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

Utkarsh Jain,Devaraj Van Der Meer,Anaïs Gauthier

doi:10.1007/s00348-021-03328-y

Utkarsh Jain, Devaraj Van Der Meer + Show 1 more

Open Access

https://doi.org/10.1007/s00348-021-03328-y

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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.Graphical abstract

Highlights

Measuring instantaneous free surface deformations of liquids is of general interest in several practical applications such as in coating and food industries, in large applications such as to study ship wakes, and in offshore engineering (Moisy et al 2009; Gomit et al 2013)
In general we have found it advantageous to first correct the grid in the camera images, such that the coordinates = (x, y) in the corrected camera images correspond to the coordinate system to the free surface
We described a TIR-based method to measure small-scale deformations of a water surface, consisting of two steps: first, the movement of the water surface is measured by recording the deformation of a reference pattern that is reflected in the water surface

Summary

Introduction

Measuring instantaneous free surface deformations of liquids is of general interest in several practical applications such as in coating and food industries, in large applications such as to study ship wakes, and in offshore engineering (Moisy et al 2009; Gomit et al 2013). The methods to quantitatively measure liquid surface behaviour may be broadly divided into two categories based on whether they are intrusive or not. Less intrusive methods that rely on flow velocities collected using a stereo particle-image-velocimetry setup have been shown to work for large-scale systems (Turney et al 2009; van Meerkerk et al 2020). Some nonintrusive methods for such measurements that only use reflections from the water surface and a set of multiple cameras for reconstruction have been developed (Benetazzo et al 2012; Wanek and Wu 2006)

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