Time-independent point-spread function for NMR microscopy.

The resolution of NMR microscopy is analyzed in terms of the point-spread function, PSF(r), and the equivalent k space modulation transfer function, MTF(k). The analysis is developed for NMR spin warp and projection reconstruction imaging experiments; however, the framework provided is quite general. Incoherent spin motion is analyzed to predict what limits, if any, on spatial resolution are imposed by diffusion. Previous estimates of diffusion limits at 1-5 microns were developed for specific imaging techniques, typically using a mean displacement argument. Although qualitatively correct, the quantitative predictions represent practical rather than fundamental limits. It is shown that diffusion-dependent "blurring" can be made arbitrarily small and that the practical limits are less stringent than previously thought. A major point illustrated by the PSF-MTF formulation is that the irreversible loss of coherence by randomly diffusing spins occurs faster than the physical displacement, thereby reducing their effect considerably on the frequency or phase of the net detected signal. The irreversible loss of signal due to diffusive motion will contribute to and possibly dominate the signal-to-noise limit of resolution. The resolution as measured by the width of the PSF and MTF for diffusion is shown to be independent of the signal acquisition time, and their functional forms allow selection of microscopic imaging parameters. An example of a three-dimensional spin-warp image of a green algae cell is shown with resolution of approximately 16 microns x 13 microns x 10 microns.