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

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

= + 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

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

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

Central Difference Image Correction (CDIC) Pixel displacement functions 6

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 Interrogation window Central Difference Image Correction (CDIC) - Mutipass interrogation with iterated number around 6. 7

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 Interrogation window Central Difference Image Correction (CDIC) - Mutipass interrogation with iterated number aropund 6. 8

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

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

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

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 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

–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, 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, –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