# A synthetic Schlieren method for the measurement of the topography of a liquid interface

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## Abstract

An optical method for the measurement of the instantaneous topography of the interface between two transparent fluids, named free-surface synthetic Schlieren (FS-SS), is characterised. This method is based on the analysis of the refracted image of a random dot pattern visualized through the interface. The apparent displacement field between the refracted image and a reference image obtained when the surface is flat is determined using a digital image correlation (DIC) algorithm. A numerical integration of this displacement field, based on a least square inversion of the gradient operator, is used for the reconstruction of the instantaneous surface height, allowing for an excellent spatial resolution with a low computational cost. The main limitation of the method, namely the ray crossing (caustics) due to strong curvature and/or large surface-pattern distance, is discussed. Validation experiments using a transparent solid model with a wavy surface or plane waves at a water–air interface are presented, and some additional time-resolved measurements of circular waves generated by a water drop impact are discussed.

## Keywords

Particle Image Velocimetry Displacement Field Digital Image Correlation Surface Slope Wave Crest## Notes

### Acknowledgments

The authors whish to thank Harold Auradou, Raphael Pidoux, Edouard Pinsolle, Joran Rolland and Jacopo Seiwert for their help during the experiments, Maurice Rossi for enlightening comments on the optical part, and the Reviewers for pointing key references. Guy Demoment and John D’Errico are also acknowledged for fruitful discussions about the algorithm of inversion of the gradient operator, and Francois Lusseyran and Luc Pastur for interesting discussions about the use of Optical Flow algorithms. This work was supported by the ANR grant no. 06-BLAN-0363-01 “HiSpeedPIV”.

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