Application of Image Restoration Technique in Flow Scalar Imaging Experiments Guanghua Wang

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1 Application of Image Restoration Technique in Flow Scalar Imaging Experiments Guanghua Wang Center for Aeromechanics Research Department of Aerospace Engineering and Engineering Mechanics The University of Texas at Austin April 28 th, 23

2 Introduction Acetone PLIF image Scalar Dissipation PLIF (Planar Laser Induced Fluorescence) image Re d1/2 =96, Sc=1.5, [Tsurikov, 22] Flow scalar imaging experiments! Resolution requirements λ λ V D δ Re δ Sc 3/ 4 δ 1 2 " λ v and λ D : smallest local length scales! Resolution restrictions " CCD camera pixel spacing/size; " Imaging system blurring effect (especially for FAST optics);! In this project Re 3/ 4 δ #Using image restoration technique to correct imaging system blurring effect; #Improve resolution and dissipation measurement accuracy;

3 Blurring Model! Blurring model o(x, = i(x,**h(x, + n(x,! True image o(x, Flow Scalar field! LSI Filter h(x, Point Spread Function (PSF) of imaging system! Noise n(x, Additive noise, i.e. CCD camera readout noise Inverse problem: " Known i(x, and PSF h(x, " Prior knowledge of o(x, and n(x, # How to get o(x,?

4 Prior Knowledge of the PLIF Image From N 2 tanks Valve PLIF camera Sheet forming optics Flow meter Acetone bubblers Laser sheets PIV camera PLIF laser PIV laser Gas heater Jet facility Fog machine Coflow blower Timing electronics! For acetone PLIF, differential cross section is 1-24 cm 2 /sr! High signal # Photon counting statistics noise is dominant;! True image o(x, # Shot-noise limited;! Poisson noise = Shot-Noise limited Image acquisition computers PLIF (Planar Laser Induced Fluorescence) Experiment Setup [Tsurikov, 22]

5 Point Spread Function (PSF) Measurement SRF (x) SRF(x) Measured SRF(x) Curve fit LSF(x) x(mm) Measured SRF, curve-fitted SRF cf and LSF for a Nikon 15mm f/2.8 [Tsurikov, 22] Scanning knife edge technique References: "N.T. Clemens (22) "W.J. Smith (2) "T.L. Williams (1999)! SRF m & SRF cf : Measured & Curve-fitted Step Response Function curve fit d dx! LSF: Line Spread Function SRFm SRFcf LSF! PSF: Point Spread Function Isotropic Fourier transform! MTF: Modulation Transfer Function PSF MTF LSF(x)

6 k o ( k + 1) = k + 1 R-L-EM Algorithm o () k = ( k ) i( x, = o h ( k ) h( x, o ( 1) o k+! Richardson-Lucy Expectation Maximization (R-L-EM)! Richardson (1972) and Lucy (1974)! Well developed in 199 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;

7 Results Initial conditions Observed Concentration field 2.39E-1.2 Measured PSF E Noise Handling R-L-EM Deconvolution Stopping Rules Starck, Pantin and Murtagh (22) Molina, Nunez, Cortijo and Mateos (21) Hanisch, White and Gilliland (1997) O(x,

8 Results Convergence and Conservation Relative Error o ( k + 1) o o ( k ) ( k ) ε Where ε is a small number "V. M. R. Banham and A. K. Katsaggelos (1997) Ratio of Total Flux Number of Iterations Number of Iterations Total Flux Ratio = x, y o x, y ( k ) i( x, The blurring should not alter the total number of photons detected.

9 Results Dissipation fields 3.51E-4.4 Dissipation - Restored Dissipation - Original Observed Dissipation field Dissipation.3.2 Horizontal cut E Pixel Restored Dissipation field 3.51E-4 Dissipation.5 Dissipation - Restored Dissipation - Observed Vertical cut E Pixel

10 Results Dissipation fields Observed Restored 5.95E E-4 Cross-cut profile.6 Dissipation - Restored Dissipation - Original.5 Dissipation E E Pixel 1.8E E-3.1 Dissipation - Restored Dissipation - Original.8 Dissipation E E Pixel

11 What is the impact? Buch and Dahm (1996), Sc=275, Re= 21, Fig.13 and Fig.28(b)

12 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;