Patent ID: 7088099

Claim:
A method for forming an image of an object using a magnetic resonance imaging system which (i) comprises X, Y and Z gradient magnets and (ii) defines an origin of an (x, y, z) coordinate system (the “x,y,z-coordinate system”), said X, Y, and Z gradient magnets producing magnetic fields having gradients (G X , G Y , G Z ), respectively, said method comprising: (A) acquiring a magnetic resonance signal data set (the “MR data set”) for the object in three dimensions in data space using the X, Y, and Z gradient magnets; (B) producing an uncorrected image function ρ(x,y,z) from the MR data set by a process which comprises performing a three dimensional fast Fourier transform on said data set; and (C) producing a corrected image function ρ(x′,y′,z′) from the uncorrected image function ρ(x,y,z), where the coordinates (x′,y′,z′) represent a corrected position in the x,y,z-coordinate system for the value of the image function at (x,y,z), said (x′,y′,z′) coordinates being determined using an iterative mapping which employs coefficients of spherical harmonic expansions for the magnetic fields produced by the X, Y, and Z gradient magnets (the “spherical harmonic coefficients”).