Time-domain frequency-selective processing in nuclear magnetic resonance: a spatial-spectral holographic perspective

Abstract

The fundamental nuclear magnetic resonance (NMR) imaging equation can be derived from a spatial-spectral holographic wavefront reconstruction formulation similar to that in quantum optics. A spatial-spectral holographic interpretation arises naturally in NMR from the inhomogeneous linewidth broadening due to either an imposed set of linear orthogonal gradient fields or from the intrinsic chemical anisotropy of the spin system. We can thus think of NMR k-space as a spatial-spectral holographic grating. The spatial holographic component arises from dielectric effects at high field strength (>4 T) when the excitation wavelength is less than or commensurate with the size of the imaging sample. The holographic properties of storage, time-reversal, recognition, and triple correlations are experimentally demonstrated in an inhomogeneously broadened NMR sample. This holographic NMR interpretation has additional implications on selective radio-frequency pulse design, microscopy imaging, and the use of conjugate imaging for field inhomogeneity corrections using the time-reversed component of the readout, to be the subject of a subsequent paper.