Uncertainty amplification due to density/refractive index gradients in background oriented schlieren experiments

<p>Background-Oriented Schlieren (BOS) is a technique used to measure fluid density from the apparent distortion of a target dot pattern. In this work we model how non-linearities in the density gradient fields that can be present in flows with shocks, boundary layers etc., can blur the dot pattern image and increase the position uncertainty. A concept called the Cramer-Rao lower bound (CRLB) from the field of parameter estimation is used to develop this model. A parameter termed the Amplification Ratio (<img height="14" src="blob:https://purr.purdue.edu/7dfb1ddd-9076-49e3-ac3b-744b8b4e13fa" width="14" />) is proposed that describes the ratio of position uncertainties of a dot in the reference (no-flow) and gradient (with flow) images and is shown to be a function of the ratio of the dot diameters and dot intensities. The uncertainty amplification is demonstrated on synthetic and experimental BOS images, where it is seen 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.</p>