Figure 1
Principle of DPIV: A laser sheet illuminates the particles contained in the fluid. A high-speed camera records the displacement of the particle pattern.
Figure 2
DPIV analyses in PIVlab. Overview of the workflow and the implemented features that are presented in the next sections.
Figure 3
The effect of several pre-processing techniques, see text for a description.
Figure 4
Calculation of the correlation matrix using DCC as it is performed in MATLAB. Interrogation area A (size 4·4 pixels) is correlated with interrogation area B (size 8·8 pixels) and yields the correlation matrix (size 9·9 pixels). Adapted from [8].
Figure 5
Correlation matrices of the DCC (top) and the DFT approach (bottom), interrogation area A is 64·64 pixels for both DCC and DFT. Area B is 128·128 pixels in DCC and 64·64 pixels in DFT. In DCC, the background noise does not increase up to a displacement of 32 pixels. In DFT, background noise immediately increases if the displacement is larger than 0 pixels. A displacement of more than 32 pixels will flip the correlation peak to the opposite side of the correlation matrix, and thus makes correct measurements impossible.
Figure 6
A: Calculation speed of DCC in comparison with DFT (both calculations performed in MATLAB). For the FFT calculations, FFTW is used [17] which accepts inputs of arbitrary size, but is slow for sizes that are prime or which have large prime factors (note the peaks in the graph). Generally, the DFT approach is much faster. B: Principle of the window deformation technique. Left: After the first interrogation pass, displacement information is present at nine positions inside the interrogation area. This information is interpolated to derive the displacement of every pixel of the interrogation area. Subsequently, interrogation area B is deformed, followed by several additional interrogation passes.
Figure 7
Principle of the Gaussian 2·3-point fit: Sub-pixel precision is achieved by fitting a one-dimensional Gaussian function (solid line) to the integer intensity distribution of the correlation matrix (dots) for both axes independently (only one axis is shown here).
Figure 8
Procedure for testing several interpolation techniques. Left: Original velocity data. Middle: Data is removed at random positions. Right: Gaps are filled with interpolation and compared to the original velocity data.
Figure 9
Performance of popular interpolators. The boundary value solver performs best under the presence of larger amounts (> 10%) of missing data. n = 1000.
Figure 10
Validation of smoothing algorithms. Left: Maximum absolute difference between the calculated velocities and the true velocities in percent of the maximum true velocity. Right: Mean absolute difference. n=250.