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?

Extension of PIV technique

Technique Dimension of

velocity field

Dimension of

observation volume

 Remark

Stereoscopic PIV   

3D

 2D

Recover out-of-plane velocity

Dual plane PIV

3D Scanning PIV  3D 

Time delayed measurement

3D PTV Seldom used due to low resolution

Holographic PIV True volumetric measurement with high ressolution

3D Scanning PIV

Laser

Cam

era

Drum scanner

1) Scanning a volume to get the depth information

2) Multiple frames recording and high-speed scanner are required

3) Time lag between frames: quasi-3D measurement

Scanning volume

3D Particle Tracking Velocimetry (PTV)

1) Extracting 2D particle locations from images captured from different views;

2) Reconstructing 3D particle locations according to the parameters of cameras and calibration information;

3) Tracking 3D particles in the volume to get the velocity

4) Extremely low resolution (hundreds of velocity map in one volume): cannot overlap

Fundamentals of stereo vision

True 3D displacement (X,Y,Z) is estimated from a pair of 2D dis- placements (x,y) as seen from left and right camera respectively

45° 45°

Truedisplacement

Displacementseen from left

Displacementseen from right

Focal plane =Centre oflight sheet

Leftcamera

Rightcamera

Types of Stereo recording geometry

Cam

era

Cam

era

45° 45°

Truedisplacement

Displacementseen from left

Displacementseen from right

Focal plane =Centre oflight sheet

Leftcamera

Rightcamera

Camera Cam

era

Parallel arrangement:Share only partial field of view

Angular arrangement:Different parts of the plane cannot be all in focus

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

Objectcoordinates(X,Y,Z)

Object plane(Lightsheetplane)

Lens planeleft & right

Left imagecoordinates(x,y)

Right imagecoordinates(x,y)

Image planeleft & right

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

Mapping from 2D image back to 3D

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.

i

i

i

w

yw

xw

a

a

a

a

a

a

a

a

a

w

Yw

Xw

33

23

13

32

22

12

31

21

11

0

0

0

Overlapping fields of view

Overlap area

-0.20 -0.10 0.00 0.10 0.20

-0.20

-0.15

-0.10

-0.05

0.0

0.05

0.10

Right camera'sfield of view

Left camera'sfield of view

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 2D vector maps

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.

3D reconstruction

Resulting 3D vector map

Overlap area withinterrogation grid

Left 2D vector map Right 2D vector map

Dantec 3D-PIV system components

Seeding

PIV-Laser(Double-cavity Nd:Yag)

Light guiding arm &Lightsheet optics

2 cameras on stereo mounts

FlowMap PIV-processor with two camera input

Calibration target on a traverse

FlowManager PIV software

FlowManager 3D-PIV option

Recipe for a 3D-PIV experiment

Record calibration images in the desired measuring position(Target and traverse defines the co-ordinate system!)

Align the lightsheet with the calibration target

Record calibration images using both cameras

Record simultaneous 2D-PIV vector maps using both cameras

Calibration images and vector maps is read into FlowManager

Perform camera calibration based on the calibration images

Calculate 3D vectors based on the two 2D PIV vector maps and the camera calibration

Camera calibration

Importing 2D vector maps

3D evaluation & statistics