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

2 Lecture 39. Stereo High-speed Motion Tracking

3 –Stereo high-speed imaging system in wind tunnel test Stereo High-speed Motion Tracking 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

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

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

2. Forward shifted target at z s /2 –Calibrate stereo system with target shift 6 Stereo High-speed Motion Tracking

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

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

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

–Stereo coordinate reconstruction 10 Camera coordinates: (x’ a, y’ a, H a ) for left camera, (x’ b, y’ b, H b ) for right camera Image coordinates: (x a, y a ) for left camera, (x b, y b ) for right camera Reconstructed physical coordinates: (x, y, z) Camera view angle at image frame center (x 0, y 0, z 0 ): Stereo High-speed Motion Tracking

11 –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 Stereo High-speed Motion Tracking

12 Available data - surface markers (L n, R n,  n ) - tracked position (x n, y n, z n ) - n=1, 2, 3, …,M First step - determine ,  at minimum of D 1 ( ,  ) - y c determined accordingly Second step - determine  at the minimum of D 2 (  ) - x c determined accordingly Third step - determine z c with known variables –Least square approach Stereo High-speed Motion Tracking

13 –Simulated 3D motion (300mmx150mm,  =0-45 ,  =0-20 ,  =0-10  ) - 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  Stereo High-speed Motion Tracking

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

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

16 –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 Stereo High-speed Motion Tracking

17 –4-point tracking method 1. Distribution of markers “1”, “2”, “3” and “4” - Line “1-3” parallel to model axis - 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” - 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 Stereo High-speed Motion Tracking

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

19 –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: Stereo High-speed Motion Tracking

20 –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  Stereo High-speed Motion Tracking

21 –Experimental results - x-motion: linear, dx/dt = m/s - y-motion: parabolic, dy/dt 2 = m/s 2 - z-motion: linear, dz/dt = 0.16 m/s - roll angle: linear, d  /dt = r/s - pitch angle: linear, d  /dt = r/s - yaw angle: linear, d  /dt = 0.05 r/s Stereo High-speed Motion Tracking

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

23 –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 Stereo High-speed Motion Tracking

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

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

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

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

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

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

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

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

20.Please list two methods that can be used to identify evaluation errors in a vector map with regular grid. 21.Please explain how to use target vector method to correct evaluation errors. 22.What is the peak-locking effect? 23.What are the sources of the peak-locking effect? 24.Please suggest an algorithm with the least peck-locking. 25. Please list two methods that can be used to enable a phase-separated measurement with PIV. 26.Please list at least 5 particle image parameters that are determined with particle image identification and used to track particle images between two frames. 27.Please explain how to evaluate low image number density recording with high accuracy. 28.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. 29.Please briefly explain how the stereo PIV determines the particle image displacement component perpendicular to the measurement plane. 30.Please list advantages and disadvantages of the translation system and rotational system of stereo PIV. Exercises for final exam