Measurement and Control of Magnetic Field Homogeneity

Methods for the measurement and control of magnetic field homogeneity are described. They are designed for application in magnetic resonance spectroscopy. It is shown that field homogeneity can be described satisfactorily by properties of the observed spectral line shape only. Possible criteria include the moments, peak height, and signal energy of a typical resonance line. The moments are equivalent to the Lp norm of the magnetic field configuration. Only the second moment and related criteria allow the construction of a complete set of noninteracting shims which can be adjusted independently for any field configuration. The other moments may provide noninteracting control for certain simple field configurations only. For a resonance line with a sufficient natural width, peak height and energy can be related to the second moment and may also give noninteracting control. Iterative methods for automatic control by means of digital computers are described and applied to a high resolution nuclear magnetic resonance spectrometer.