Total-internal-reflection deflectometry for measuring small deflections of a fluid surface

TL;DR

This paper introduces a highly sensitive optical method using total internal reflection to measure tiny deflections of a water surface, enabling detailed surface reconstruction even with an object nearby.

Contribution

It presents a novel total internal reflection deflectometry technique that detects small surface disturbances through pattern distortion analysis, suitable for complex environments.

Findings

High sensitivity to small surface disturbances

Accurate surface gradient and shape reconstruction

Effective with objects close to the water surface

Abstract

We describe a method that uses total internal reflection at the water-air interface inside a large, transparent tank, to measure the interface's deflections. Using this configuration, we obtain an optical set-up where the liquid surface acts as a deformable mirror. The set-up 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 set-up. 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.