Composite pulse sequences

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.

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

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. 

A composite-pulse sequence to cancel the spurious signals has been described. " The main advantage of this sequence over the Hahn echo sequence has been shown to be in the simplicity of optimizing the line intensity the optimization of only one pulse duration for this sequence but of two pulse durations and the interpulse delay for the Hahn echo sequence. The effects of the first-order quadrupole interaction during the pulses have been considered (spin I = 3/2 nuclei). It has been shown that the size of the sample must be much smaller than that of the r.f. coil in order for the r.f. magnetic field to become homogeneous for the sample. 

In binomial composite pulse sequences the amplitudes of the pulses are proportional to the binomial coefficients of -t-1 square pulses separated by equal interpulse delays, r. These sequences provide broad regions of near-zero excitation at the solvent frequency while the solute resonances are... 

The first of these arises when the long spin-lock pulse acts in an analogous fashion to the last 90" pulse of the COSY experiment so causing coherence transfer between J-coupled spins. The resulting peaks display the usual antiphase COSY peak stmcture and tend to be weak so are of least concern. A far greater problem arises from TOCSY transfers which arise because the spin-lock period in ROESY is similar to that used in the TOCSY experiment (Section 5.7). This may, therefore, also induce coherent transfers between J-coupled spins when these experience similar rf fields, that is, when the Hartmann-Hahn matching condition is satisfied. Since the ROESY spin-lock is not modulated (i.e. not a composite pulse sequence), this match is restricted to mutually coupled spins with similar chemical shift offsets or to those with equal but opposite... 

Table 9.2. Selected composite-pulse sequences for broadband decoupling and spin-locking...

A 90° pulse of less than 2.5 jus is also necessary for reasonable excitation of the spectral bandwidth, particularly for the three-pulse sequences (Figures 8.2(b), (c)) where roll-off at the edge of the bandwidth and the effects of virtual signals are magnified. A typical deuterium probe is a 5 or 7 mm horizontal solenoid and for this configuration, pulse power should be about a kilowatt. Several commercial amplifiers supply this power level. Composite pulse sequences [120] extend the spectral bandwidth but are less useful when echo distortion is present. Noticeable roll-off is always present with any pulse sequence and correction of simulations for finite-pulse should always be used [121]. 

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-... 

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.

Figure 22 Pulse sequence of the HMBC-RELAY experiment. Filled and open bars represent 90° and 180° pulses, respectively. All other phases are set as x, excepted otherwise stated. A two-phase cycle x, —x is used for the pulse phases (j>, and

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 Section II.3 we have seen that a specific chemical species existing in a given physicochemical environment is characterized by specific values of 7) and T2, and that this fact is important both in the implementation of imaging pulse sequences to obtain quantitative information and in the modification of the pulse sequences to image selectively one species and/or phase within the sample. While exploitation of relaxation time contrast is not likely to become a routine approach for chemical mapping in reactors, there will be niche applications in which it will continue to have use—three of these are identified below. The limitations of the approach derive from that fact that the relaxation times characterizing a system will not only be influenced by chemical composition but also by temperature and the proximity of the molecules to a solid surface or interface. The three case studies illustrated below in which relaxation time contrast has been used with considerable success are (i) an... 

Very few of the references in Tables 1-3 attempt any quantitative modelling of their NMR data in terms of cell microstructure or composition. Such models would be extremely useful in choosing the optimum acquisition pulse sequences and for rationalising differences between sample batches, varieties and the effects of harvesting times and storage conditions. The Numerical Cell Model referred to earlier is a first step in this direction but more realistic cell morphologies could be tackled with finite element and Monte Carlo numerical methods. 

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. 

Figure 3.24 Schematic diagram of the pulse sequence in the composite STIRAP protocol. Note the Stokes and pump pulses are reversed between successive pulse pairs when the Stokes and pump pulses are resonant with the level spacing, whereas they are not reversed between successive pulse pairs when the Stokes and pump pulses are off resonance with the level spacing. (From Ref. 77).

Fig. 1. Pulse sequence for the X/Y H PFG-HSQC experiment as employed for 19F/13C correlation spectroscopy in Ref. 21. 90° and 180° hard pulses are denoted by solid and open bars, respectively groups of two solid and one open bars denote 90° 0 — 180° +9o — 90° pulse sandwiches that serve as composite 180° pulses. 2 are delays of length 1 /(2 Jx,v), and r is a short delay of the same length as the gradient pulse (typically 1 ms). Phase cycles are as in the standard HSQC experiment, and the ratio of gradient pulse strengths is set to G2/G1 = Yy/Yx- Decoupling is employed using WALTZ-16 ( H) and GARP (Y) pulse trains.

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... 

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