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What is Particle Size Distribution Weighting

Introduction: Some particle size instruments determine the size of individual particles. They are single-particle counters. Some instruments determine the surface area as a function of particle size. Some instruments determine mass or volume vs size. And some instruments determine various functions of scattered light intensity as a function of size. All can produce particle size distributions. And, in principle, one can transform from one type to the other in order to compare results. For example, if a measurement with a single particle counter produced a differential number-weighted Size distribution and you wanted to compare the results to a measurement with another type of instrument that produced a differential volume-weighted size distribution, what would you do?