Abstract
This paper presents a method of accurately determining the displacement of tracer particles between two images using recursive correlation. The local correlation value is iteratively arrived at through successive approximations of local displacement using increasingly smaller regions of determination. By starting with a large search area and iteratively narrowing the search restricting the search after each iteration based on the resulting calculation, very high-resolution PIV processing can be achieved. Spurious vectors are eliminated and accuracy and processing speed is maintained by correlating images in compressed (sparse array) format using second-order spatial correlation. The methodology of this unique image analysis method is presented along with a discussion of its limitations and applicability.
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Abbreviations
- Φ:
-
Correlation function
- Δ:
-
Correlation search length [pixels]
- Δt :
-
Time between image exposures [sec.]
- Δi,Δj :
-
Difference in pixel image [pixels]
- ∇:
-
Gradient operator
- γ:
-
Image compression ratio
- \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {v} \) :
-
Flow velocity [m/s]
- \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {v} '\) :
-
Unsteady flow velocity component [m/s]
- d :
-
Particle image diameter [pixels]
- f :
-
Spatial frequency [1/m]
- I :
-
Pixel intensity
- i,j :
-
Image coordinates [pixels]
- m,n :
-
Data array indices
- M :
-
Image magnification [m/pixels]
- M, N :
-
Interrogation image diameter [pixels]
- x,y :
-
Pixel image coordinates
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Douglas Payton Hart: He received his BSc degree in aeronautical/astronautical engineering in 1983 from the University of Illinois, his S.M. degree in mechanical engineering from the Massachusetts Institute of Technology in 1985, and his Ph.D. in mechanical engineering from the California Institute of Technology in 1992. As a student at MIT, he worked for Electromagnetic Launch Research, Inc. on satellite propulsion. After receiving his S.M degree, he worked as a systems engineer for Northrop Aerospace before starting his Ph.D. in the area of hydrodynamics at Caltech. He joined the faculty at MIT in the Department of Mechanical Engineering in 1993 and is currently an associate professor and the director of the Fluid Mechanics Laboratory. His current research interests include instrumentation and optical diagnostics relating to fluid mechanics and tribology.
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Hart, D.P. Super-resolution PIV by recursive local-correlation. J Vis 3, 187–194 (2000). https://doi.org/10.1007/BF03182411
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DOI: https://doi.org/10.1007/BF03182411