  We present an uncertainty quantification methodology for density estimation
from Background Oriented Schlieren (BOS) measurements, in order to provide
local, instantaneous, a-posteriori uncertainty bounds on each density
measurement in the field of view. Displacement uncertainty quantification
algorithms from cross-correlation based Particle Image Velocimetry (PIV) are
used to estimate the uncertainty in the dot pattern displacements obtained from
cross-correlation for BOS and assess their feasibility. In order to propagate
the displacement uncertainty through the density integration procedure, we also
develop a novel methodology via the Poisson solver using sparse linear
operators. Testing the method using synthetic images of a Gaussian density
field showed agreement between the propagated density uncertainties and the
true uncertainty. Subsequently the methodology is experimentally demonstrated
for supersonic flow over a wedge, showing that regions with sharp changes in
density lead to an increase in density uncertainty throughout the field of
view, even in regions without these sharp changes. The uncertainty propagation
is influenced by the density integration scheme, and for the Poisson solver the
density uncertainty increases monotonically on moving away from the regions
where the Dirichlet boundary conditions are specified.
