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

Utkarsh Jain*, Anaïs Gauthier, Devaraj Van Der Meer

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)
53 Downloads (Pure)


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: [Figure not available: see fulltext.]

Original languageEnglish
Article number235
JournalExperiments in fluids
Issue number11
Publication statusPublished - 22 Oct 2021


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