### Document

```Paths to 3D PIV

Through 2D Recording
Scanning
Multiple Projection
Digital
Image
Processor
Stroboscope

Through 3D Recording
Holography
Principle of HPIV
Recording
Laser
Pulse
Reconstruction
Laser
Beam
8ns
CCD
Interrogation
camera
Hologram
3D flow seeded with particles
Holocine (time resolved)
t1
t2
t3
Double Exposure
t1 t1+ Dt
t2 t2+ Dt
Displacement
Velocity
True 3D imaging
Instantaneous Volumetric
High Information Capacity
(106 - 109 Particles)
Real-Time Recording but Off-line Data Transfer
& Processing
How to get true 3D imaging?
Phase Preservation
O=Oexp[i(f-wt)]
or: O=Osin(f-wt)
How to record f?
Any light sensitive media records intensity
I=|O|2 =O2
Need to “encode” phase f into some intensity
modulation
Encoding Phase
-- Use interference of coherent light!
E
=
R
+
Reference wave
O
Object wave
where R = R exp[i(j-wt)] , O=Oexp[i(f-wt)]
Recorded Intensity:
I=|R+O|2 = R2 + O2 +2ROsin(f-j)
Principle of Holography
O
I =|R+O|2 = R2 + O2 +2ROsin(f-j)
Object
0
q
x
R
z
I =(R+O)(R+O)*
= R2 + O2 + R*O+RO*
Hologram
Recording
Virtual Image
O*
y
Real Image
0
q
x
Usually R= exp(-iwt)
T ~ 1 + O2 + O + O*
z
Hologram
Reconstruction
T ~ R2 + O2 + R*O+RO*
O
Experimental Demonstration
Reference beam, object beam
Virtual, real image
*Transmission or Reflection Hologram?
Setup Considerations:
Coherence length vs. path length difference
Exposure energy: In the linear range
R:O ratio
Transmission or Reflection Hologram
Transmission hologram
created by 2 plane waves
traveling towards the same
side
Reflection hologram
created by 2 plane waves
traveling towards opposite
sides
(Volume Hologram)
Reflection Hologram
Bragg Condition
2dsinq=ml
In-line (Gabor) Holography

Reference wave

Simple geometry
Low coherence &
energy requirement
LASER
Speckle noise
(limit seeding density
& seeding depth)
 Large depth of focus
(practically only 2D
vectors)

Object wave
Viral Image Real Image
LASER
Speckle Noise (in-line hologram)
Ok = S ok= Sk exp(ifk) : Random Walk
Reconstruction field of an in-line hologram for an ensemble of
particles: B + S ok+ S o*k
Type-I speckle -- interference between B and the scattered
waves Major Source of Speckle
Type-II speckle -- self-interference of the scattered waves.
Speckle noise: decrease Signal-toNoise Ratio
1 particle /mm3
6 particles /mm3
40 particles /mm3
Off-Axis Holography as Solution
In-Line HPIV:
Virtual
Image
Hologram
Reference
Beam
Hologram
Real
Image
Reference
Beam
Intrinsic Speckle Noise
Lower Seeding Density
Reconstruction
Recording
In-line HPIV
Reference
Beam
Reference
Beam
Hologram
Illuminating
Beam
Recording
Virtual
Image
Hologram
Off-axis HPIV
Reconstruction
Simple Geometry
Lower Coherence Required
Real
Image
Off-axis HPIV:
Higher SNR
Higher Seeding Density
Complex Geometry
Higher Coherence Required
IROV - In-line Recording Off-axis
Viewing Holography
Hologram
Referenc e
Beam
Virtual
Hologram
Im age
Real
Im age
Conventional
In-line
Referenc e
Beam
Recording
Reconstruction
IROV
IROV: Use side scattering
 Suppresses speckle noise
 Reduces image depth of focus
Meng & Hussain (1995): Appl. Opt. 34, 1827
Making In-line based
HPIV feasible
IROV Experimental Setup
Recording
Reconstruction
Use of High-Frequency Fringes on In-Line
Holograms
Negligible influence
of forward scattering:
Since |OL| << |R|,
IL << I sig
IROV suppresses speckle noise
Reconstruction field of an in-line hologram for an ensemble of
particles: B + S ok+ S o*k
•Completely avoids type-I
speckle
•greatly reduces type-II
speckle
Off-axis Viewing: receives only S o*k
Improved SNR by IROV
In-line Viewed
IROV
Reduction of Depth of Focus by IROV
+100 mm
In focus
-100 mm
0 degree
20 degree
In-line: Fraunhofer diffraction
Proof of Principle Experiment
IROV Measurement of a Vortex Ring
Post Processing
IROV Data Processing:
Genetic Algorithm Particle Pairing
 

Pi - Pi 
Vii 
, Pi  x, y, z   R3 
t2 - t1
Interrogation Cell
4’
3’
3
4
2
5
6’

1’
1
7
2’
5’
6
7’

Low density requires
intelligent pairing
GA searches large
solution space
Genetic Algorithm
Particle Pairing
Why Genetic Algorithm?
Many possibilities to pair particles
Need to numerate and filter
Large solution space
Conventional searching
methods
Computation intensive
Difficult to incorporate
intelligence
Time consuming
Genetic Algorithm
Efficient in searching large space
dynamics
Fast and inherent parallel processing
speed
Two Approaches of HPIV
Developed at LFD
Off-axis HPIV
high-end
In-line (IROV) HPIV
low-cost
Digital In-line Holography
Dual-Reference Off-Axis Technique
High Seeding Density Allowed
Small Depth of Focus
Image Separation Removes
Direction Ambiguity
Complex Optical Geometry
High Energy Laser Required
High Coherence of Beam
Needed
Gemini Off-axis HPIV System
HEM
Reference 2 Beam Expander
3D Traverse
System
Reference 1
Mirror
Beam Expander
Reference 1
HEM
PBS
PBS
Variable Beam Splitter HEM
HEM
BS
BS
HEM HEM HEM HEM
Beam Handling Unit
Dumper
Motion
Controller
Shutter 2
PCI Bus
HEM
200MHz
Pentium Pro
Processor
Beam Expander
Illuminating Beam
Motor
Driver
Digital Image
Framegrabber
Variable Beam Splitter HEM
WP
WP
HEM
Digital
Camera
Holographic
Reconstruction
Unit
Holographic Exposure Unit
Illuminating Beam
Reconstructed
Particle
Image
HEM
Beam Expander
Mirror
Hologram
Shutter 1
Synchronizer
Shutter 2
Digital
Delay
Generator
Hologram
Particle
Field
(Vortex)
Reference 2
Shutter 1
Mirror
Beam Expander
Dual Seeded YAG
Laser (PIV-400)
PBS
Mirror
Dual Seeded YAG
Laser (PIV-400)
PBS
Dumper
HEM
WP
WP
BS
BS
HEM HEM HEM HEM
Beam Handling Unit
Hard
Disk
64MB
Memory
Concise Cross Correlation
(CCC) Algorithm





Matching by particle groups
Uses particle centroids only
Group shifting for matching
Decomposition of operation
Low data volume / high
compression rate
 High-speed processing
System Test Flow
- Excited Air Jet
Beam Expander
Dual Seeded
YAG Laser
(PIV-400)
Digital Delay
Generator
PLL
Vaiable
Delayer
Object
Beam Vortex
Droplet-seeded
Injection Air Flow
Frequency
Multiplier
Waveform
Shaper
Vortex Synchronizer
Speaker/
Exciter
Power
Amplifier
Phase-Locked Vortex
Side View
Top View
Vorticity
Vorticity Iso-surface
Y
Z
X
30
00
25
00
20
00
15
00
10
00
50
0
0
0
0
0
50
50
00
10
10
00
15
15
00
20
20
00
25
25
00
30
30
00
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00
00
00
0
HPIV Measurement of Tab Wake
Vortab Flow: HPIV Measurement Result
 Amount of Data:
400,000 Vectors
 Mean Velocity:
16.67 cm/sec.
Vortab Flow: Vorticity Iso-Surfaces
Fundamental Challenges
Hologram captures 3D instantly
HPIV =
3D Information
Transfer & Processing
Turbulent
Flow Field
Flow Field
Reconstruction
3D Signal Decoding
Complex Flow Mapping
Large Data Quantity
User-friendly?

Holographic
Flow Visualization
a Tool for Studying 3D
Coherent Structures and Instabilities
Kansas State University, ISSI,
Wright Laboratory, WP/AFB
Off-Axis HFV of Vortex Flame
(a)
Holographic Images of
Three Vortex-Flame
Systems Photographed
from Two Angles (a)
or Using Two
Magnifications (b and
c).
(b)
(c)
IROV HFV of Turbulent Milk Drop
Holographic Images of A Milk Drop Undergoing Bag Instability (a, b)
a
b
c
Holographic Images of A Turbulent Milk Drop (a) and Its Downstream Breakdown (b, c)
Naturally, HPIV is an ideal
diagnostic tool for studying
particulate phase
- 3D and dynamically
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