# Analysis of velocity interpolation schemes for image deformation methods in PIV

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- 25 Citations

## Abstract

The spatial resolution of PIV can be increased significantly by using an image deformation method (IDM) and very small grid distance (i.e. the final distance between vectors), therefore, also increasing the processing time. By using an interpolation scheme with a good spectral response, in the dense predictor step of the algorithm, it is possible to increase the grid distance without decreasing the spatial resolution therefore decreasing the total processing time.

## Keywords

Modulation Transfer Function Interpolation Scheme Interrogation Window Total Processing Time Dense Predictor## Abbreviations

- FFT
Fast Fourier transform

- IDM
Image deformation method

- IS
Interpolation scheme

- MTF
Modulation transfer function

- PIV
Particle image velocimetry

- WW
Weighting window

## List of symbols

*a*modulation factor associated to the correlation step of the algorithm, dimensionless

*b*modulation factor associated to the weighted average step of the algorithm, dimensionless

*c*modulation factor associated to the dense predictor step of the algorithm, dimensionless

*E*_{21}power spectra, pixels

^{2}*k*iteration number, dimensionless

*m*^{k}modulation factor at iteration

*k*, dimensionless*n*random noise level, dimensionless

*N*number of measurement points, dimensionless

**r**displacement field, pixels

**r**_{c}corrector displacement field, pixels

**r**_{p}dense predictor displacement field, pixels

**r**^{k}displacement field at iteration

*k*, pixels- \( \overline{{\varvec{r}^{{k - 1}}_{p} }} \)
weighted average of the dense predictor displacement field, pixels

*t*_{e}percentage time needed to perform the dense predictor step, dimensionless

*v*vertical displacement, pixels

*v*_{i}local measured displacement, pixels

*W*_{a}interrogation window linear dimension, pixels

*W*_{b}linear dimension of the weighting window used in the weighted average step of the algorithm, pixels

*W*_{c}grid distance, pixels

*x*horizontal image coordinate, pixels

*y*vertical image coordinate, pixels

*δ*total error, pixels

*λ*spatial wavelength, pixels

*ω*normalised spatial frequency (

*W*_{ a }/*λ*), dimensionless

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