Estimation of centres and radial intensity profiles of spherical nano-particles in digital microscopy

Control of the microscopic characteristics of colloidal systems is critical in a wealth of application areas, ranging from food to pharmaceuticals. To assist in estimating these characteristics, we present a method for estimating the positions of spherical nano-particles in digital microscopy images. The radial intensity profiles of particles, which depend on the distances of the particles from the focal plane of the light microscope and have no closed functional form, are modelled using a local quadratic kernel estimate. We also allow for the case where pixel values are censored at an upper limit of 255. Standard errors of centre estimates are obtained using a sandwich estimator which takes into account spatial autocorrelation in the errors. The approach is validated by a simulation study.