Determinations of angular stiffness in rotational optical tweezers

Rotational optical tweezers are used to probe the mechanical properties of unknown microsystems. Quantifying the angular trap stiffness is essential for interpreting the rotational dynamics of probe particles. While methods to determine trap stiffness are well established for translational degrees of freedom, angular trapping is often treated analogously even though rotational and translational motions are sensitive to distinct experimental parameters and offer separate insights. This work details passive analysis techniques for determining the angular trap stiffness within the linear restoring torque model and examines the influence of several factors unique to rotational optical tweezers. We show that the parameters of an ancillary measurement beam can be tuned to minimise its influence on angular trapping dynamics, providing necessary improvements for nanoparticle-scale analysis. We also explore the combined effects of shape-induced and material birefringence in spheroidal vaterite probes, and present a framework for assessing hydrodynamic and inertial contributions.