An analysis of the fraunhofer diffraction method for particle size distribution analysis and its application to aerosolized sprays

Abstract

The Fraunhofer Diffraction technique is used widely for particle sizing applications in the 1–200 μm size range. The technique is suitable for use with liquid-borne and gas-borne suspensions, and is therefore well suited for use in the characterization of aerosol dosage forms. While the theory relating to Fraunhofer Diffraction and the determination of particle sizes from the diffraction patterns has been fairly well worked out, there is little quantitative information in the literature on the extent of variability, the accuracy and the precision to expect in the measurements. This work therefore addresses the nature and magnitude of errors in determining size distributions by the Fraunhofer Diffraction technique. The diffraction patterns to be expected from known particle size distributions are calculated from first principles and compared with experimental data acquired on a commercial Fraunhofer instrument. Known noise levels are imposed on the simulated data in order to approximate experimental conditions. These noisy data sets are then inverted by a minimization procedure to yield particle size distributions which can be compared with the distributions used to simulate the data in the first place. This comparison provides information on the errors and variability to be expected in such measurements under a variety of controlled experimental conditions and allows us to assign error limits to measurements made using the Fraunhofer technique. The report thus provides a mathematical basis for setting reasonable particle size specifications as a way of quantitative assessment of product performance in vitro.