Gradient Spin Echoes for Selective Excitation

Shaped excitation pulses can replace the non-selective hard pulses typically used in a one-pulse measurement to achieve selective excitation. Another method of achieving selective excitation is the gradient spin echo using a selective 180° pulse. This technique is demonstrated in the figure below. A non-selective hard 90°_x pulse is first given followed by a pair of identical pulsed field gradients sandwiching a soft selective 180° pulse about the y axis. The hard 90° pulse rotates all spin vectors onto the -y axis. During the first gradient pulse the spin vectors dephase and evolve according to their offset frequencies. The soft 180°_y pulse flips a single resonance 180° about the y axis leaving all other resonances untouched. During the second gradient pulse, the "selected" resonance is rephased and its offset frequency evolution is refocused. The unselected resonances dephase more and continue to evolve according to their offset frequencies. The receiver is then turned on to collect the FID of the "selected" resonance, all others are dephased and therefore suppressed. This is demonstrated in the figure below which shows ¹H NMR spectra for a mixture of methylence chloride and acetone. The bottom trace shows a standard one-pulse measurement. The middle and top traces show results from a selective gradient spin echo measurement with the selective 180° pulse set for methylene chloride and acetone, respectively.

Spin Echos for Uncoupled Spins

The spin echo is one of the most fundamental building blocks for NMR pulse sequences. Its main purpose is to refocus chemical shifts. The simplest spin echo is that for uncoupled spins where only the offset, Ω (i.e. the frequency difference between the carrier and the resonance) need be considered. The pulse sequence is represented in the upper portion of the figure with the vector and product operator representations below. A 90_x pulse is first given to create magnetization along the -y axis of the rotating frame. During the first delay period, τ, the magnetization rotates in the x-y plane at a rate, Ω. The 180_x pulse rotates the magnetization 180 degrees about the x axis. During the second delay period, the magnetization again rotates in the x-y plane at a rate, Ω in the same direction as during the first delay. At the end of the second delay, the magnetization is on the y axis and the collection of the FID is started. It is important to note that the echo will always have its maximum at 2τ after the 90 degree pulse regardless of its offset, Ω or the duration of τ. The value of τ however is limited by the T₂.

Echoes and Fourier Transforms

NMR data are often collected using pulse sequences involving echoes. These sequences are usually of the form:

pulse1 - delay1 - pulse2 - delay 2 - acquire data

In theory the echo occurs when delay1 = delay2. Often, this is not quite correct in practice due to the pulses having finite duration and short hidden pre-acquisition delays before the receiver is turned on. It is a good idea to set delay2 < delay1 so that the entire echo is captured. In such cases it is important to discard the data before the top of the echo before Fourier transformation. Failure to do so will result in improper line shapes (in the case of broad lines) or phasing errors. The figure below shows the ²H quadrupolar echo data for perdeuterated PMMA. The effect on the line shape is shown when the data are Fourier transformed before the echo (top trace) and after the echo (bottom trace). The correct line shape is only obtained when the data are Fourier transformed precisely at the top of the echo (middle trace).