Abstract

It has been shown in a previous paper [J. Opt. Soc. Am. A 15, 1689 (1998)] that the expected value and the variance of the fluctuating regular transmittance through a dispersion of slender cylinders can be used to measure properties such as the size and concentration of the dispersed particles. The theory is valid, however, only for very low concentrations or very short path lengths. In practical applications, such as on-line applications, it is often desirable to work at higher $\mathrm{concentration}\times \mathrm{path}-\mathrm{length}$ products p to avoid complicated sensor constructions. An extension of the previous theory toward higher values of p is presented. It is based on the assumption of the independence of the regular transmittance of parallel layers of the dispersion. The extended theory shows that information about the dispersion found in the expected value and variance at very low values of p can also be obtained for higher values of p with a few simple expressions. Therefore applications possible in the case of low p values are also possible for higher p values. Two experimental examples have been included to facilitate the discussion of the theory presented.

© 1999 Optical Society of America

Applications of the theory of fluctuation in the regular transmittance through a dispersion of large cylindrical particles to concentration and size measurements

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