The fundamentals of particle size analysis by transmission fluctuation spectrometry. Part 2: A theory on transmission fluctuations with combined spatial and temporal averaging

The extinction of radiation in suspensions is traditionally described by th e Bouguer-Lambert-Beer law (BLBL). Based on a quasi-continuum approach, the BLBL does not account for the discrete nature of particles or their spatia l extension and arrangement. If an extinction measurement is made with a hi gh spatial and temporal resolution, the transmitted intensity signal shows significant fluctuations. The strength of fluctuation is related to the phy sical properties of the suspension and the process of spatial and temporal averaging. Exploiting this connection, it is possible to calculate the part icle size distribution and the particle concentration from transmission mea surements. This second part provides an analytical solution for the descrip tion of transmission fluctuations in terms of the expectancy of the transmi ssion square, including both variations of the beam diameter to particle di ameter ratio and variation of the temporal resolution of the signal capture . The result also provides the basis for describing the transmission fluctu ations for beams of variable diameter and allows to define a measurement vo lume for the case of focussed beams.