Optical diffraction tomography in fluid velocimetry: the use of a priori information

Abstract

Holographic particle image velocimetry (HPIV) has been used successfully to make three-dimensional, three-component flow measurements from holographic recordings of seeded fluid. It is clear that measurements can only be made in regions that contain particles, but simply adding more seeding results in poor quality images due to the effects of multiple scattering. In this paper, we describe optical diffraction tomography (ODT) techniques and consider its use as a means to overcome the problems of multiple scattering in HPIV. We consider several approaches to tomographic reconstruction that are essentially based on linear and nonlinear combinations of holographic reconstructions of the scattered fields observed under varied illuminating conditions. We show that linear reconstruction provides images of highest fidelity, but none of the methods properly accounts for the effects of multiple scattering. We go on to consider nonlinear optimization methods in ODT that attempt to minimize the error between the scattered field computed from an estimate of the particle distribution and that measured in practice. We describe an optimization procedure that is based on the conjugated gradient method (CGM) that makes use of a priori information (the size and refractive index of the seeding particles) to effectively reduce the problem to that of finding the set of particle locations. Some 2D numerical experiments are computed and some promising results are shown.