Reference-free digital shadowgraphy using a moving BOS background

A method of measuring density second derivative (shadowgraph) as a variant of background oriented schlieren (BOS) is presented. Pairs of images of a moving background with a small time difference are analysed using moving-window cross-correlation, giving the second derivative of density in the axis of background travel. The advantage over standard BOS is that no reference image is required. In contrast to the existing “reference-free BOS” method, no double-image is produced, making the data interpretation simpler. The sum-of-correlation (ensemble correlation) method can be used on an image series, where the flow is constant over the series time, to significantly reduce the size of the cross-correlation window. The reduction in the window size and sharpening of the resulting image is similar to that achieved by optical flow, but this method is easily automatable, without knowledge of the flow, and can be used with any existing BOS analysis software.