Instructor: Lichuan Gui lichuan-gui@uiowa lcgui

1. Measurements in Fluid Mechanics058:180:001 (ME:5180:0001)Time & Location: 2:30P - 3:20P MWF 218 MLHOffice Hours: 4:00P – 5:00P MWF 223B-5 HL Instructor: Lichuan Gui lichuan-gui@uiowa.edu http://lcgui.net

2. Lecture 39. Stereo High-speed Motion Tracking

3. Stereo High-speed Motion Tracking • Stereo high-speed imaging system in wind tunnel test Test model- length: 7 inches (178 mm)- diameter: 0.7 inches (0.18 mm) High-speed cameras- lenses: 60mm Nikon Micro-Nikkor- 30 view angle difference- frame rate: up to 4000 fps- resolution: 1024X512 pixels Measurement volume- width: 305 mm- height: 152 mm- maximal depth: 104 mm Strobe light- Synchronized with camera

4. Stereo High-speed Motion Tracking • Stereo system coordinates Physical coordinates: (x, y, z) Image coordinates: (x*, y*) Camera coordinates: (x’, y’, H) Camera view angles: (, )

5. Stereo High-speed Motion Tracking • Calibrate stereo system with target shift 1. Image calibration target at z=0

6. Stereo High-speed Motion Tracking • Calibrate stereo system with target shift 2. Forward shifted target at zs /2

7. Stereo High-speed Motion Tracking • Calibrate stereo system with target shift 3. Backward shifted target at -zs /2

8. Stereo High-speed Motion Tracking • Calibrate stereo system with target shift Geometrical relations: Reduced equations for calibration points k=1,2,3,, N : Sum square difference function:

9. Stereo High-speed Motion Tracking • Calibrate stereo system with target shift Conditions for achieve a minimal sum square difference: Linear equation system to determine H and x’ : Equation to determine y’ :

10. Stereo High-speed Motion Tracking • Stereo coordinate reconstruction Camera coordinates: (x’a, y’a, Ha) for left camera, (x’b, y’b, Hb) for right camera Image coordinates: (xa, ya) for left camera, (xb, yb) for right camera Reconstructed physical coordinates: (x, y, z) Camera view angle at image frame center (x0, y0, z0):

11. Stereo High-speed Motion Tracking • 3D motion tracking Tracking variables- model center: (xc, yc, zc)- roll angle: - pitch angle: - yaw angle:  Surface marker local coordinates- L: axial coordinate - R: radius coordinate- : angular coordinate Surface marker coordinates (x, y, z)- image pattern tracking results Geometrical relations- three equations- known variables: (x, y, z, L, R, )- unknown variables: (xc, yc, zc, , , )- multiple surface markers required

12. Stereo High-speed Motion Tracking • Least square approach Available data - surface markers (Ln, Rn, n)- tracked position (xn, yn, zn)- n=1, 2, 3, …,M First step- determine ,  at minimum of D1(,  ) - yc determined accordingly Second step - determine  at the minimum of D2( )- xc determined accordingly Third step - determine zc with known variables

13. Stereo High-speed Motion Tracking • Simulated 3D motion - 7-inch revolving surface model, 120 frames- red image from left camera with view angle =15 , =3-green image for right camera with view angle =-22.5 , =-2 (300mmx150mm, =0-45, =0-20, =0-10)

14. Stereo High-speed Motion Tracking • Tracked surface makers - spherical dots & cross-sections of grid lines - combination of 18 surface markers for 9 test cases

15. Stereo High-speed Motion Tracking • Simulation results - 4-point results agree well with given values - coordinate biases < 0.5 mm - angular biases < 1

16. Stereo High-speed Motion Tracking • Simulation results - minimum of 3 surface marker required - 4 surface markers sufficient to achieve high accuracy - more markers not help because of add-in noises- discussion limited in high image quality cases

17. Stereo High-speed Motion Tracking • 4-point tracking method 1. Distribution of markers “1”, “2”, “3” and “4” - Plane “2-4-c” perpendicular to model axis(“c” on axis, may not be at center) - Point “2” and “4” at the same radius R - Sufficient angular difference between line “c-2” and “c-4” - Line “1-3” parallel to model axis - When line “1-3” not parallel to model axis, plane “1-c-3” line “2-4” 4-point method less sensitive to image noises than multi-point least square approach

18. Stereo High-speed Motion Tracking • 4-point tracking method 2. Pitch and yaw angle determined with line “1-3”that parallel to model axis

19. Stereo High-speed Motion Tracking • 4-point tracking method 3. Roll angle and “c” position determined in “2-4-c” plane Define midpoint “m” on line “2-4”: Line “c-m” determined with “c-m”“1-3” & “c-m”“2-4”: Length of “m-c”: Model position: Roll angle:

20. Stereo High-speed Motion Tracking • Experimental results - 80mm cylindrical model, 20mm diameter, 2000 fps, 1024x512 pixels- left image from left camera with view angle =16.0 , =-0.3- right image from right camera with view angle =-15.3 , =-.1

21. 21 Stereo High-speed Motion Tracking • Experimental results - x-motion: linear, dx/dt = -0.00 m/s- y-motion: parabolic, dy/dt2 = -9.25 m/s2- z-motion: linear, dz/dt = 0.16 m/s - roll angle: linear, d/dt = -3.00 r/s- pitch angle: linear, d/dt = -0.02 r/s- yaw angle: linear, d/dt = 0.05 r/s

22. Stereo High-speed Motion Tracking • Experimental results - 7” test model 0.7” in diameter- drop & bounce motion - 2000 fps w. 1024x512 pixels- playback at 30 fps - 551 frames in 275 ms- left camera with view angle =16 , =-0.3-right camera w. view angle =-15.3 , =-0.1

23. Stereo High-speed Motion Tracking • References • Lichuan Gui, Nathan E. Murray and John M. Seiner (2010) Tracking an aerodynamic model in a wind tunnel with a stereo high-speed imaging system. The 3rd International Congress on Image and Signal Processing (CISP’10), October 16-18, Yantai, China • Practice with EDPIV • Application example #a

24. Phase-resolved Stereo PIV Measurement - Experimental setup • Schematic illustration of the measurement system • PCO 2000 cameras , 26.7 fps @ 10241024 pixels • Nd:YAG laser up to 30 Hz • Air flow visualized with fog particles of micro-meters in diameter • 1271 stereo PIV recordings in each camera shot • 10,000 instantaneous 3D velocity maps for each test cases

25. Phase-resolved Stereo PIV Measurement - Experimental setup • Measurement planes Rear view Side view

26. Phase-resolved Stereo PIV Measurement - Experimental setup • Picture of the measurement system

27. Background image Phase information Particle image Velocity vector map Phase-resolved Stereo PIV Measurement - PIV image processing Low-pass filtering Original image Compare to guidelines Images pair correlation High-pass filtering

28. Phase-resolved Stereo PIV Measurement - Test results • Side view test results for a male fire ant Velocity distribution Vorticity distribution

29. Phase-resolved Stereo PIV Measurement - Test results • Rear view test result for a male fire ant Wing motion Velocity distribution

30. Phase-resolved Stereo PIV Measurement - Test results • Rear view test result for a male fire ant Wing motion Vorticity contours

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

32. Exercises for final exam • Please list two methods that can be used to identify evaluation errors in a vector map with regular grid. • Please explain how to use target vector method to correct evaluation errors. • What is the peak-locking effect? • What are the sources of the peak-locking effect? • Please suggest an algorithm with the least peck-locking. • Please list two methods that can be used to enable a phase-separated measurement with PIV. • Please list at least 5 particle image parameters that are determined with particle image identification and used to track particle images between two frames. • Please explain how to evaluate low image number density recording with high accuracy. • Please explain why micro PIV recordings usually have lower signal-to-noise ratio, and list at least two methods that can be used to increase the accuracy of the micro PIV. • Please briefly explain how the stereo PIV determines the particle image displacement component perpendicular to the measurement plane. • Please list advantages and disadvantages of the translation system and rotational system of stereo PIV.