Estimating orientation of optically trapped, near vertical, microsphere dimers using central moments and off-focus...

Near vertical optically trapped dimers, composed of pairs of microspheres, and constructed in situ, were imaged in bright-field in flow and at rest, and with displacement Δz from the transverse xy imaging plane of an inverted microscope. Image first central moments μ₀₁ were measured, and their dependence on the imposed flow velocity of the surrounding fluid was calculated. This dependence was related to the at-rest restricted diffusion statistics. It was assumed that, for small perturbations, the torque T on the dimer was proportional to the velocity of flow v and resulting angular deflection Δθ so that T∝v∝Δθ. Displacements Δz at which v∝Δμ₀₁∝Δθ, which are typically off focus, were examined in more detail; in this range, Δθ=hΔμ₀₁. The hydrodynamics of the dimer were modeled as that of a prolate ellipsoid, and the constant of proportionality h was determined by comparing the short-time mean-squared variation measured during diffusion to that predicted by the model calculation: h²⟨Δμ012(t)⟩=⟨Δθ²(t)⟩. With h determined, the optical trap stiffness k_θ was determined from the long-time restricted diffusion of the dimer. The measured k_θ and Δθ can then be used compute torque: T=k_θΔθ, potentially enabling the near vertical optically trapped dimer to be used as a torque probe.