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Free-Surface Synthetic Schlieren (FS-SS): A tutorial

By F. Moisy and M. Rabaud

September 10, 2008.

1. What is FS-SS?

Free-Surface Synthetic Schlieren (FS-SS) is an optical method developed for the measurement of the instantaneous topography of the interface between two transparent fluids.

This method is based on the analysis of the refracted image of a random dot pattern visualized through the interface, as in classical Synthetic Schlieren (SS) or Background-Oriented Schlieren (BOS). The surface gradient field is obtained from the apparent displacement between the refracted image and a reference image obtained when the surface is flat, and the surface topography is reconstructed by a least-square inversion of this gradient field.

Details about this method can be found in Moisy, Rabaud and Salsac (2009), and some applications are described in this page.

2. About this tutorial

An FS-SS system needs an imaging system, a Digital Image Correlation (DIC) algorithm or equivalent, and an integration algorithm for the surface height reconstruction. Several commercial and open-source solutions exist for DIC and for the integration procedure, and the system described here should be easily reproduced using different solutions.

The present tutorial aims to implement a FS-SS system under Windows based on the following tools:

(The first two ones are commercial softwares, the third one is freeware). Only the basic steps are given here; details concerning the parameters for the DIC computations or the surface height reconstruction can be found in the user manuals of those softwares.

DIC algorithms for DaVis are available either in the FlowMaster (for PIV) or StrainMaster packages. The present tutorial is based on the FlowMaster package, but can be probably easily reproduced with the StrainMaster package.

3. Design of the random dot pattern

The requirements for the random dot pattern for FS-SS applications are the same as for standard SS or BOS applications.

Best results for the Digital Image Correlation (DIC) are obtained for a pattern satisfying the following criteria:

  • At least 5 dots ('particles') per interrogation window (IW)
  • Typical displacement of about 1/3 of the IW size
Under typical conditions, interrogation windows are 16x16 pixels, and contain dots of diameter 2-5 pixels, with displacements of order of 5 pixels.

The random dot pattern can be numerically generated under Matlab using the function makebospattern, following this procedure:

  • Download makebospattern.m into a directory recognized by your Matlab installation (this function is already present in the PIVMat toolbox).
  • Type makebospattern(50000,1,'w','myfig') to produce a Synthetic Schlieren pattern made of 50000 white dots of 1 mm diameter on a black ground, and save it as myfig.tif.
  • Type doc makebospattern for more details about this function.
  • Print the TIF file on normal paper or overhead transparency, using a standard Windows viewer.

The printed pattern is usually located below the interface, and is imaged from above. The pattern, when imaged by the camera, should look like the example of Fig. 1. See the reference paper (Moisy et al, 2009) for details or hints about the optical setup.

Fig. 1 Magnifications at scales 1:1 (a) and 20:1 (b) of the random dot pattern used in the present experiments, as imaged by the 2048^2 pixels camera on a 14 x 14 cm field. Dots of diameter d = 0.4 mm were numerically generated, with a density of 50%, resulting in dots of approximately 6 pixels in the camera sensor. The magnification (b) represents 32 x 32 pixels, and 4 interrogation windows of size 16 x 16 pixels, used for the Digital Image Correlation, are shown for reference. From Moisy et al (2009).

4. Image acquisition and import

First, take the images with your usual imaging system:

  • Take one picture of the pattern through the fluid layer at rest (horizontal surface).
  • Take one picture or a series of pictures (movie) of the pattern through the fluid layer under the experimental conditions you wish to investigate.

Second, import the images into DaVis:

  • Under DaVis, create a project of type 'PIV', say MyExperiment, and open it.
  • Click on Import and select your images, such that the first one is the reference image (flat interface) and the following ones are for deformed interface. Once imported, you can navigate through yours images using DaVis, as shown in Fig. 2.
  • In the Windows explorer, check that your reference image has been named B00001.IM7, and that the following ones have been named B0000n.IM7, with n = 2..N.

Last, calibrate the images:

  • Step 1: Define experimental setup. Click on 'Calibrate', choose 'define scale, no image distortion'.
  • Step 2: Load one of your images. Use the 1st or 2nd icon 'Scale' to define the pixel-mm calibration. Click on 'finish', and choose 'Overwrite active project ... AND rescale all root image...'. This will write the calibration directly into each .IM7 file.

Fig. 2 Images of the pattern as imported in DaVis.

5. Computation of the displacement field

  • Under DaVis, select the set containing your images and enter the Batch mode (Fig. 3).
  • In the Operation list, set Operation 1 as:
    • Group: copy and reorganize
    • Operation: create multiframes from time series
    • Parameter> Mode: create (n-1) images: 1+2, 1+3, 1+4 (not 1+2, 2+3, 3+4!)
    • Storage mode: off
    (Note that this mode is available only since DaVis If your version is older, please upgrade.)
  • In the Operation list, set Operation 2 as:
    • Group: vector field computation
    • Operation: PIV (Particle Image Velocimetry)
    • Set your parameters for the Vector calculation and Vector postprocessing (see the DaVis manual for details).
  • Click on Start Processing; once done, close the Batch processing mode.

Fig. 3 Typical DaVis screen in 'Batch processing' mode. The bottom-right panel shows the displacement field computed by DIC from the images in the bottom left panel. The 'Operation list' dialog box is at the top middle.

6. Surface height reconstruction

This last step is performed under Matlab. First install the PIVMat toolbox available here (don't forget to also install the ReadIMX package from LaVision: Read carefully the installation instructions for PIVMat).

Once the toolbox is installed, follow the instructions:

  • Set the Current Directory as the subdirectory of the DaVis project where the vector fields have been stored (files in the form B0000n.VC7, with n=1..N-1)
  • Load the vector fields into a Matlab structure array: dr=loadvec('*');. See loadvec for details. dr is a structure array (see the Matlab reference manual to learn about structure arrays).
  • Compute the surface height: h=surfheight(dr, h0); where h0 is the surface-pattern distance (in mm). See surfheight for details.
  • Type showf(h) to display the reconstructed surface height (see Fig. 4). See showf for details.
  • Type save('mysurface.mat','h'); to save the result in a Mat-file.
  • The values of the surface height at each point of the domain are stored in the matrix h(n).w, with n the image number.

Fig. 4 Typical Matlab screen, showing the DaVis .VC7files (left), the commands used to import, compute the surface height and display (bottom), and the result (top).

7. Conclusion

That's all. Please feel free to send an email to F. Moisy to report a bug or suggest improvements.

Note: DaVis runs only on Windows. Matlab runs under any operating system, but the import of DaVis files into Matlab can be performed only on Windows. However, the DaVis files may be first converted into Matlab files, so that the surface reconstruction procedure can be performed under any operating system (e.g., Linux/Mac).

8. Acknowledgments

The FS-SS method has been developed with the experimental help of R. Pidoux, J. Rolland, K. Salsac and E. Pinsolle. We thank fruitful discussions with G. Demoment, M. Rossi, and the referees of the paper Moisy et al (2009). J. D'Errico has provided the least-square inverse gradient algorithm for Matlab (see File 9734 on the Matlab Central server), which has been included in the PIVMat toolbox. The developper team of LaVision is also thanked for adding the 'create multiframes from time series' option in the operation list (see Sec. 5).

9. References

  • Crosswaves induced by the vertical oscillation of a fully immersed vertical plate
    F. Moisy, G.-J. Michon, M. Rabaud, E. Sultan, Phys. Fluids 24, 022110 (2012).
    [Abstract | PDF | movies]
  • Unpredictable tunneling of a classical wave-particle association
    A. Eddi, E. Fort, F. Moisy, Y. Couder, Phys. Rev. Lett. 102, 240401 (2009).
  • A Synthetic Schlieren method for the measurement of the topography of a liquid interface
    F. Moisy, M. Rabaud, K. Salsac, Exp. in Fluids 46 (6), 1021-1036 (2009).
  • Measurement by Digital Image Correlation of the topography of a liquid interface
    F. Moisy, M. Rabaud, E. Pinsolle, ISFV13 - 13th International Symposium on Flow Visualization, and FLUVISU12 - 12th French Congress on Visualization in Fluid Mechanics, Paper #326, July 1-4, 2008, Nice (2008).
  • Optical measurement of ship waves by Digital Image Correlation
    M. Rabaud, F. Moisy, International Conference on Innovation in High Performance Sailing Yachts, 29-30 May 2008, Lorient, France, ISBN 978-1-905040-46-9e, pages 23-25 (2008).
  • Mesure de la déformation d’une surface libre par analyse du déplacement apparent d’un motif aléatoire de points
    M. Rabaud, F. Moisy and J. Rolland, Congrès Français de Mécanique (2007).

Last modification: April 19 2013, 12:56:24.