Excitation profile Gaussian pulse

A sine-shape has side lobes which impair the excitation of a distinct slice. Other pulse envelopes are therefore more commonly used. Ideally, one would like a rectangular excitation profile which results from a sine-shaped pulse with an infinite number of side lobes. In practice, a finite pulse duration is required and therefore the pulse has to be truncated, which causes oscillations in the excitation profile. Another frequently used pulse envelope is a Gaussian frmction ... 

Gaussian pulses are frequently applied as soft pulses in modern ID, 2D, and 3D NMR experiments. The power in such pulses is adjusted in milliwatts. Hard" pulses, on the other hand, are short-duration pulses (duration in microseconds), with their power adjusted in the 1-100 W range. Figures 1.15 and 1.16 illustrate schematically the excitation profiles of hard and soft pulses, respectively. Readers wishing to know more about the use of shaped pulses for frequency-selective excitation in modern NMR experiments are referred to an excellent review on the subject (Kessler et ai, 1991). 

Frequency-selective REDOR (fsREDOR) is a very powerful technique developed for the study of 13C and 15N uniformly labeled peptides or proteins [92]. The basic idea of this technique is to combine REDOR and soft n pulses to recouple a selected 13C-15N dipole-dipole interaction in a multiple-spin system. Usually one could use Gaussian shaped pulses to achieve the required selective n inversions. Other band selective shaped pulses have been developed for a more uniform excitation profile [93]. In its original implementation, fsREDOR was used to extract the intemuclear distances of several model crystalline compounds [92], In the past few years, this technique has proven to be very useful for the study of amyloid fibrils as well. For the Ure2p10 39 fibril samples containing 13C and 15N uniformly... 

Fig. 9.1. (A) Gaussian (a) and sine (b) excitation profiles. (B) Composite (G3) Gaussian pulse. (C) Train of soft pulses modified after the DANTE sequence to achieve selective off-resonance excitation. (D) Redfield 21412 sequence. (E) Binomial 11, 121, 1331, 14641 sequences. (F) JR (a) and compensated JR (or 1111) (b) sequences. (G) Watergate sequence. (H) Weft (Superweft) sequence. (I) Modeft sequence. (J) MLEV16 sequence. (K) NOESY sequence with trim pulse. (L) MLEV17 sequence with trim pulses. (M) Clean-TOCSY sequence.

Figure 8.15(b) shows the spectrum of sucrose with a 90° Gaussian pulse applied to the triplet at 3.99 ppm, compared to a normal 1H spectrum (Fig. 8.15(a)). This is done by moving the reference frequency to place the 3.99 ppm triplet at the center of the spectral window (on-resonance), which is the center of the Gaussian-shaped excitation profile... 

It is rather tedious to move the spectral window every time we want to select a peak with a shaped pulse, but it is necessary as the center of the Gaussian excitation profile is at... 

The amplitude modulated pulses may require special equipment such as a waveform generator which, however, has become a standard constituent of the modem commercial spectrometers. The amplitude modulated pulses are usually windowless and the sidebands produced by these pulses, in most cases, are very weak and can be neglected. The simplest amplitude modulated pulses are Gaussian pulse, sine pulse or sine-square pulse [1]. The main drawback of these simple shapes is that they produce a phase gradient over the excitation bandwidth and their excitation profiles are non-uniform over the bandwidth of interest. The amplitude modulated pulses can easily be shifted off-resonance by applying a phase ramp over the pulse according to equation (4). 

Figure 9.12. Absolute value frequency domain excitation profiles for (a) a rectangular pulse and (b) a Gaussian shaped pulse.

Universal pulses act equally on any initial magnetisation state whereas excitation and inversion pulses are designed to act on longitudinal magnetisation only. The bandwidth factor is the product of the pulse duration. At, and the excitation bandwidth, Af, which is here defined as the excitation window over which the pulse is at least 70% effective (net pulse amplitude within 3 dB of the maximum other publications may define this value for higher levels and so quote smaller bandwidth factors). Use this factor to estimate the appropriate pulse duration for the desired bandwidth. The attenuation factor is used for approximate power calibration and represents the amount by which the transmitter output should be increased over that of a soft rectangular pulse of equal duration. The Gaussian based profiles are truncated at the 1% level. 

Figure 9. Experimental excitation profiles for the double pulsed field gradient spin-echo excitation sequences in which the element S is a 180° Gaussian pulse (truncated at 1%) of the duration shown.

For use in the laboratory, it is convenient to choose a simple, robust inversion pulse as the element S, and the Gaussian pulse is well suited to routine use. Example excitation profiles for this are illustrated in Fig. 9.20 and offer guidance on selection of pulse duration for a desired excitation window. For proton spectroscopy, a Gaussian pulse of around 40 ms proves suitable for many applications. 

The following Check its will use the Bloch simulator module of NMR-SIM to study and analyse a number of different shaped pulses. Time Evolution, the Excitation Profile and the Rf field profile simulation are illustrated using a 90° Gaussian pulse while an adiabatic CHIRP pulse is used for the Waveform analysis. 

In Check it 5.2.2.1(b) the profiles of both components are simulated and compared using the multiple display mode of ID WIN-NMR. The Bloch module excitation profile of the same Gaussian pulse using the time evolution calculation illustrates in a very impressive way that the y-magnetization component for different offsets show a symmetrical evolution relative to the on-resonance magnetization whereas the x-magnetization shows an unsymmetrical evolution. 

In Check it 5.3.1.4 the x- and y-profiles of the transverse magnetization for a 270° Gaussian pulse [5.91], a 90° half-GAUSSiAN pulse [5.92] and a 90° Gaussian Pulse Cascade G4 [5.93] are compared. Finally the H spectra of dibromopropionic acid with selective excitation of the proton at 2.85 ppm is simulated for all three shaped pulses. 

The excitation profile of soft pulses is defined by the duration of the pulse, these two factors sharing an inverse proportionality. More precisely, pulse shapes have associated with them a dimensionless bandwidth factor, which is the product of the pulse duration. At, and its effective excitation bandwidth, Af for a correctly calibrated pulse. This is fixed for any given pulse envelope and represents its time efficiency. It is used to estimate the required pulse duration for a desired effective bandwidth Table 10.3 summarises these factors for some common pulse envelopes. Thus, an excitation bandwidth of 100 Hz requires a 21-ms 90° Gaussian pulse but a 49-ms EBURP2 pulse clearly the Gaussian pulse is more time-efficient but has a poorer excitation profile. 

Figure 4.5 Time (right) and frequency O ft) profiles of some soft tt pulses used for narrow band excitation in NMR spectroscopy, (a) Gaussian pulse Hermite pulse and RE-BURP pulse. It is supposed that before the pulse the magnetization was in the z direction, (b) Typical magnetization trajectories for a inversion RE-BURP pulse with distinct frequency offsets. Adapted with permission from References [12,15] (Copyright 2007 American Physical Society and Elsevier).

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