Experiments in Fluids

, 46:1021 | Cite as

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

  • Frédéric MoisyEmail author
  • Marc Rabaud
  • Kévin Salsac
Research Article


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.


Particle Image Velocimetry Displacement Field Digital Image Correlation Surface Slope Wave Crest 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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”.


  1. Adrian RJ (1991) Particle-image techniques for experimental fluid mechanics. Annu Rev Fluid Mech 23:261–304CrossRefGoogle Scholar
  2. Andrieu C, Chatenay D, Sykes C (1995) Measuring dynamic contact angles. C R Acad Sci Paris 320:351–357Google Scholar
  3. Barron JL, Fleet DJ, Beauchemin SS (1994) Performance of optical flow techniques. Int J Comput Vis 12(1):43–77CrossRefGoogle Scholar
  4. Cox CS (1958) Measurement of slopes of high frequency wind waves. J Mar Res 16: 199–225Google Scholar
  5. Dabiri D, Gharib M (2001) Simultaneous free-surface deformation and near-surface velocity measurements. Exp Fluids 30:381CrossRefGoogle Scholar
  6. Dalziel SB, Hughes GO, Sutherland BR (2000) Whole-field density measurements by “synthetic Schlieren”. Exp Fluids 28:322–335CrossRefGoogle Scholar
  7. DaVis, by LaVision GmbH, Anna-Vandenhoeck-Ring 19, 37081 Goettingen, Germany, complemented with the PIVMat toolbox for Matlab.
  8. D’Errico J, “Inverse (integrated) gradient" for Matlab. File 9734
  9. Elwell FC (2004) Flushing of embayments. PhD thesis, University of CambridgeGoogle Scholar
  10. Hild F, Roux S (2006) Digital image correlation: from displacement measurement to identification of elastic properties—a review. Strain 42:69–80CrossRefGoogle Scholar
  11. Jähne B, Riemer KS (1990) Two-dimensional wave number spectra of small-scale water surface waves. J Geophys Res 95:11531–11546CrossRefGoogle Scholar
  12. Jähne B, Schmidt M, Rocholz R (2005) Combined optical slope/height measurements of short wind waves: principle and calibration. Meas Sci Technol 16:1937–1944CrossRefGoogle Scholar
  13. Keller WC, Gotwols BL (1983) Two-dimensional optical measurement of wave slope. Appl Opt 22:3476–3478CrossRefGoogle Scholar
  14. Kurata J, Grattan KTV, Uchiyama H, Tanaka T (1990) Water surface mesurement in a shallow channel using the transmitted image of a grating. Rev Sci Instrum 61(2):736CrossRefGoogle Scholar
  15. Lange PA, Jähne B, Tschiersch J, Ilmberger I (1982) Comparison between an amplitude-measuring wire and a slope-measuring laser water wave gauge. Rev Sci Instrum 53:651CrossRefGoogle Scholar
  16. Liu J, Paul JD, Gollub JP (1993) Measurements of the primary instabilities of film flows. J Fluid Mech 250:69–101CrossRefGoogle Scholar
  17. Meier GEA (2002) Computerized background-oriented Schlieren. Exp Fluids 33:181Google Scholar
  18. Moisy F, Rabaud M, Pinsolle E (2008) Measurement by digital image correlation of the topography of a liquid interface, ISFV13—13th international symposium on flow visualization, and FLUVISU12—12th French congress on visualization in fluid mechanics, paper 326, 1–4 July 2008, NiceGoogle Scholar
  19. Périe JN, Calloch S, Cluzel C, Hild F (2002) Analysis of a multiaxial test on a C/C composite by using digital image correlation and a damage model. Exp Mech 42:318–328CrossRefGoogle Scholar
  20. Raffel M, Willert CE, Kompenhans J (1998) Particle image velocimetry: a practical guide. Springer, HeidelbergGoogle Scholar
  21. Roesgen T, Lang A, Gharib M (1998) Fluid surface imaging using microlens arrays. Exp Fluids 25:126CrossRefGoogle Scholar
  22. Savalsberg R, Holten A, van de Water W (2006) Measurement of the gradient field of a turbulent free surface. Exp Fluids 41:629–640CrossRefGoogle Scholar
  23. Sutherland BR, Dalziel SB, Hughes GO, Linden PF (1999) Visualization and measurement of internal waves by ‘synthetic Schlieren’. Part 1. Vertically oscillating cylinder. J Fluid Mech 390:93–126zbMATHCrossRefGoogle Scholar
  24. Tober G, Anderson RC, Shemdin OH (1973) Laser instrument for detecting water ripple slopes. Appl Opt 12(4):788–794CrossRefGoogle Scholar
  25. Zhang X (1996) An algorithm for calculating water surface elevations from surface gradient image data. Exp Fluids 21:43–48CrossRefGoogle Scholar
  26. Zhang X, Cox CS (1994) Measuring the two-dimensional structure of a wavy water surface optically: a surface gradient detector. Exp Fluids 17:225–237zbMATHCrossRefGoogle Scholar
  27. Zhang X, Dabiri D, Gharib M (1996) Optical mapping of fluid density interfaces: concepts and implementations. Rev Sci Instrum 67(5):1858–1868CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Frédéric Moisy
    • 1
    • 2
    • 3
    Email author
  • Marc Rabaud
    • 1
    • 2
    • 3
  • Kévin Salsac
    • 1
    • 2
    • 3
  1. 1.Fluides, Automatique et Systèmes Thermiques (FAST)University of Paris-SudOrsayFrance
  2. 2.Fluides, Automatique et Systèmes Thermiques (FAST)University Pierre et Marie CurieOrsayFrance
  3. 3.Fluides, Automatique et Systèmes Thermiques (FAST)CNRSOrsayFrance

Personalised recommendations