Tutorial: Guide to error propagation for particle counting measurements

Forward error propagation is an established technique for uncertainty quantification (UQ). This article covers practical applications of forward error propagation in the context of particle counting measurements. We begin by presenting pertinent error models, including the Poisson noise model, and assess their role in UQ. Next, we describe several basic techniques for UQ, including Gauss's formula, its generalization to the Law of Propagation of Uncertainty (LPU), and the use of Monte Carlo (MC) sampling. We conclude with demonstrations of increasing complexity, including total number concentration, total mass concentration, penetration, and mass-based filtration efficiency scenarios. These examples serve two functions: (1) providing examples in which theoretical concepts are practically applied to interpret particle counting data and (2) presenting expressions that can be used to compute uncertainties for specific problems in particle counting measurement.