Assessment of the mean and variance of the random regular transmittance through a dispersion of large cylinders using numerical simulations.
In two previous papers [J. Opt. Soc. Am. A15, 1698 (1998)JOAOD60740-323210.1364/JOSAA.15.001698; J. Opt. Soc. Am. A16, 2737 (1999)JOAOD60740-323210.1364/JOSAA.16.002737] the theory of fluctuations in the regular transmittance T through a flowing dispersion of large slender cylindrical particles was presented. The theory covers, among other things, expressions for the expected value muT and the variance sigma(T)(2) of T in the two extreme cases when the cylinders are much shorter or much longer than the diameter of the optical beam used. Intermediate lengths were not treated. Numerical simulation is used to demonstrate the random behavior of T for intermediate cylinder lengths. The simulation results are consistent with the theory and provide a reliable estimate of the measurements produced by this analysis process. The result of the simulation is summarized as a fitted Bézier function model. The advantage of the simulation lies primarily in estimating measurement errors caused by the presence of intermediate length particles in measurement applications.
Rydefalk
Staffan
S
STFI-Packforsk AB, Box 5604, 114 86 Stockholm, Sweden. staffan.rydefalk@stfi.se