1 Imaging Techniques for Flow and Motion Measurement Lecture 19 Lichuan Gui University of Mississippi 2011 Stereoscopic Particle Image Velocimetry (SPIV)

2 Stereo PIV system –Two cameras –Translation and angular configurations –Distorted particle images (angular system) –3-D displacement reduced from two 2-D displacements –3 velocity components in a plane Stereoscopic PIV Example G. Calcagno, F.D. Felice, M. Felli, and F. Pereira, 24 th Sym. Naval Hydro. (2002) Test region Test result

3 Laser light sheet X Z Stereoscopic PIV SPIV data reduction t=t 0 t=t 0 +  t S Laser light sheet X Z S XX ZZ Standard PIV view XX  Z not sensible

4 Stereoscopic PIV SPIV data reduction Laser light sheet X Z S XX ZZ 11 X1X1 camera #1 X2X2 22 camera #2 Stereo view

5 Stereoscopic PIV SPIV data reduction - Particle image displacements: (  X’ 1,  Y’ 1 ) and (  X’ 2,  Y’ 2 ) - Imaging scale factor: M 1 and M 2 No stereo effect in yz-plane

6 Stereoscopic PIV Error propagation in SPIV

7 Stereoscopic PIV Error propagation in SPIV

8 Stereoscopic PIV Error propagation in SPIV Define:

9 Stereoscopic PIV Error propagation in SPIV - Optimal view angle 45 

10 Camera #1Camera #2 Lens Plane  Stereoscopic PIV - Object plane || Lens plane || Image plane - Uniform magnification (M n =d i /d o ) - Easy to focus - Off-axis angle  restricted by the lens (application limited) Translation (lateral displacement) system

11 Object planeLens planeImage plane Mirror pair 1 Mirror pair 2 Aperture stop Stereoscopic PIV Translation (lateral displacement) system - Single camera configuration - View angle  is limited Test region Image #1 Image #2

12 Stereoscopic PIV Rotational (angular displacement) system - Scheimpflug condition - Distorted image (M n  constant)

13 Stereoscopic PIV SPIV recording evaluation 1. Evaluation with image calibration Distorted ImageCalibrated ImageVelocity map Positive: a. Uniform spatial resolution b. Simple procedure Negative: Image interpolation error Image calibration methods Polynomial mapping Preservation of straightness of lines – for high quality camera lens

14 Stereoscopic PIV SPIV recording evaluation 2.Evaluation with velocity calibration Distorted ImageVelocity mapVelocity calibration Positive: No image interpolation Negative: a. Non-uniform spatial resolution b. Evaluation grid transfer required Basic evaluation steps: 1.Determine transformation function between physical and image plane 2.Transfer uniform evaluation grid in physical plane to image plane 3.Evaluate the distorted SPIV recordings with the transformed evaluation grid 4.Transfer the evaluated displacement components to the physical plane

15 –References Prasad AK (2000) Stereoscopic particle image velocimetry. Exp. Fluids 29, pp Willert C (1997) Stereoscopic digital particle image velocimetry for application in wind tunnel flows. Meas. Sci. Technol. 8, pp –Practice with EDPIV Compare image calibration and vector calibration with application example #9 Homework