Measurement of the location of a particle in three dimensions using Mie scattering theory and wave optics: Application to flow in a microscopic field of view

In this research, we have sought to develop a technique for measuring three-dimensional flow fields in small fluid volumes seeded with small spherical particles using a high numerical aperture (NA) microscope. The technique relies upon the knowledge of how the light is scattered from the particles to accurately determine their three dimensional position.; We have combined Mie scattering theory and wave optics to predict the scattered field from spherical particles in a fluid medium using high NA collection optics. The model uses Mie scattering theory to calculate the optical field distribution on the intermediate planar interface between glass and air and then adopts a ray approach to propagate the field to the entrance pupil of an imaging system. We do not use a paraxial (parabolic wavefront) approximation and, therefore, our approach is applicable to the modeling of imaging systems with high aperture objectives. We have verified our theoretical model by measuring the scattering from polystyrene spheres illuminated with partially coherent, Koehler illumination in a transmitted light microscope with a 0.5 NA objective. Good agreement between our model and the experiment was achieved.; We also developed a non-paraxial transformation for the lens and a vectorial model for the electromagnetic fields collected by a high NA objective. The model was also to determine the three-dimensional microscale based upon the motion of small particles in a seeded fluid. Application to laminar flow in a sub-millimeter channel and a thin liquid film demonstrate the utility of the technique. Preliminary results show that a wavelet based denoising technique may be used to process the data without loss of resolution.