Compensation of radiation damping during selective pulses in NMR spectroscopy

摘要

A method for compensating radiation damping (=RD) effects during selective or non-selective radio frequency (=rf) pulses in nuclear magnetic resonance (=NMR) spectroscopy comprises the following steps:1) Choose an rf pulse suitably shaped for a selective or non-selective excitation, inversion or refocussing experiment and calculate the expected transverse magnetisation$\[ {\text{M}}_{\text{+}}{\text{(t) = M}}_{\text{x}}{\text{(t) + i M}}_{\text{y}}\text{(t),} \]$ where i = $$ \sqrt{\text{-1}}$$ by solving the Bloch equations on-resonance, assuming that there is no RD;2) Calibrate the rf amplitude on-resonance on a sample with little RD;3) Estimate the RD rate$\[ {\text{R}}_{\text{rd}}{\text{= 1 / T}}_{\text{rd}}{\text{= 2πγηQM}}_{\text{0}}\text{,} \]$ for a sample with RD, where γ is the gyromagnetic ratio, η is the filling factor, Q is the quality factor and M₀ is the equilibrium magnetisation;4) Define a compensated rf pulse shape using the estimate of step 3), given by$\[ {\text{ω}}_{\text{+}}{}^{\text{comp}}{\text{(t) = ω}}_{\text{+}}{}^{\text{unc}}{\text{(t) + ω}}_{\text{+}}{}^{\text{corr}}{\text{(t) = ω}}_{\text{+}}{}^{\text{unc}}{\text{(t) + i R}}_{\text{rd}}{\text{M}}_{\text{+}}\text{(t) ,} \]$ where i = $$ \sqrt{\text{-1}}$$ , ω₊^unc(t) is the ordinary uncompensated shape of the selective or non-selective rf pulse and M₊(t) is the time dependent transverse magnetisation;5) Record the on-resonance response for the said selective or non-selective excitation, inversion or refocussing experiment.;This method has general applicability for any amplitude or frequency modulated rf pulse and presents a general way to compensate for radiation damping during the application of selective rf pulses.