1. 1 Imaging Techniques for Flow and Motion Measurement Lecture 11 Lichuan Gui University of Mississippi 2011 Interrogation Window Shift

2. 2 Reduced working region for correlation interrogation Interrogation Window Shift Evaluation error for ideal PIV recordings by using different algorithms with a 64x64-pixel interrogation window Original peak search radius usually M/3 or N/3 Reduced peak search radius o r r < o

3. 3 Discrete window shift (DWS) Interrogation Window Shift G 2 (x,y) o y x xmxm ymym o j i g 1 (i,j) S WS x m +x s y m +y s f 2 (i,j) o j i S S Cross-correlation of single exposed PIV recording pair

4. 4 Discrete window shift (DWS) Interrogation Window Shift Auto correlation of double exposed PIV recording No secondary maximum detected because of noises g(i,j)

5. 5 Cross-correlation of double exposed PIV recording Secondary maximum appears S ws Limited search area: <x s & <y s Discrete window shift (DWS) Interrogation Window Shift g(i,j)f(i,j)

6. 6 Discrete window shift (DWS) Interrogation Window Shift Determine initial window shift S WS Determine g 1 (i,j) Determine f 2 (i,j) Compute (m,n) from g 1 (i,j) and f 2 (i,j) Maximum search to determine S, S=S WS +S S small enough? S WS =S YES NO Too many iterations? NO YES Begin By previous knowledge or set to zero Usually 3 or 4 iterations Accelerated with FFT Sub-pixel fit End S: integer number of pixels DWS Flow Chart

7. 7 Continuous window shift (CWS) Interrogation Window Shift S ws ={I+x, J+y} – I,J: integer numbers – x and y: decimal numbers and 0 x<1;0 y< 1 BA DC ab cd g(i,j) I+i J+j i j f(i,j) x y Binlear interpolation Other interpolation methods available

8. 8 Continuous window shift (CWS) Interrogation Window Shift Determine initial window shift S WS Determine g 1 (i,j) Determine f 2 (i,j) Compute (m,n) from g 1 (i,j) and f 2 (i,j) Maximum search and sub-pixel fit to determine S, S=S WS +S S small enough? S WS =S YES NO Too many iterations? NO YES Begin By previous knowledge or set to zero Usually 4 to 6 iterations Accelerated with FFT End Bilinear interpolation or other CWS Flow Chart

9. 9 Evaluation error distribution of DWS and CWS Interrogation Window Shift Test of three different algorithms with synthetic PIV images Periodical functions of particle image displacement of 1-pixel period; DWS better than correlation tracking around integer-pixel displacements but worse around mid-pixel displacements CWS has much lower error level than DWS and correlation-based tracking

10. 10 –Practice with EDPIV Evaluate PIV recording D001_1.bmp with evaluation settings as - Exposure type: Double- Flow direction: E - Interrogation grid: 32x32- Error limits: Dx=4, Dy=2 - interrogation window: 64x64- Iteration number: 0,1 - Search radius: 20- Range limit: 20, 4, Absolute Remove erroneous vectors with 3x3 median filter - click menu Edit \ Vector filtering \ regular to select median filter Interpolate vectors - click menu Edit \ Vector interpolation \ With data in M0 Smooth vector map with 3x3 filter - click menu Edit \ Vector filtering \ regular to select smooth filter Save vectors into memory #1 - click menu Edit \ Save vectors into \ M1 Clear vectors and change evaluation settings as - Exposure type: Single- Window shift: M1 - Iteration number: 0,3- Search radius: 4 Evaluate the PIV recording with the interrogation window shift Homework