3D tracking the Brownian motion of colloidal particles using digital holographic microscopy and joint reconstruction

In-line digital holography is a valuable tool for sizing, locating and tracking micro- or nano-objects in a volume. When a parametric imaging model is available, Inverse Problems approaches provide a straightforward estimate of the object parameters by fitting data with the model, thereby allowing accurate reconstruction. As recently proposed and demonstrated, combining pixel super-resolution techniques with Inverse Problems approaches improves the estimation of particle size and 3D-position. Here we demonstrate the accurate tracking of colloidal particles in Brownian motion. Particle size and 3D-position are jointly optimized from video holograms acquired with a digital holographic microscopy set up based on a "low-end" microscope objective ($\times 20$, $\rm NA\ 0.5$). Exploiting information redundancy makes it possible to characterize particles with a standard deviation of 15 nm in size and a theoretical resolution of 2 x 2 x 5 nm$^3$ for position under additive white Gaussian noise assumption.