  We propose a robust imaging technique that makes it possible to distinguish
vortices from antivortices in quasi-two-dimensional Bose--Einstein condensates
from a single image of the density of the atoms. Tilting the planar condensate
prior to standard absorption imaging excites a generalized gyroscopic mode of
the condensate revealing the sign and location of each vortex. This technique
is anticipated to enable experimental measurement of the incompressible kinetic
energy spectrum of the condensate and the observation of a negative temperature
phase transition of the vortex gas, driven by two-dimensional superfluid
turbulence.
