1. Imaging Techniques for Flow and Motion Measurement Lecture 14 Lichuan Gui University of Mississippi 2011 Central Difference Image Correction

2. PIV Recording with Distorted Image Pattern Correlation interrogation without window shift g 1 (i,j)g 2 (i,j) Correlation function of distorted image patterns No correlation high peak at the particle image displacement 2

3. = + Complex flowDistortionTanslation Complex flow that results in image distortion PIV Recording with Distorted Image Pattern - Pixel displacement = window shift + image distortion - Displacements of 9 points available with 50% window overlapping - Interpolation necessary to determine the image distortion function Image distortion function S dis (i,j) 3

4. Correlation interrogation with central difference window shift PIV Recording with Distorted Image Pattern Low contrast among correlation function high peaks f 1 (i,j) f 2 (i,j) Correlation function improved with window shift 4

5. Central difference window shift & image corection PIV Recording with Distorted Image Pattern Clear correlation function high peak at the particle image displacement f 1 (i,j) f 2 (i,j) Correlation function improved with window shift (red) & image correction (blue) 5

6. Central Difference Image Correction (CDIC) Pixel displacement functions 6

7. 9-point image corection method - Window shift determined with displacement in the window center, i.e. S ws =S 5 - Image distortion at the 9 points determined as - S dis (i,j) determined with interpolation according to S dis (k) - f(i,j) determined with interpolation according to S ws and S dis (i,j) - Particle image sisplacements at 9 points (S 1  S 9 ) determined according to a previus estimation 123 46 789 5 Interrogation window Central Difference Image Correction (CDIC) - Mutipass interrogation with iterated number around 6. 7

8. 4-point image corection method - Window shift determined with displacement in the window center, i.e. S ws =S 5 - Image distortion at the 4 points determined as - S dis (i,j) determined with bilinear interpolation according to S dis (k) - f(i,j) determined with bilinear interpolation according to S ws and S dis (i,j) - Particle image sisplacements at center and 4 corners (i.e. S 1, S 3, S 5, S 7, S 9 ) determined according to a previus evaluation 123 46 789 5 Interrogation window Central Difference Image Correction (CDIC) - Mutipass interrogation with iterated number aropund 6. 8

9. Central Difference Image Correction (CDIC) Tests on image corection methods Tested with synthetic PIV recordings of simulated 4-roll-mill flow - Mutipass interrogation conveges after 6 iterations - 9-piont method better with given (ideal) displacements - 4-piont method better with with nulti-pass interations - RMS evaluation error reduction more than 50% 9

10. 10 Test of CDIC with Four-Roll Mill Flow Top view Velocity field Without image correctionWith image correction 10

11. 9-Point CDIC: Adjust Window Shift Possible 9-point image corection methods 123 46 789 5 Interrogation window - Different ways to determine window shift S ws 11

12. Tests on image corection methods - Best in the ideal cases: 9P algorithm 0, i.e. - Best in iterated cases: 9P algorithm 3, i.e. Tested with synthetic PIV recordings of simulated periodical flow of wave length (L: window width) 9-Point CDIC: Adjust Window Shift 12

13. Different Base-algorithms for CDIC  Correlation interrogation better than correlation tracking for CDIC Test results with synthetic PIV recordings of simulated periodical flow 13

14. 14 Image Pattern Correction Options 1. Central difference window shift & central difference image correction (CDIC) Image interpolation required for both the two evaluation samples 2. Central difference window shift & forward difference image correction (FDIC) When x pix1 and y pix1 are set to integer numbers, image interpolation only required for the second evaluation sample

15. –Reading Wereley ST, Gui L (2003) A correlation-based central difference image correction (CDIC) method and application in a four-roll-mill flow PIV measurement. Exp. Fluids 34, 42-51 Gui L, Seiner JM (2004) An improvement in the 9-point central difference image correction method for digital particle image velocimetry recording evaluation. Meas. Sci. Technol. 15, 1598-1964 –Practice with EDPIV Application example #1 - follow instruction #1 - change evaluation settings to compare different results Application example #2 - follow instruction #2 - change evaluation settings to compare different results Homework 15