Spatio-temporal image-based parametric water surface reconstruction: a novel methodology based on refraction

This paper presents a low-cost and easy-to-implement image-based reconstruction technique for laboratory experiments, which results in a temporal description of the water surface topography. The distortion due to refraction of a known pattern, located below the water surface, is used to fit a low parameter surface model that describes the time-dependent and three-dimensional surface variation. Instead of finding the optimal water depth for characteristic points on the surface, the deformation of the entire pattern is compared to its original shape. This avoids the need for feature tracking adopted in similar techniques, which improves the robustness to suboptimal optical conditions and small-scale, high-frequency surface perturbations. Experimental validation, by comparison with water depth measurements using a level gauge and pressure sensor, proves sub-millimetre accuracy for smooth and steady surface shapes. Although such accuracy cannot be achieved in case of highly dynamic surface phenomena, the low-frequency and large-scale free surface oscillations can still be measured with a temporal and spatial resolution mostly limited by the available optical set-up. The technique is initially intended for periodic surface phenomena, but the results presented in this paper indicate that also irregular surface shapes can robustly be reconstructed. Therefore, the presented technique is a promising tool for other research applications that require non-intrusive, low-cost surface measurements while maintaining visual access to the water below the surface. The latter ensures that the suggested surface reconstruction is compatible with simultaneous image-based velocity measurements, enabling a detailed study of the flow.