Determining the size of individual colloidal hard spheres from tracking information

In experiments with densely-packed colloidal particles, key material properties like local density, free volume, and elastic modulus depend exquisitely on the precise interparticle separations. However, although it is possible to determine the location of colloidal individual particles with very high precision using confocal microscopy and image analysis, it is usually not straightforward to determine each particle’s size. Recent advances in 3D image processing have made this possible for some colloidal samples, but particle sizing remains a major challenge in many experiments. In this work, we present a new, efficient approach to measuring individual particle radii using linear programming to solve a system of equations derived from closest approach data. We test our algorithm on both simulated and experimentally-measured polydisperse hard-sphere colloidal crystals, glasses, and liquids. We further discuss the sensitivity of our method to noise in the tracking and compare to earlier tracking-based algorithms.