High-precision measurement and inference of short-ranged colloidal interactions

Understanding the interactions between colloidal particles is essential for controlling self-assembly. Methods to characterize these interactions generally rely on imaging the particles, usually within an optical potential, and inferring the distribution of distances between them to extract the potential. Such methods must account for how the scattering of light from the particles changes as a function of distance, as well as how out-of-plane fluctuations affect the inferred distance distribution. We demonstrate an alternative method based on holographic microscopy and Bayesian inference. This method rigorously accounts for scattering effects, works in three dimensions, and does not require the particles to be trapped in an optical potential. With this method, we precisely track pairs of freely-diffusing spheres in three dimensions and at high frame rates. We show that the method can measure separation distances as small as a few nanometers between micrometer scale particles to 3 nm precision. We infer the pair potential from measurements of fluctuations in the particle separation distances in two ways: by analyzing uncorrelated samples of the separation distance, and by fitting equations of motions to the full three-dimensional trajectories of the two particles. We validate the results by comparison to indirect measurements of the interaction.