Approximation formulas are derived for small spherical aerosols (<i>r</i><λ) by using the series expansion of the exact solution (Mie theory). The first three terms of the series are given for real, complex, and infinite indices of refraction. The new formulas allow for computing the scattering and absorption coefficients for small aerosols more simply and faster than the Mie formulas. The error of our approximation formulas is determined, and it is found that the useful size range is extended by about a factor 2.
RUDOLF B. PENNDORF, "Scattering and Extinction Coefficients for Small Absorbing and Nonabsorbing Aerosols," J. Opt. Soc. Am. 52, 896-902 (1962)