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

A method of operating a medical instrument comprising a magnetic resonance imaging system with an imaging zone, wherein the magnetic resonance imaging system comprises a gradient coil system for generating a gradient magnetic field within the imaging zone, wherein the gradient coil system comprises three orthogonal gradient coils, wherein the method comprises:

• repeatedly controlling the magnetic resonance imaging system with calibration pulse sequence commands to acquire the magnetic resonance calibration data for multiples slices using at least one of the three orthogonal gradient coils to generate the slice select gradient magnetic field, wherein the calibration pulse sequence commands are configured for acquiring magnetic resonance calibration data from a magnetic resonance imaging phantom within the imaging zone according to a calibration magnetic resonance imaging protocol with two-dimensional phase encoding perpendicular to a slice select gradient magnetic field, wherein the calibration pulse sequence commands are configured for acquiring slices divided into voxels by the two-dimensional phase encoding;
• computing a Fourier transform of the magnetic resonance calibration data for each of the voxels of the multiple slices in the phase encoding directions;
• computing an expansion of the Fourier transformed magnetic resonance calibration data into spherical harmonics;
• and
• calculating a three-dimensional gradient impulse response function for the at least one of the three orthogonal gradient coils using the expansion into spherical harmonics.

A computer program product comprising machine executable instructions for execution by a processor configured for controlling a medical instrument, wherein the medical instrument comprises a magnetic resonance imaging system with an imaging zone, wherein the magnetic resonance imaging system comprises a gradient coil system for generating a gradient magnetic field within the imaging zone, wherein the gradient coil system comprises three orthogonal gradient coils, wherein execution of the machine executable instructions causes the processor to:

• repeatedly control the magnetic resonance imaging system with the calibration pulse sequence commands to acquire magnetic resonance calibration data for multiples slices using the at least one of the three orthogonal gradient coils to generate the slice select gradient magnetic field, wherein the calibration pulse sequence commands are configured for acquiring magnetic resonance calibration data from a magnetic resonance imaging phantom within the imaging zone according to a calibration magnetic resonance imaging protocol with two-dimensional phase encoding perpendicular to a slice select gradient magnetic field, wherein the calibration magnetic resonance imaging protocol is configured for acquiring slices divided into voxels by the two-dimensional phase encoding;
• compute a Fourier transform of the magnetic resonance calibration data for each of the voxels of the multiple slices in the phase encoding directions;
• compute an expansion of the Fourier transformed magnetic resonance 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.