# Particle sizing from disk images by counting contiguous grid squares or vidicon pixels

## Abstract

The location of the light-scattering image of a particle with respect to the grid pattern of pixels on a vidicon screen used in particle surface monitoring can cause variation in the response of the vidicon for particles giving the same amount of light scattering. A simple disk-and-square model of the interaction is used to predict such geometrical interaction effects, which are shown to influence the mean number of pixels (squares) activated by particle images (disks) and the variation in the number of pixels activated. The same problem exists when trying to estimate disk area from squares covered or squares covered and touched. If one counts all squares touched by the disk, the mean number of squares, E(n), is shown to be exactly equal to the following equation, for image diameters (D) smaller than the edge length (D < L) and approximately equal to it for larger images: E(n) = 1 + 2( D L) + ( π 4)( D L)2. The variance of n is calculated for D < L. The variation in n for D > L is demonstrated through geometrical modeling and square counting, distinguishing between the number of squares touched and the number completely covered. The geometrical interaction effects on the mean number of squares touched or mean number completely covered can be compensated for by calibration, but the effects on variation cannot. The variation of number of pixels activated compared to the mean number of pixels activated is predicted to be roughly 50% for situations where tens of pixels or less are activated by the particle image. Data that support this by showing substantially greater variability in the pixel distributions than the variability in the particle distributions are presented. The data show particles being missed in some readings and being counted in others, as the analysis predicts. The data also show relatively small error in the total counts, believed due to compensating errors. © 1988.