Holograph
g phic Particle
Image Ve
elocimetry
Michael Barry, Alish
ha Schor, Anna Shih
Mayy 6, 2009
Motivation
Image removed due to copyright restrictions. Please see Fig. 7
in Meng, Hui, et al. "Holographic Particle Image Velocimetry."
Measurement Science and Technology 15 (2004): 673-685
673 685.
Near field of a laminar je
jet
image from Meng et. al, 2000
Turbulent flow in a square duc
duct
Image from http://www.me.jhu.edu/meneveau/gallery.html
Courtesy of Bo Tao. Used with permission.
Holography - Basic
B
Principles
Recording
g
Reconstruction
Image removed due to copyright restrictions. Please see Fig. 1
in Meng,
g, Hui,, et al. "Holographic
g p
Particle Image
g Velocimetry."
y
Measurement Science and Techn
nology 15 (2004): 673-685.
3d information to 2d
representation
p
Reconstruct at
discrete z depths
image from Meng et. al, 2000
Basic Illumin
nation Types
In-Line
• ‘in-line’ reference beam
• simpler
p set up
p
• small diameter particles
Image removed due to copyright restrictions. Please see Fig. 6a,b
in Meng, Hui, et al. "Holographic Particle Image Velocimetry."
Measurement Science and Technology 15 (2004): 673-685.
Off A is
Off-Axis
•obliquely incident reference
beam
• real and virtual images
separate during reconstruction
reconstructio
• higher seeding densities
• for digital holography:
i id t angle
incident
l < 2°
2°
image from Meng et. al, 2000
Experimental Design Considerations
• Recording distance
e (Zhang 2006)
- If large z: low pas
ss filter
- If small z: limited FOV, aliasing
• Particle concentratiion (Kim,
(Kim 2008)
- Speckle noise vs. flow information
recovery
• CCD: size
size, pixel sizze
Experimen
ntal Setup
Camera
Flow
tank
Iris
Spatial
filter
Neutral density
f
filter
Diode laser
Collimating
lens
Raw Image
Cylinderr
Flow Direction
Crop initial image to
square
Reconstruc
ction Code
(Convolutio
on Method)
Take the Fourier
Transform
Reconstructed
R
t t d
image
Multiply this by the
Fresnel “diffraction
kernel”
Take the inverse
Fourier
Transform
exp{-iπλz (u2+v2)}
note the
dependence on z dept
depth
Reconstruc
cted
cted Image
Out of focus
particle
In focu
focus
particle
Reconstructtion
tion In Depth
p
Particle D
Detection
t1
t2
tn
Input: Time series of
raw holograms
1. Image Preproc
cessing
and Reconstrruction:
• Subtract
S bt t b
backg
kground
d
• Reconstruction
n
• Threshold
• Convert to B&W
W
2. Locate Particles in x
2
x-y:
-y:
• bwlabel (MATLAB)
• Bounding box and
a
centroid of contiguous
white zones
3. Eliminate invallid particles
3
• Outside of expeccted size
• Double-counting a single
particle
Output: matrix of labeled
particles with x-y position
of centers and area for
each zz-plane
plane
Lab
el
1
2
…
n
x
y
are
a
Particle Dete
Detection
ction (cont’d)
(cont d)
z1
z2
zn
x-y info
Input: xx-y
-y coordinate
matrices at each z-plane
1. Load output of
o
previous step
p
• zz-plane
plane is determined
by step size
2. Eliminate dou
ubles:
• Particles may appear in
focus in multiple
e planes
• Choose based on
o
minimum radiuss
Output: matrix of labeled
particles with x-y-z position
of centers and radius for
each time step
Label
x
y
z
radius
1
2
…
n
t
Result: 3
3D
D Flow
Flow
Calculating V
Velocity Maps
Map
• HPIV typically uses 3
3D coordinates as dat
data
- Computing cost of images is high (96 GB)
• Tradeoffs depending
g on complexity of flow,
mean velocit
velocity
- Correlation: complex flows, dense particle
seeding
- Particle tracking: lo
ow velocity flow
flows,
sparse seeding (re
educes speckle noise)
Velocity Maps
Map by Correlation
Correlatio
• Correlation (Pu & Meng,
M
2000)
noise
0
1
2
t1
1
0
2
4
3
3
4
t2
Two spatially shifted
images (time sequence
sequence)
t1t
1
10
1
0
1
1
0 0
0
0 1
3
1
33
3
3
3
2
2
2 2
4
4 2
2
4 4
4
4
t2t
2
t2t
2
Mean
Meandisplacement
displacementvector
vector
•
Shift images according to
o mean velocity vector
•
Within discrete interrogation windows, pair particles
based on closest distance
e, group deformation threshold
Velocity Map
ps by Particle
Trac
T cking
ki
• Pair particles by miinimizing a cost function
(Stellmacher & Obe
ermayer 2000)
• Utilize
Utili kknowledge
l d about
ab t flow:
fl
rr r
Yi = AX
AXi + t
• Cost function
J
K
E(m,t, A) = ∑ ∑ m jk Y j − t − AX k
j =1 k =1
2
J
K
j =1
k =1
+ g(A) + α ∑ m j (K +1) + α ∑ m( J +1)k
re
egularizer”
egularizer
Yk “re
Cost for unmatched particles
• Maximize expectatiion
Velocity Ma
Maps - Others
• Genetic algorithm p
pa
article pairing (Shen
(Sheng
and Meng 1998)
- Treat
T t pairings
ii
lik
like chromosomes
ch
- Choose “most fit” pairs
p
to p
propogate
p g
• Optical correlation (C
Coupland and Halliwell
1997)
- Expand 2D autocorrrelation to 3D
- Can utilize FFT
Velocity
y Maps
Map
Image from http://www.me.jhu.edu/lefd/hpivv/3d_vec.pdf
Courtesy of Bo Tao. Used with permission.
•
Questions?
Bibliog
graphy
•
Arroyo M; Hinsch K (2008) Recent developments
v
of PIV towards 3d
measurements. Topics Appl. Physics (112) 127-154
•
Hinsch KD (2002) Holographic image velocimetry. Meas. Sci. Technol. (13) R61R72
•
Kim S; Lee S (2008)
(
) Effect of particle numb
ber density
y in in-line digital
g
holographic
g
particle
velocimetry (44) 623-631
•
Meng H; Pan G; Pu Y; Woodward S (2
2004) Holographic particle image
velocimetry: from film to digital recordiing. Meas. Sci. Technol. (15) 673-685
•
Pu Y., Meng H. (2000) An advanced off-axis
o
holographic partcile image
velocimetry (HPIV) system). Exp in F luids (29) 184-197
•
Pu Y; Song X; Meng H (2000) Off
Off-axis
axiss holographic particle image velocimetry fo
for
diagnosing particulate flows. Exp in Fluids
F
[Suppl.] S117-S128
•
Sheng, J., Meng, H. (1998) A genetic algorithm particle pairing technique for 3D
g p
p
particle
image
g velocimetry.
y Exp
p in Fluids
velocityy field extraction in holographic
(25) 461-473
•
Stellmacher, M; Obermayer, K. (2000)) A new particle tracking algorithm based on
deterministic annealing and alternative
e distance measures. Exp in Fluids (28) 506518
•
Zhang Y; Shen G; Schroder A (2006) Influe
ence of some recording parameters on digital
holographic particle image velocimetry. Opttical Engineering (45) 075801
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