3-D Interpolation Technique for Total Volume Imaging in NMR Tomography

Total volume NMR imaging using a 3-D inverse Fourier transform (3DIFT) is described. Since the free induction decay (FID) signal is proportional to the Fourier transform of the spin density, if the volume to be imaged is sampled with a 4π geometry one obtains the spherical coordinate representation of the object in the frequency domain. A 3DIFT of this volume results in the 3-D spatial representation of the object. The efficient implementation of the 3DIFT requires the employment of the Fast Fourier Transform (FFT) in a cartesian coordinate system. An interpolation scheme for obtaining the cartesian representation from a spherical coordinate system is introduced.