PERFORMANCE ANALYSIS AND APPLICATION OF GRID INTERPOLATION TECHNIQUESFOR FLUID-FLOWS

Although it is common for automated image processing techniques to cla im subpixel accuracy in the identification of particles, or centroids of displacements of groups of particles, additional errors are inevita bly introduced when and if these data are reinterpolated back onto a g rid mesh whose nodes lie at different locations from the original data . Moreover, these errors can be large compared to the errors introduce d in the original image processing step. Two different techniques, con volution with an adaptive Gaussian window (AGW), and a two-dimensional thin-shell spline (STS), have been compared and contrasted for interp olating irregularly spaced data onto a regular grid. Both techniques a re global interpolators; the Gaussian kernel applies an ad hoc choice of smooth function, while the thin-shell spline minimises a global fun ctional proportional to the Laplacian of the velocity held. In this wa y, the smoothness constraint on the spline coefficients may be thought of as akin to a viscous smoothing of the fluid flow. Performance curv es are given, enabling the investigator to make an informed choice of interpolating routine and grid interpolation parameters to minimise th e interpolation errors, given various external constraints. Some illus trative example applications on real experimental data are described. In general, the importance of matching the interpolation technique to the characteristics of the original data is stressed. It is also point ed out that a correct interpretation of grid interpolated data must be based on a basic knowledge of the performance characteristics of that interpolator. Finally, recommendations are made concerning the develo pment of surface spline techniques for problems involving large number s of data points.