 5° above the y -axis. The 180 pulse at this stage will bring the magnetization vector 5° below the y -axis (to the mirror image position). Applying another similarly maladjusted 90° pulse causes a further bending of the magnetization vector precisely to the — z-axis. The composite pulse sequence (i.e., 90°-180°-90°) is thus employed to remove imperfections in the 90° pulse.

Composite pulses have also been used in overcoming problems due to sample overheating during broadband decoupling experiments. A widely used pulse sequence is Waltz-16 (Shaka et al., 1983), which may be repre-... 

What are the advantages of using composite pulses instead of a... 

Composite pulses reduce the error introduced due to the delay between the start of the pulse and when it reaches full power. They have also been used to overcome problems of sample overheating during broadband decoupling and in experiments in which pulses have to be applied for long durations. 

Figure 4.7 Pulse schemes representing separation of decoupling effects from the nOe during X nucleus acquisition. The decoupler is programmed to produce noise-modulated irradiation or composite pulse decoupling at two power levels. Suitable setting of the decoupler may produce either (a) nOe only, (b) proton decoupling only, or (c) both nOe and proton decoupling.

Composite pulse A composite sandwich of pulses that replaces a single pulse employed to compensate for B] field inhomogeneities, phase errors, or offset effects. 

Composite pulses Use of a series of pulses of varying duration and phase in place of a single pulse. Such systems, when used in the pulse sequences of many modem NMR techniques, give improved performance as they are more tolerant to r.f. inhomogeneity. 

Figure 9 Timing diagram of the BIRD-HMBC pulse sequence for the detection of nJch correlations, including an additional two-step low-pass J filter. Thin and thick bars represent 90° and 180° pulses, respectively. 13C180° pulses are replaced by 90°y — 180°x — 90°y composite pulses. <5 is set to 0.5/(Vch) and A is set to 0.5/("JCH). Phases are cycled as follows fa = y, y, —y, —y 4>j = x, —x fa — 8(x), 8(—x) fa = 4(x), 4(— x) ( rec = 2 (x, — x), 4(—x, x), 2(x, —x). Phases not shown are along the x-axis. Gradient pulses are represented by filled half-ellipses denoted by Gi-G3. They should be applied in the ratio 50 30 40.1.

Now consider the pulse sequence in Fig. 10. Each repetition of C spans one rotor period. Between 0 and tr/2, the composite On pulse 90o360igO270o is applied. This composite pulse, which has been commonly referred to as POST, is chosen because it has been shown to compensate for effects of rf inhomogeneity [83], The mirror-image composite pulse is applied between xr/2 and xr. With this particular design of ROCSA, the homonuclear dipole-dipole interaction is considerably suppressed relative to the CSA. 

Fig. 10 ROCSA pulse sequence based on Cn symmetry. The rectangular blocks in black represent jt/2 pulses. The recoupling period (q) comprises k cycles of Cnln. Each complete cycle of Cnln spans n rotor periods (nzR). The rf phase of each Cq subcycle is set equal to 2nq/n, where q is an index running from 0 to n — 1. Within each Cq subcycle, azR and bzR indicate the position and the duration of the POST composite pulse, respectively. We find that the solution (a, b) = (0.0329,0.467) is a favorable choice for the suppression of the homonuclear dipole-dipole interaction. The bracketed and subscripted values indicate the pulse length and rf phase in radians, respectively. (Figure and caption adapted from [158], Copyright [2003], American Institute of Physics)...

In this section, three experiments are going to be discussed. Two of them, a broadband inversion and a Hahn spin echo, are well-known in the rotating frame. They need to meet the requirement of the phase coherence in PIPs in order to work properly in the Eigenframe. The third is a composite pulse with offset modulation. 

As shown in Fig. 21a, the simulated broadband inversion profile by the three PIPs resembles the profile by the composite pulse 90°180°90° except for a different excitation region. The inversion profile is severely distorted (Fig. 21b) if the three initial phases, phase relationship in the rotating frame is the wrong one in the Eigenframe. The phase coherence in PIPs needs to be considered even for PIPs with the same frequency shift, A/ = 50 kHz in this case. 

The two PIPs constitute an offset modulated composite pulse for use with a 900 MHz NMR instrument. As a result, the centre of 13C is subjected to two consecutive 2ir rotations of opposite offsets, one positive and the other negative, but of the same (x) phases in the two different Eigenframes as shown in Fig. 23. In the vicinity of the centre of the 13C , the sum of the two rotation angles can be expressed as... 

Exploitation of the TROSY effect is rather straightforward. In contrast to 15N-HSQC (Heteronuclear Single Quantum Coherence) or standard triple-resonance experiments based on 15N-HSQC, no radio frequency pulses or composite pulse decoupling should be applied on amide protons when HN spin is not in the transverse plane. Likewise the 15N decoupling should be... 

Composite-pulse decoupling schemes like WALTZ [36, 37], DIPSI [38], or GARP [39], which are used in solution-state NMR, have failed to offer any significant improvements in the solid state compared to CW decoupling. The residual line width in CW-decoupled spectra is dominated by a cross term between the chemical-shielding tensor of the protons and the heteronuclear dipolar-coupling tensor [40, 41]. 

The classical cure 130), involving the use of various composite pulses, is perfectly applicable in FFC relaxometry also. 

The use of composite pulses is subject to several counter-indications, the principle of which is the fact that they last much longer than their simple prototypes. This makes their employment problematic in the case of rigid solids, as well as in the detection of sub-sequences which rely on extremely closely-spaced echoes. 

In general, there is not much need for composite pulses in FFC relaxometry where the only aim is to encounter the inherent instrumental B inhomogeneity. One usually delimits the sample height so as to make it fit inside the measurement coil, which is a less controversial way of reducing B inhomogeneity than composite pulses. However, the employment of composite pulses is indicated in two cases ... 

N. V. Vitanov. Arbitrarily accurate narrowband composite pulse sequences. Phys. Rev. A, 84(6) 14-17(2011). 

HSQC rather than HMQC-based transfer schemes have recently in particular been employed in various indirectly detected two- and three-dimensional 111/X/Y correlation experiments involving multi-step coherence-transfer in either direction.38 40 43 44 The application of PFG s appears to be essential to obtain a sufficiently clean spectrum that is free of artefacts, and in many cases the pulse sequence shows only a satisfactory performance if composite pulses, with a larger excitation bandwidth than normal ones, are employed.21,38,39,43 The pulse schemes yield generally phase-sensitive spectra with pure absorptive lines and do not suffer from splitting or broadening of the cross peaks as a consequence of the undesired evolution... 

Figure 5. Composite pulse trains for control of fluorescence and echo. Also shown are the echoes (iodine gas) and T i and 7 2 at different pressures.

A number of different multiple pulse sequences (8-, 24- and 52-pulse sequences) have also been introduced in order to obtain better resolution or line narrowing, i.e. to affect the first- and second-order terms in the average Hamiltonian. Since pulse imperfections are the major source of resolution limitations, these composite pulse sequences are designed with corresponding symmetry properties which allows the canceling of specific rf pulse imperfections. 

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