3D Measurements by PIV. PIV is 2D measurement 2 velocity components: out-of-plane velocity is lost; 2D plane: unable to get velocity in a 3D volume. Extending PIV to 3D?. Technique. Dimension of velocity field. Dimension of observation volume. Remark. Stereoscopic PIV. 3D. 2D.
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Dimension of velocity field
Dimension of observation volume
Recover out-of-plane velocity
Dual plane PIV
3D Scanning PIV
Time delayed measurement
Seldom used due to low resolution
True volumetric measurement with high ressolution
True 3D displacement (DX,DY,DZ) is estimated from a pair of 2D dis- placements (Dx,Dy) as seen from left and right camera respectively
Different parts of the plane cannot be all in focus
Share only partial field of view
The proper stereo recording geometry
Properly focusing the entire field of view with an off-axis camera requires tilting of the camera back-plane to meet the Scheimpflug condition
— The image, lens and object planes must cross each other along a common line in space
3D evaluation requires a numerical model, describing how objects in 3D space are mapped onto the 2D image plane of each of the cameras
- The pinhole camera model is based on geometrical optics, and leads to the so-called direct linear transformation (DLT)
- With the DLT model, coefficients of the A-matrix can in principle be calculated from known angles, distances and so on for each camera.
- In practice not very accurate, since, as any experimentalist will know, once you are in the laboratory you cannot set up the experiment exactly as planned, and it is very difficult if not impossible to measure the relevant angles and distances with sufficient accuracy.
Hence, parameters for the numerical model are determined through camera calibration
Images of a calibration target are recorded.
The target contains calibration markers (dots), true (x,y,z) positions are known.
Comparing known marker positions with corresponding marker positions on each camera image, model parameters are adjusted to give the best possible fit.
3D evaluation is possible only within the area covered by both cameras.
Due to perspective distortion each camera covers a trapezoidal region of the light sheet.
Careful alignment is required to maximize the overlap area.
Interrogation grid is chosen to match the spatial resolution.
Left & Right camera images are recorded simultaneously.
Conventional PIV processing produce 2D vector maps representing the flow field as seen from left & right.
Using the camera model including parameters from the calibration, the points in the chosen interrogation grid are now mapped from the light sheet plane onto the left and right image plane (CCD-chip) respectively.
The vector maps are re-sampled in points corresponding to the interrogation grid.
Combining left / right results, 3D velocities are estimated.
Overlap area withinterrogation grid
Resulting 3D vector map
Left 2D vector map
Right 2D vector map
two camera input