Essential parameters in particle sizing by integral transform inversions

We show that integral transform inversions for Fraunhofer-diffraction particle sizing possess an important feature that has useful implications. The selection of three angular parameters, Δθ (angular resolution), θmin (minimum scattering angle), and θmax (maximum scattering angle), necessary for reconstructing a given kind of particle size distribution without undergoing mathematical limits that contradict the Fraunhofer theory and exceed practical measurement limitations, depends inverselinearly on the optical size parameter x, x = 2πα/λ (α, particle radius; λ, wavelength). Two series of numerical experiments, in which the Chin-Shifrin inversion is used, are performed to assess the reconstruction of original discontinuous (narrow-type) and continuous (board-type) particle size distributions from simulated Fraunhofer-diffracted patterns, assuming linear- and log-scaled light detector configurations, respectively. New and useful findings regarding the roles of these three key angular parameters in the Chin-Shifrin inversion process, including general criteria relating the x and the selections of Δθ and θmax for effective size retrieval, were obtained.