FreeSurface Synthetic Schlieren (FSSS): A tutorial
1. What is FSSS?
FreeSurface Synthetic Schlieren (FSSS) 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 BackgroundOriented 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 leastsquare 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 FSSS 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 opensource 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 FSSS 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 FSSS 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 25 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.
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 pixelmm calibration. Click on 'finish', and choose 'Overwrite active project ... AND rescale all root image...'. This will write the calibration directly into each .IM7 file.
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 (n1) 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 7.2.2.224.
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.
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..N1)
 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 surfacepattern 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 Matfile.
 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.
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 FSSS 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 leastsquare 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 waveparticle association
A. Eddi, E. Fort, F. Moisy, Y. Couder, Phys. Rev. Lett. 102, 240401 (2009).
[Abstract]
 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), 10211036 (2009).
[PDF]
 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 14, 2008, Nice (2008).
[PDF]

Optical measurement of ship waves by Digital Image Correlation
M. Rabaud, F. Moisy, International Conference on Innovation in High
Performance Sailing Yachts, 2930 May 2008, Lorient, France,
ISBN 9781905040469e, pages 2325 (2008).
[PDF]

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).
[PDF]
