  Magnetic Resonance Imaging (MRI) can characterize and discriminate among
tissues using their diverse physical and biochemical properties. Unfortunately,
submicrometer screening of biological specimens is presently not possible,
mainly due to lack of detection sensitivity. Here we analyze the use of a
nitrogen-vacancy center in diamond as a magnetic sensor for nanoscale nuclear
spin imaging and spectroscopy. We examine the ability of such a sensor to probe
the fluctuations of the "classical" dipolar field due to a large number of
neighboring nuclear spins in a densely protonated sample. We identify detection
protocols that appropriately take into account the quantum character of the
sensor and find a signal-to-noise ratio compatible with realistic experimental
parameters. Through various example calculations we illustrate different kinds
of image contrast. In particular, we show how to exploit the comparatively long
nuclear spin correlation times to reconstruct a local, high-resolution sample
spectrum.
