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Global measurement of water waves by Fourier transform profilometry

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Abstract

In this paper, we present an optical profilometric technique that allows for single-shot global measurement of free-surface deformations. This system consists of a high-resolution system composed of a videoprojector and a digital camera. A fringe pattern of known characteristics is projected onto the free surface and its image is registered by the camera. The deformed fringe pattern arising from the surface deformations is later compared to the undeformed (reference) one, leading to a phase map from which the free surface can be reconstructed. Particularly, we are able to project wavelength-controlled sinusoidal fringe patterns, which considerably increase the overall performance of the technique and the quality of the reconstruction compared to that obtained with a Ronchi grating. In comparison to other profilometric techniques, it allows for single-shot non-intrusive measurement of surface deformations over large areas. In particular, our measurement system and analysis technique is able to measure free surface deformations with sharp slopes up to 10 with a 0.2 mm vertical resolution over an interrogation window of size 450 × 300 mm2 sampled on approximately 6.1 × 106 measurement points. Some illustrative examples of the application of this measuring system to fluid dynamics problems are presented.

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Notes

  1. As a matter of fact, these conditions are not necessary but strongly simplify the equations. Moreover, Chan et al. (1994) have showned that the parallel–optical-axes geometry provides a wider range of measurement.

  2. In the case of a transparent liquid, projection onto its free surface is attained by the addition of dye. See Sect. 3.1. for further details.

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Authors and Affiliations

  1. Laboratoire de Physique et Mécanique des Milieux Hétérogènes, UMR CNRS 7636, École Supérieure de Physique et de Chimie Industrielles, 10 rue Vauquelin, 75231, Paris Cedex 05, France

    Pablo Javier Cobelli & Philippe Petitjeans

  2. Laboratoire Ondes et Acoustique, UMR CNRS 7587, École Supérieure de Physique et de Chimie Industrielles, 10 rue Vauquelin, 75231, Paris Cedex 05, France

    Agnès Maurel

  3. Laboratoire d’Acoustique de l’Université du Maine, UMR CNRS 6613, Avenue Olivier Messiaen, 72085, Le Mans Cedex 9, France

    Vincent Pagneux

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  1. Pablo Javier Cobelli
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  2. Agnès Maurel
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  3. Vincent Pagneux
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  4. Philippe Petitjeans
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Correspondence to Pablo Javier Cobelli.

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Cobelli, P.J., Maurel, A., Pagneux, V. et al. Global measurement of water waves by Fourier transform profilometry. Exp Fluids 46, 1037–1047 (2009). https://doi.org/10.1007/s00348-009-0611-z

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  • DOI: https://doi.org/10.1007/s00348-009-0611-z

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