The range of validity of the Rayleigh–Debye–Gans approximation for the optical cross sections of fractal aggregates (RDG-FA) that are formed by uniform small particles was evaluated in comparison with the integral equation formulation for scattering (IEFS), which accounts for the effects of multiple scattering and self-interaction. Numerical simulations were performed to create aggregates that exhibit mass fractallike characteristics with a wide range of particle and aggregate sizes and morphologies, including xp = 0.01–1.0, ‖m − 1‖ = 0.1–2.0, N = 16–256, and Df = 1.0–3.0. The percent differences between both scattering theories were presented as error contour charts in the ‖m − 1‖xp domains for various size aggregates, emphasizing fractal properties representative of diffusion-limited cluster–cluster aggregation. These charts conveniently identified the regions in which the differences were less than 10%, between 10% and 30%, and more than 30% for easy to use general guidelines for suitability of the RDG-FA theory in any scattering applications of interest, such as laser-based particulate diagnostics. Various types of aggregate geometry ranging from straight chains (Df ≈ 1.0) to compact clusters (Df ≈ 3.0) were also considered for generalization of the findings. For the present computational conditions, the RDG-FA theory yielded accurate predictions to within 10% for ‖m − 1‖ to approximately 1 or more as long as the primary particles in aggregates were within the Rayleigh scattering limit (xp ≤ 0.3). Additionally, the effect of fractal dimension on the performance of the RDG-FA was generally found to be insignificant. The results suggested that the RDG-FA theory is a reasonable approximation for optics of a wide range of fractal aggregates, considerably extending its domain of applicability.
© 1996 Optical Society of America
T. L. Farias, Ü. Ö. Köylü, and M. G. Carvalho, "Range of validity of the Rayleigh—Debye—Gans theory for optics of fractal aggregates," Appl. Opt. 35, 6560-6567 (1996)