Density Determination via Time-Resolved Diffraction Analysis of 2D Images Based on Kirchhoff Theory

Conventional methods for particle density measurement provide only ensemble-averaged values and do not allow direct determination of density for individual particles. In this study, a method was developed to estimate particle density from time-resolved diffraction patterns contained in two-dimensional microscopic images. The axial position of a particle was determined from the temporal evolution of diffraction fringes using a model based on Kirchhoff diffraction theory, allowing sedimentation velocity to be evaluated without direct observation of motion along the optical axis. Particle size was obtained independently from Brownian motion by particle tracking analysis. Combining these measurements enabled density determination for individual particles. The method was examined using polystyrene latex, silica, and gold particles. For silica and gold particles, the measured densities agreed with the corresponding bulk values within experimental uncertainty. Because particle size and sedimentation behavior were obtained by tracking individual particles, the relationship between particle size and the calculated density could be examined. However, the uncertainty in particle-size determination substantially affects the calculated density, limiting the precision of individual-particle density estimates under the present experimental conditions. The results demonstrate the feasibility of extracting particle-density information from conventional two-dimensional particle images through diffraction-pattern analysis and provide a basis for future improvements toward single-particle density determination.