1

Imaging Techniques for Flow and Motion Measurement

Lecture 19

Lichuan Gui

University of Mississippi

2011

Stereoscopic Particle ImageStereoscopic Particle Image

Velocimetry (SPIV)Velocimetry (SPIV)

2

Stereo PIV system– Two cameras– Translation and angular configurations– Distorted particle images (angular system)– 3-D displacement reduced from two 2-D displacements– 3 velocity components in a plane

Stereoscopic PIVStereoscopic PIV

Example

G. Calcagno, F.D. Felice, M. Felli, and F. Pereira, 24th Sym. Naval Hydro. (2002)

Test region

Test result

3

Laser light sheet X

Z

Stereoscopic PIVStereoscopic PIV SPIV data reduction

t=t0

t=t0+tS

Laser light sheet X

Z

S

XZ

Standard PIV view

X Z not sensible

4

Stereoscopic PIVStereoscopic PIV SPIV data reduction

Laser light sheet X

Z

S

XZ

1

X1

camera #1

X2

2

camera #2

11 tanZXX

22 tanZXX Stereo view

5

Stereoscopic PIVStereoscopic PIV SPIV data reduction

- Particle image displacements: (X’1, Y’1) and (X’2, Y’2)

- Imaging scale factor: M1 and M2

11 tanZXX

YYY 21

22 tanZXX

21

2211

tantan

XMXM

Z

21

221112

tantan

tantan

XMXM

X

22211 YMYM

Y

No stereo effect in yz-plane

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Stereoscopic PIVStereoscopic PIV Error propagation in SPIV

221 XX

X

221 YY

Y

22

2

22

2

11

2214

1XXXXX X

X

X

X

22

21

2

22

2

11

2

4

1YYYYY Y

Y

Y

Y

212

1

2

1XXX

212

1

2

1YYY

,2

1

1

X

X

2

1

2

X

X

,2

1

1

Y

Y

2

1

2

Y

Y

:,,For 212121 YYXX

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Stereoscopic PIVStereoscopic PIV Error propagation in SPIV

21

21

tantan

XX

Z

211 tantan

1

X

Z

212 tantan

1

X

Z

21

12

12

221

21

1 tantan

tan1tan1

tantan

ZXXZ

21

22

2 tantan

tan1

ZZ

2

22

2

11

2

22

2

11

2

ZZ

X

Z

X

ZXXZ

8

Stereoscopic PIVStereoscopic PIV Error propagation in SPIV

,cot2

1

21

X

Z

X

Z

tancot

2tan2

tan1 2

21

ZZZZ

:and,,2For 212121 XXX

2

22

2

11

2

22

2

11

2

ZZ

X

Z

X

ZXXZ

222

22 tancot2

cot

Z

X

ZZ

2

tancotDefine: ,cot XZ

222ZZZ

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Stereoscopic PIVStereoscopic PIV Error propagation in SPIV

[ ]

Z

/X

0 10 20 30 40 50 60 70 80 900

1

2

3

4

5

6

[ ]

[

]

10 20 30 40 50 60 70 800.0

1.0

2.0

3.0

4.0

5.0

6.0

0.5000.4750.4500.4250.4000.3750.3500.3250.3000.2750.2500.2250.2000.1750.1500.1250.1000.0750.0500.0250.000

Z/|Z|

- Optimal view angle 45

222ZZZ

,cot XZ

ZZ

2

tancot

10

Camera #1 Camera #2

Lens Plane

Stereoscopic PIVStereoscopic PIV

- Object plane || Lens plane || Image plane- Uniform magnification (Mn=di/do)- Easy to focus- Off-axis angle restricted by the lens (application limited)

Translation (lateral displacement) system

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Object plane Lens plane Image plane

Mirror pair 1

Mirror pair 1 Mirror pair 2

Mirror pair 2

Aperture stop

Stereoscopic PIVStereoscopic PIV Translation (lateral displacement) system

- Single camera configuration

- View angle is limited

Tes

t re

gio

n

Ima

ge #

1Im

age

#2

12

Stereoscopic PIVStereoscopic PIV Rotational (angular displacement) system- Scheimpflug condition - Distorted image (Mnconstant)

13

Stereoscopic PIVStereoscopic PIV SPIV recording evaluation

1. Evaluation with image calibration

Distorted Image Calibrated Image Velocity mapPositive: a. Uniform spatial resolution

b. Simple procedure

Negative: Image interpolation error

Image calibration methods

Polynomial mapping

Preservation of straightness of lines – for high quality camera lens

1,

1 54

876

54

321

ybxb

bybxbY

ybxb

bybxbX

65432

22

1

65432

22

1

bybxbxybybxbY

ayaxaxyayaxaX

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Stereoscopic PIVStereoscopic PIV SPIV recording evaluation

2.Evaluation with velocity calibration

Distorted Image Velocity map Velocity calibration

Positive: No image interpolation

Negative: a. Non-uniform spatial resolution

b. Evaluation grid transfer required

Basic evaluation steps:

1.Determine transformation function between physical and image plane

2.Transfer uniform evaluation grid in physical plane to image plane

3.Evaluate the distorted SPIV recordings with the transformed evaluation grid

4.Transfer the evaluated displacement components to the physical plane

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– References

• Prasad AK (2000) Stereoscopic particle image velocimetry. Exp. Fluids 29, pp. 103-116

• Willert C (1997) Stereoscopic digital particle image velocimetry for application in wind tunnel flows. Meas. Sci. Technol. 8, pp. 1465-1479

– Practice with EDPIV

• Compare image calibration and vector calibration with application example #9

HomeworkHomework