Theoretical calculation of uncertainty region for spherical particles based on a picket fence, quasi-monodisperse particles

In order to confirm the reliability of particle size measurement technique and to prepare standard reference particles for calibrating particle size measurement devices, experimental and theoretical studies have been conducted about the uncertainty region of particle size measurement for the picket fence and quasi mono-disperse particles. The vertical and horizontal uncertainty regions based on Tschebyscheff theory are calculated to the picket fence distribution composed of two kinds of nearly mono-disperse particles. The uncertainty region increases around the intermediate particle diameters between the two kinds of particles. Because the original particle size distribution is nearly mono-disperse, the uncertainty regions around the minimum and maximum particle diameter are small compared to the intermediate particle diameters between the two kinds of particles. The uncertainty region in vertical and horizontal direction changes to decrease with the increase of sample size. For the picket fence distribution composed of two kinds of nearly mono-disperse particles, the sample size about more than 10,000 is necessary to obtain the reliable results in particle size counting process.