Concentration measurements in single particle microscopy

Abstract: The topic of this thesis is the introduction of two novel methods for using single particle microscopy as a tool for absolute number concentration measurements of Brownian particles. The key idea of both methods is that in order to estimate number concentration, the size of the (three-dimensional) particle detection region has to be estimated. Typically, this size has until now been estimated by means of a separate a priori calibration measurement. Thus, in many cases the influence of for example particle brightness and image analysis settings on the final result have been ignored. In the first paper, we use single particle tracking to estimate the size of the detection region. This is based on modeling the distribution of trajectory lengths within the detection region. The modeling is simplified by assuming that particles enter and exit the detection region only by means of axial diffusion, i.e. parallel to the optical axis and orthogonal to the focal plane. In the second paper, we study a time series of particle counts known as a Smoluchowski process. We approximate this non-Markov process by a Markov chain and demonstrate that this model can be used to estimate the size of the detection region. This implies that individual particles need not be tracked. We also introduce a method for automatic selection of a threshold for minimum contrast between particles and the image background, based on analyzing the correlations between particle counts in consecutive frames. In both cases, we perform experimental validation by estimation of the number concentration of different dilutions of a nanosphere water dispersion, and we find close agreement with validation measurements.