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1. Applications of the theory of fluctuation in the regular transmittance through a dispersion of large cylindrical particles to concentration and size measurementsRydefalk, Staffan

Four measurement principles based on the theory of fluctuation in the regular transmittance through a dispersion of large cylindrical particles are presented. The principles concern the measurement of particle concentration, particle length classes, particle length, and particle width. In previous publications, the measurement principles were briefly presented. A more complete description, experimental demonstrations, and a number of considerations needed to understand the region of validity of the different principles, as well as their uncertainty, are presented. A recently published simulation model [Appl. Opt. 47, 993 (2008)] is used. The basic ideas of the measurement principles within their respective regions of validity are supported.

2. Assessment of the mean and variance of the random regular transmittance through a dispersion of large cylinders using numerical simulationsRydefalk, Staffan

In two previous papers [J. Opt. Soc. Am. A 15, 1698 (1998); J. Opt. Soc. Am. A 16, 2737 (1999)] the theory of fluctuations in the regular transmittance T through a bowing dispersion of large slender cylindrical particles was presented. The theory covers, among other things, expressions for the expected value AT and the variance sigma(2)(T) 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 Bezier function model. The advantage of the simulation lies primarily in estimating measurement errors caused by the presence of intermediate length particles in measurement applications.

3. Fluctuations in the regular transmittance of dispersions of straight circular cylinders with a diameter much larger than the wavelength of the radiationRydefalk, Staffan

The expected value and the variance of the regular transmittance of a dilute dispersion of slender straight circular cylinders with a diameter much larger than the wavelength of the radiation are studied theoretically in relation to the dimensions of the cylinders and the diameter of the radiation beam used. Both monodisperse and heterodisperse dispersions are considered. The study is Limited to two particle categories: (i) particles that are short and (ii) particles that are long but thin compared with the diameter of the radiation beam. The expected value is a function of concentration and particle diameter. The variance is proportional to the concentration. The variance is also proportional to particle length in the case of short particles but not in the case of long particles. The results explain interesting possibilities for the characterization of dispersions of large cylindrical particles shown earlier in industrial on-line applications.

4. Particle Measurements Using Fluctuations in the Regular Transmittance of Light Through a Particle Dispersion

Rydefalk, Staffan

KTH, Skolan för industriell teknik och management (ITM), Industriell produktion.

The regular transmittance of light or similar radiation through a flowing suspension of particles fluctuates because of the random occurrence of particles in the beam.In the work presented here, a theory for this fluctuating behaviour with the emphasison dispersions of mm-length slender cylindrical particles having circular crosssections is given. The particles in question are wood pulp fibres, which as a first approximation are considered to have a cylinder shape. Four possible measurementprinciples are described theoretically and experimentally. The four principles are for the measurement of concentration, length distribution characterized as lengthclasses, mean length, and mean width. The usefulness in industrial process monitoring of two of these principles is exemplified with pulp measurements. In order to estimate model errors, numerical simulations were used. Although other techniques such as image analysis may compete, the technique presented here is attractive because of the simplicity of the measurement device used.

It has been shown in a previous paper [J. Opt. Sec. 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 concentration X path-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.

6. Validation of a simulation algorithm for the mean and variance of the random regular transmittance through a dispersion of large cylindersRydefalk, Staffan