  We describe an easily implementable method for non-destructive measurements
of ultracold atomic clouds based on dark field imaging of spatially resolved
Faraday rotation. The signal-to-noise ratio is analyzed theoretically and, in
the absence of experimental imperfections, the sensitivity limit is found to be
identical to other conventional dispersive imaging techniques. The dependence
on laser detuning, atomic density and temperature is characterized in a
detailed comparison with theory. Due to low destructiveness, spatially resolved
images of the same cloud can be acquired up to 2000 times. The technique is
applied to avoid the effect of shot-to-shot fluctuations in atom number
calibration, to demonstrate single-run vector magnetic field imaging and
single-run spatial imaging of the system's dynamic behavior. This demonstrates
that the method is a useful tool for the characterization of static and
dynamically changing properties of ultracold atomic clouds.
