Density gradients amplify uncertainty in Background-Oriented Schlieren experiments
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Graphical abstract.

Density gradients amplify uncertainty in Background-Oriented Schlieren experiments

Background-Oriented Schlieren (BOS) is a technique used to measure fluid density from the apparent distortion of a target dot pattern. Here, we model how non-linearities in the density gradient fields can blur the dot pattern image and increase the position uncertainty. To develop this model, we employ the Cramer-Rao lower bound (CRLB) concept, adopted from parameter estimation theory. We introduce a new parameter termed the Amplification Ratio to describe the ratio of position uncertainties of a dot in the reference (no-flow) and gradient (with flow) images and show that this is a function of the ratio of the dot diameters and dot intensities.

BOS measurements from flow induced by a spark discharge show that the regions of displacement gradients correspond to regions with uncertainty amplification.

We demonstrate the uncertainty amplification on synthetic and experimental BOS images and show that regions of high amplification ratio correspond to regions of density gradients. This analysis elucidates the dependence of the position uncertainty on density and refractive-index-gradient-induced distortion parameters, provides a methodology for accounting its effect on uncertainty quantification, and provides a framework for optimizing experiment design.

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