Template matching for improved accuracy in molecular tagging velocimetry

Abstract

In 2D molecular tagging velocimetry (MTV), tags are written into a fluid flow with a laser grid and imaged at discrete times. These images are analyzed to calculate Lagrangian displacement vectors, often by direct cross correlation. The cross correlation method is inherited from particle imaging velocimetry, where the correlated images contain a random pattern of particles. A template matching method is presented here which takes advantage of the known geometry of laser written tag grids in MTV to achieve better accuracy. Grid intersections are explicitly located in each image by correlation with a template with several linear and rotational degrees of freedom. The template is a continuous mathematical function, so the correlation may be optimized at arbitrary sub-pixel resolution. The template is smooth at the spatial scale of the image noise, so random error is substantially suppressed. Under typical experimental conditions at low imaging resolution, displacement uncertainty is reduced by a factor of 5 compared to the direct cross correlation method. Due to the rotational degrees of freedom, displacement uncertainty is insensitive to highly deformed grids, thus permitting longer delay times and increasing the relative accuracy and dynamic range of the measurement. In addition, measured rotational displacements yield velocity gradients which improve the fidelity of interpolated velocity maps.