Synthetic Schlieren Method Using Total-Internal-Reflection Deflectometry

We describe a method that uses total internal reflection (TIR) at the water-air interface inside a large, transparent tank filled with water to measure the interface's deflections. Using this configuration, we obtain an optical setup where the liquid surface acts as a deformable mirror. The setup is shown to be extremely sensitive to very small disturbances of the reflecting water surface, which are detected by means of visualising the reflections of a reference pattern. When the water surface is deformed, it reflects a distorted image of the reference pattern, similar to a synthetic Schlieren setup. The distortions of the pattern are analysed using a suitable image correlation method. The displacement fields thus obtained correlate to the local spatial gradients of the water surface. The gradient fields are integrated in a least-squares sense to obtain a full instantaneous reconstruction of the water surface. This method is particularly useful when a solid object is placed just above water surface, whose presence makes the liquid surface otherwise optically inaccessible.