  Sub milli-arcsecond astrometry and imaging of the black hole Sgr A* at the
Galactic centre may become possible in the near future at infrared and
sub-millimetre wavelengths. Motivated by observations of short-term infrared
and X-ray variability of Sgr A*, in a previous paper we computed the expected
images and light curves, including polarization, associated with an compact
emission region orbiting the central black hole. We extend this work, using a
more realistic hot-spot model and including the effects of opacity in the
underlying accretion flow. We find that at infrared wavelengths the qualitative
features identified by our earlier work are present, namely it is possible to
extract the black hole mass and spin from spot images and light curves of the
observed flux and polarization. At radio wavelengths, disk opacity produces
significant departures from the infrared behaviour, but there are still generic
signatures of the black hole properties. Detailed comparison of these results
with future data can be used to test general relativity and to improve existing
models for the accretion flow in the immediate vicinity of the black hole.
