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Phase correlation processing for DPIV measurements

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Abstract

A novel digital particle image velocimetry (DPIV) correlation method is presented, the Gaussian transformed phase correlation (GTPC) estimator, using nonlinear filtering techniques coupled with the phase-transform (PHAT) generalized cross-correlation filter. The use of spatial windowing is shown to be ideally suited for the use of phase correlation estimators, due to their invariance to the loss of correlation effects. Error analysis demonstrates the increased valid vector detection and measurement accuracy of the windowed GTPC over the traditional Fourier based estimator in a series of uniform displacement Monte Carlo simulations. Analysis of the GTPC performance in the PIV standard image sets shows error reductions on the order of 15–45% over the range of simulations. Experimental DPIV images from a turbulent rib roughened channel flow are used to validate the use of the GTPC, which shows a strong reduction in peak locking effects, background noise errors, and erroneous vectors. Together, these results demonstrate the coupled benefits provided by the use of advanced filtering techniques applied to the phase correlation estimator. With the correct implementation of these filters, the GTPC is able to provide substantial improvements to the robustness of DPIV estimation.

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Abbreviations

C(i,j):

loss of correlation function

C ij :

cross-power spectrum magnitude

d i :

image displacement

DFT:

discrete Fourier transform

e x :

displacement estimation uncertainty

e Ψ :

spatial correlation uncertainty

F i :

in-plane loss of correlation factor

F o :

out-of-plane loss of correlation factor

G(k):

Gaussian temporal filter

GCC:

generalized cross-correlation

GTPC:

Gaussian transformed phase correlation

GTPCC :

bias corrected GTPC

I i(x):

image window intensity distribution

I i(k):

Fourier transformed image window

I 0i :

zeropadded image window

IDFT:

inverse discrete Fourier transform

M,N :

window size

N i :

image window source density

PHAT:

phase transform filtered correlation

SCC:

standard cross-correlation

SCOT:

smoothed coherence transform filter

W(k):

spectral filter

W(x):

spatial window

δ :

discrete delta function

Ψ:

spatial correlation function

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Acknowledgments

The authors would like to thank M. Plesniak and W. Schultz for their support of this project. This material is based upon work supported by the National Science Foundation under Grant No. 0521102.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, USA

    Adric C. Eckstein & Pavlos Vlachos

  2. School of Biomedical Engineering and Sciences, Virginia Tech, Blacksburg, VA, USA

    John Charonko

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  1. Adric C. Eckstein
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  2. John Charonko
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  3. Pavlos Vlachos
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Correspondence to Adric C. Eckstein.

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Eckstein, A.C., Charonko, J. & Vlachos, P. Phase correlation processing for DPIV measurements. Exp Fluids 45, 485–500 (2008). https://doi.org/10.1007/s00348-008-0492-6

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  • DOI: https://doi.org/10.1007/s00348-008-0492-6

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