Global measurement of water waves by Fourier transform profilometry

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 x 300 mm(2) sampled on approximately 6.1 x 10(6) measurement points. Some illustrative examples of the application of this measuring system to fluid dynamics problems are presented.