Tuning the detection sensitivity: a model for axial backfocal plane interferometric tracking.

Backfocal plane (BFP) interferometry is a single particle tracking technique that allows one to measure minute displacements of a microscopic particle from the center of a beam's focus in three dimensions. In this Letter, we present a Fourier optics model to describe the interference effects that allow one to track the position of a particle moving along the optical axis. A detection numerical aperture is derived theoretically and confirmed experimentally, within which the interference intensity has a positive correlation with the axial position of the scatterer. For larger detection angles, the correlation is negative. The model helps to understand previously reported measurements and to optimize BFP interferometric tracking.