Determination of higher order terms of the three-dimensional gradient impulse response function

Abstract

A medical instrument includes a magnetic resonance (MR) imaging system with an imaging zone and a gradient coil system with three orthogonal gradient coils. A processor controls the medical instrument to: repeatedly control the MR imaging system with calibration pulse sequence commands to acquire the MR calibration data for multiples slices using at least one of the three orthogonal gradient coils to generate the slice select gradient magnetic field; compute a Fourier transform of the MR calibration data for each of the voxels of the multiple slices in the phase encoding directions; compute an expansion of the Fourier transformed MR calibration data into spherical harmonics; and calculate a three-dimensional gradient impulse response function for the at least one of the three orthogonal gradient coils using the expansion into spherical harmonics. The calibration pulse sequence commands are configured to acquire MR calibration data from a phantom according to a calibration protocol with two-dimensional phase encoding perpendicular to a slice select gradient magnetic field.