Monday, December 14, 2009
Defining the Excitation Profile
The excitation profile of an rf pulse is determined by its Fourier transform. The Fourier transform of rectangular pulses of monochromatic radiation, typically used in NMR measurements, are (sin(x) /x) (or sinc(x)) functions. The sinc(x) function has a large central lobe with satellite lobes of alternating positive and negative sign. In order to obtain uniform excitation and therefore quantitative data, one must ensure that the excitation pulse is sufficiently short to allow the entire spectral width of interest to fit within a small region of the central sinc(x) lobe. The pulse must also have sufficient amplitude to produce a 90° rotation of the magnetization. The excitation profile of four pulses is shown in the figure below.The data were obtained by measuring a 300 MHz 1H NMR spectrum of HDO as a function of transmitter frequency. The power level for each of the pulses was set such that the pulses provided a 90° flip angle for an on-resonance signal. Each spectrum was phased independently. The first zero crossings of the sinc(x) function are at + 1/(PW) and -1/(PW) where PW is the duration of the pulse. It is therefore important that the spectral width of interest be less than ~1/(10PW) to ensure uniform excitation. One can see that a 10 µsec pulse provides essentially flat excitation across 40 kHz whereas 50, 100 and 200 µsec pulses do not.