On the characterization of bias errors in defocusing-based 3D particle tracking velocimetry for microfluidics

In this work, we provide a systematic theoretical and experimental characterization of bias errors in defocusing particle tracking (DPT) methods based on a single calibration function, with respect to microfluidic applications, in which it is not possible to use calibration targets inside the measurement volume. This approach is widely used in microfluidic experiments, but bias errors are often neglected and to date only few works reported empirical procedures to compensate for that. A systematic characterization of the impact of such error in DPT measurements is still lacking. We show that the field curvature aberration and the refractive index mismatch are the main sources of bias error in these applications. We present a correction methodology for the bias error based on the determination of a reference surface, and in addition we propose a procedure based on a reference measurement of a Poiseuille flow to determine the reference surface on microfluidic channels with constant cross section. We discuss the impact of the refractive index mismatch and how to correctly compensate for it. We validated our methodology and quantified the bias errors on 10 different experimental setups, using different working fluids, materials, geometries, and microscope objective lenses ranging from 5 x to 40x magnification. Our results indicate that the impact of this type of bias errors is in general not predictable and must be evaluated case by case. The proposed methodology allows to estimate and minimize the bias error in most microfluidic setups and is suitable for any single-camera DPT approach.