3-D rotation tracking from 2-D images of spherical colloids with textured surfaces.

Tracking the three-dimensional rotation of colloidal particles is essential to elucidate many open questions, e.g. concerning the contact interactions between particles under flow, or the way in which obstacles and neighboring particles affect self-propulsion in active suspensions. In order to achieve rotational tracking, optically anisotropic particles are required. We synthesise here rough spherical colloids that present randomly distributed fluorescent asperities and track their motion under different experimental conditions. Specifically, we propose a new algorithm based on a 3-D rotation registration, which enables us to track the 3-D rotation of our rough colloids at short time-scales, using time series of 2-D images acquired at high frame rates with a conventional wide-field microscope. The method is based on the image correlation between a reference image and rotated 3-D prospective images to identify the most likely angular displacements between frames. We first validate our approach against simulated data and then apply it to the cases of: particles flowing through a capillary, freely diffusing at solid-liquid and liquid-liquid interfaces, and self-propelling above a substrate. By demonstrating the applicability of our algorithm and sharing the code, we hope to encourage further investigations in the rotational dynamics of colloidal systems.