Forward scattering particle image velocimetry (FSPIV): Application of Mie and imaging theory to measure 3D velocities in microscopic flows using partially coherent illumination and high aperture optics

We have combined Mie scattering theory and image theory to predict the forward scattering of light from spherical particles in a seeded fluid using high numerical aperture collection optics. Using this method, it is possible to determine all three components of a fluid's velocity by measuring the scattering from homogeneous spherical particles without moving the optics. The transverse velocity component is determined by following the centroid of the scattering pattern (with respect to time), while the component along the optical axis is determined by comparing the experimental data with numerical computations. We have verified our theoretical model and computer code by measuring the scattering from polystyrene particles illuminated with partially coherent, Koehler illumination in a transmitted light microscope. The three-dimensional scattering data is in quite good agreement with our model. To further verify our approach, we have measured the three- dimensional (parabolic) profile of a parallel flow of a low viscosity, seeded fluid in a straight channel (6 mm x 48 mm x 0.315 mm). The channel was placed on the stage of a conventional microscope equipped with a long working distance microscope objective, with the narrow dimension along the optical axis (OA). Instead of directly imaging the seed particles, the forward scattered light is recorded from the spherical, polystyrene seed particles (7 μm diameter).