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

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