Accuracy of the Magnetic Field Gradient Waveform Monitor Technique and Consequent Accuracy of Pre‐Equalized Gradient Waveform

The magnetic field gradient waveform monitor (MFGM) technique permits characterization of the temporal evolution of magnetic field gradients in magnetic resonance (MR) instruments (MRIs). Knowledge of the gradient waveform performance permits the development of further techniques, such as gradient waveform pre-equalization, that correct and optimize gradient waveform distortions due to eddy currents induced during the application of switched magnetic fields and other system limitations. The accuracy of the MFGM technique is important since the overall uncertainty of the gradient waveform measurement will propagate into an uncertainty in corrected gradient waveforms impacting the precision of the resulting MR/MRI measurements. The accuracy of MFGM is investigated through a treatment of the noise present in a MRI. A noisy receiver model provides the basis for characterization of the noise and permits examination of the overall impact of noise on the phase accumulated in a pure-phase encoded MR signal. Ultimately, a relationship between the signal-to-noise ratio of a measurement and the corresponding MFGM uncertainty is developed. The theoretical development is supported through simulation in conjunction with experimental results. The propagation of uncertainties to gradient waveform pre-equalization is also discussed.