Measurements in Fluid Mechanics 058:180:001 (ME:5180:0001) Time & Location: 2:30P - 3:20P MWF 218 MLH Office Hours: 4:00P – 5:00P MWF 223B-5 HL Instructor: Lichuan Gui Students are encouraged to attend the class. You may not be able to understand by just reading the lecture notes.

2 Lecture 31. 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 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) 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 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) 6

Central Difference Image Correction (CDIC) Pixel displacement functions 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 Interrogation window Central Difference Image Correction (CDIC) - Mutipass interrogation with iterated number around 6. 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 Interrogation window Central Difference Image Correction (CDIC) - Mutipass interrogation with iterated number aropund 6. 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% 10

11 Test of CDIC with Four-Roll Mill Flow Top view Velocity field Without image correctionWith image correction 11

9-Point CDIC: Adjust Window Shift Possible 9-point image corection methods Interrogation window - Different ways to determine window shift S ws 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 13

Different Base-algorithms for CDIC  Correlation interrogation better than correlation tracking for CDIC Test results with synthetic PIV recordings of simulated periodical flow 14

15 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

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, References 16

1.How many gray value levels are there in a 8-bit grayscale digital image? What are the minimal and maximal gray value? 2.Please estimate the minimal file size in bytes of a uncompressed true color image of 1024x1024 pixels. 3.What is the look-up table (LUT) of a digital color image? 4.What is the pixel operation and what is the filter operation in digital image processing? 5.Please describe two pixel operations that can be used to increase the contrast of digital images. 6.Please describe two digital filters that can be used to reduce the low frequency background noise in digital PIV recordings. 7.Please list basic components of standard 2D PIV system. 8.Please explain how to obtain a double exposed PIV recording and a single exposed PIV recording pair. 9.What is the traditional evaluation method for a double exposed PIV recording in positive photo film? 10.Please explain how to use auto-correlation algorithm to evaluate a double exposed digital PIV recording. 11.Please explain how to use cross-correlation algorithm to evaluate a single exposed digital PIV recording pair. 12.What are limitations of the correlation-based interrogation algorithm? 13.Please list advantages and disadvantages of the correlation-based tracking algorithm when compared to the correlation interrogation algorithm. 14.Please explain how to enable arbitrarily sized interrogation window when using radix-2 FFT to accelerate the correlation interrogation algorithm. 15.Please explain how to accelerate the correlation-based tracking algorithm with radix-2 FFT. 16.Please briefly describe the discrete and continuous window shift method and their advantages. 17.Please briefly describe the central difference interrogation (CDI) method and explain why it is better than the forward difference interrogation (FDI) method. 18.Please briefly describe the central difference image correlation (CDIC) method and its advantages. 19.Please explain how to determine the sub-pixel displacement. Exercises for final exam