Accurate Size Measurement of Individual Polydispersed Hard Spheres from Blurry Video

Polydisperse colloidal spheres serve as valuable model systems for studying single-particle dynamics in liquids, glasses, and crystals. Particle size critically influences local structure and free volume, which governs dynamics. However, accurately determining individual particle diameters from imaging data remains challenging. We introduce a linear programming method to extract hard-core diameters from particles' positions. The approach achieves sub-0.1% error using only a brief video sequence, is robust to image blurring, and requires no prior knowledge of mean particle size or size distributions. The method is validated through simulations and experimental video data across diverse polydisperse systems. When input positions are inaccurate, as in real experimental data, a correction based on systematic simulations can yield more accurate radii than the original positions. Additionally, it provides a novel approach to correct misidentified particles in image analysis.