Application of Image Restoration Technique in Flow Scalar Imaging

Experiments

Guanghua WangCenter for Aeromechanics Research

Department of Aerospace Engineering and Engineering Mechanics The University of Texas at Austin

April 28th, 2003

Flow scalar imaging experiments

! Resolution requirements

" λv and λD: smallest local length scales

! Resolution restrictions" CCD camera pixel spacing/size;

" Imaging system blurring effect (especially for FAST optics);

! In this project#Using image restoration technique to

correct imaging system blurring effect;

#Improve resolution and dissipation measurement accuracy;

Introduction

20 40 60 80 100 120

20

40

60

80

100

120

20 40 60 80 100 120

20

40

60

80

100

120

Scalar Dissipation

Acetone PLIF image

4/321

4/3

Re

Re−−

−

∝

∝

δ

δ

δλδλ

ScD

V

PLIF (Planar Laser Induced Fluorescence) image Red1/2=9600, Sc=1.5, [Tsurikov, 2002]

! Blurring model o(x,y) = i(x,y)**h(x,y) + n(x,y)! True image o(x,y) Flow Scalar field! LSI Filter h(x,y) Point Spread Function (PSF) of imaging system! Noise n(x,y) Additive noise, i.e. CCD camera readout noise

Inverse problem:

Blurring Model

# How to get o(x,y)o(x,y) ?" Known i(x,y) i(x,y) and PSF h(x,y)h(x,y)

" Prior knowledge of o(x,y) o(x,y) and n(x,y)n(x,y)

Prior Knowledge of the PLIF Image

! For acetone PLIF, differential cross section is 10-24 cm2/sr! High signal # Photon counting statistics noise is dominant;! True image o(x,y) # Shot-noise limited;! Poisson noise = Shot-Noise limited

From N2 tanks

Valve

Flow meter

Acetone bubblers

Gas heater

Fog machine Coflow blower

PIV camera

Jet facility

PLIF camera

Laser sheets

Sheet forming optics

PIV laser

PLIF laser

Timing electronics

Image acquisition computers

PLIF (Planar Laser Induced Fluorescence) Experiment Setup [Tsurikov, 2002]

Point Spread Function (PSF) Measurement

! SRFm & SRFcf: Measured & Curve-fitted

Step Response Function! LSF: Line Spread Function

! PSF: Point Spread Function

! MTF: Modulation Transfer Function MTFPSF

LSFSRFSRFtransformFourierIsotropic

dxdcf

fitcurvem

→ →

→ →

Scanning knife edge technique

References:"N.T. Clemens (2002)"W.J. Smith (2000)"T.L. Williams (1999)

Measured SRF, curve-fitted SRFcf and LSFfor a Nikon 105mm f/2.8 [Tsurikov, 2002]

x (mm)

SR

F(x

)

LSF

(x)

0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-8

-7

-6

-5

-4

-3

-2

-1SRF(x) MeasuredSRF(x) Curve fitLSF(x)

R-L-EM Algorithm! Richardson-Lucy Expectation

Maximization (R-L-EM)

! Richardson (1972) and Lucy (1974)

! Well developed in 1990’s for HST

(Hubble Space Telescope) image restoration" It converges to the Maximum Likelihood

(ML) solution for Poisson statistics in the image;

" The restored image is non-negative and flux is conserved at each iteration;

" The restored image is robust against small errors in the PSF;

! Constraints:" Non-negativity;

" Total-Flux conserved;" Finite spatial support;

" Band-limited;

1+= kk

0

),()0(

=k

yxo

∗

∗= ∗+ ),(

),(),(

),(),(),(

)()()1( yxh

yxoyxh

yxiyxoyxo

kkk

),()1( yxo k+

Results – Initial conditions

2.39E-01

7.72E-02

Observed Concentration field

-3-2

-10

12

3

-4

-2

0

2

40

0.05

0.1

0.15

0.2

Measured PSF

RR--LL--EM EM DeconvolutionDeconvolution

Stopping Rules

Noise Handling

O(x,y)O(x,y)

Starck, Pantin and Murtagh (2002)Molina, Nunez, Cortijo and Mateos (2001)Hanisch, White and Gilliland (1997)

Results – Convergence and Conservation

Number of Iterations

Rel

ativ

eE

rror

50 100 150 200 250 300 35010-3

10-2

10-1

100

Number of Iterations

Rat

ioof

To

talF

lux

50 100 150 200 250 300 3500.995

0.996

0.997

0.998

0.999

1

1.001

1.002

1.003

1.004

1.005

∑∑

=

yx

yx

k

yxi

yxo

RatioFluxTotal

,

,

)(

),(

),(

The blurring should not alter the total number of photons detected.

ε≤−+

),(

),(),()(

)()1(

yxo

yxoyxok

kk

Where ε is a small number"V. M. R. Banham and A. K. Katsaggelos (1997)

Results – Dissipation fields

ObservedDissipation

field

RestoredDissipation

field

Pixel

Dis

sip

atio

n

10 20 30 40 50 60 70 80 90 100 110 120

0

0.0001

0.0002

0.0003

0.0004

0.0005 Dissipation - RestoredDissipation - Observed

Pixel

Dis

sip

atio

n

10 20 30 40 50 60 70 80 90 100 110 120

0

0.0001

0.0002

0.0003

0.0004Dissipation - RestoredDissipation - Original

Vertical cut

Horizontal cut

3.51E-04

1.13E-05

3.51E-04

1.13E-05

Results – Dissipation fields

Observed Restored

Pixel

Dis

sip

atio

n

10 20 30 40 50 60 70 80 90 100 110 1200

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006 Dissipation - RestoredDissipation - Original

5.95E-04

1.92E-05

5.95E-04

1.92E-05

1.08E-03

3.49E-05

1.08E-03

3.49E-05

Pixel

Dis

sip

atio

n

10 20 30 40 50 60 70 80 90 100 110 1200

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

Dissipation - RestoredDissipation - Original

Cross-cut profile

What is the impact?

Buch and Dahm (1996), Sc=2075, Re= 2100, Fig.13 and Fig.28(b)

Conclusions and Future Work

! R-L-EM algorithm works well for PLIF image restoration" PLIF image is shot-noise limited (Poisson noise);" Measured PSF by scanning knife edge technique;

! Preliminary PLIF image restoration results show:" Peak dissipation rate is affected most, especially for thin and

clustered dissipation layers;! Image restoration techniques can be used to

" Improve resolution and dissipation measurement accuracy;" Especially for thin and/or clustered dissipation layers;

! Future work" Multi-Channel blind deconvolution # better PSF" Multi-Level deconvolution (i.e. wavelet-Lucy ) # better noise

handling;" Stopping rules # utilizing 2D scalar structure information;