3 D Measurements by PIV w PIV is

3 D Measurements by PIV w. PIV is 2 D measurement n n 2 velocity components: out-of-plane velocity is lost; 2 D plane: unable to get velocity in a 3 D volume. w. Extending PIV to 3 D?

Extension of PIV technique Technique Stereoscopic PIV Dimensio n of velocity field Dimension of observation volume Remark 2 D Recover out-of-plane velocity 3 D Time delayed measurement Dual plane PIV 3 D Scanning PIV 3 D PTV Holographic PIV 3 D Seldom used due to low resolution True volumetric measurement with high ressolution

3 D Scanning PIV Drum scanner 1) 2) 3) Scanning a volume to get the depth information Multiple frames recording and high-speed scanner are required Time lag between frames: quasi-3 D measurement Scanning volume Laser Camera

3 D Particle Tracking Velocimetry (PTV) 1) 2) 3) 4) Extracting 2 D particle locations from images captured from different views; Reconstructing 3 D particle locations according to the parameters of cameras and calibration information; Tracking 3 D particles in the volume to get the velocity Extremely low resolution (hundreds of velocity map in one volume): cannot overlap

Fundamentals of stereo vision True 3 D displacement (DX, DY, DZ) is estimated from a pair of 2 D displacements (Dx, Dy) as seen from left and right camera respectively

m Ca a er Angular arrangement: Different parts of the plane cannot be all in focus m Ca Camera Parallel arrangement: Share only partial field of view er a Types of Stereo recording geometry

The proper stereo recording geometry Properly focusing the entire field of view with an offaxis camera requires tilting of the camera backplane to meet the Scheimpflug condition — The image, lens and object planes must cross each other along a common line in space

Mapping from 2 D image back to 3 D 3 D evaluation requires a numerical model, describing how objects in 3 D space are mapped onto the 2 D 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

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.

Overlapping fields of view 3 D 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 2 D vector maps Left & Right camera images are recorded simultaneously. Conventional PIV processing produce 2 D 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, 3 D velocities are estimated.

3 D reconstruction Overlap area with interrogation grid Resulting 3 D vector map Left 2 D vector map Right 2 D vector map

Dantec 3 D-PIV system components w Seeding w PIV-Laser (Double-cavity Nd: Yag) w Light guiding arm & Lightsheet optics w 2 cameras on stereo mounts w Flow. Map PIV-processor with two camera input w Calibration target on a traverse w Flow. Manager PIV software w Flow. Manager 3 D-PIV option

Recipe for a 3 D-PIV experiment w Record calibration images in the desired measuring position (Target and traverse defines the co-ordinate system!) w Align the lightsheet with the calibration target w Record calibration images using both cameras w Record simultaneous 2 D-PIV vector maps using both cameras w Calibration images and vector maps is read into Flow. Manager w Perform camera calibration based on the calibration images w Calculate 3 D vectors based on the two 2 D PIV vector maps and the camera calibration

Camera calibration

Importing 2 D vector maps

3 D evaluation & statistics