## Range of validity of the Rayleigh–Debye–Gans theory for optics of fractal aggregates

Applied Optics, Vol. 35, Issue 33, pp. 6560-6567 (1996)

http://dx.doi.org/10.1364/AO.35.006560

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### Abstract

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 *x**
_{p}
* = 0.01–1.0, |

*m*− 1| = 0.1–2.0,

*N*= 16–256, and

*D*

*= 1.0–3.0. The percent differences between both scattering theories were presented as error contour charts in the |*

_{f}*m*− 1|

*x*

*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 (*

_{p}*D*

*≈ 1.0) to compact clusters (*

_{f}*D*

*≈ 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 |*

_{f}*m*− 1| to approximately 1 or more as long as the primary particles in aggregates were within the Rayleigh scattering limit (

*x*

*≤ 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.*

_{p}© 1996 Optical Society of America

**History**

Original Manuscript: November 8, 1995

Revised Manuscript: April 29, 1996

Published: November 20, 1996

**Citation**

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)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-35-33-6560

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