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
Dimensi
on of
velocity
field
Dimension
of
observation
volume
Stereoscopic PIV
Remark
Recover out-of-plane velocity
2D
Dual plane PIV
3D Scanning PIV
3D
Time delayed measurement
3D
3D PTV
Seldom used due to low
resolution
Holographic PIV
True volumetric measurement
with high ressolution
3D 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-3D measurement
Scanning volume
Laser
Camera
3D Particle Tracking Velocimetry
(PTV)
1)
2)
3)
4)
Extracting 2D particle
locations from images
captured from different
views;
Reconstructing 3D particle
locations according to the
parameters of cameras and
calibration information;
Tracking 3D particles in the
volume to get the velocity
Extremely low resolution
(hundreds of velocity map in
one volume): cannot overlap
Fundamentals of stereo vision
Displacement
seen from left
True
displacement
Displacement
seen from right
Focal plane =
Centre of
light sheet
45°
Left
camera
45°
Right
camera
True 3D displacement (DX,DY,DZ) is estimated from a pair of 2D displacements (Dx,Dy) as seen from left and right camera respectively
Types of Stereo recording geometry
Displacement
seen from left
True
displacement
Displacement
seen from right
Focal plane =
Centre of
light sheet
45°
Camera
Camera
Parallel arrangement:
Share only partial field
of view
Left
camera
45°
Right
camera
Angular arrangement:
Different parts of the plane
cannot be all in focus
The proper stereo recording geometry
Object plane
(Lightsheet
plane)
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
Object
coordinates
(X,Y,Z)




Left image
coordinates
(x,y)
Right image
coordinates
(x,y)
Lens plane
left & right
Image plane
left & right
Mapping from 2D image back to 3D
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
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.
w0 X   a11 a12
 w Y   a
 0   21 a22
 w0  a31 a32
a13   wi x 
a23   wi y 
a33   wi 
Overlapping fields 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.
Right camera's
field of view
Left camera's
field of view
0.10
0.05
Overlap area
0.0
-0.05
-0.10
-0.15
-0.20
-0.20
-0.10
0.00
0.10
0.20
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
Overlap area with
interrogation grid
Resulting 3D vector map
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