A single-camera synthetic Schlieren method for the measurement of free liquid surfaces

A single-camera synthetic Schlieren method is introduced to measure the height of a dynamic free liquid surface in container with flat bottom. Markers placed on bottom, seen through surface, are virtually displaced due light refraction at surface. According Snell’s law, marker displacements depend refractive indices transparent and air, its spatial gradients. We solve resulting governing nonlinear equation Newton–Raphson obtain height. Our does not require reference height, which allows measurement surfaces topography situations where depth unknown. demonstrate accuracy by performing experiments ripples dam-break flows discuss uncertainty, errors limitations.