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Optical Scattering per Unit Mass of Single Particles F. R. Faxvog General Motors Research Laboratories, GM Technical Center, Warren, Michigan 48090. Received 9 September 1974. The optical scattering of airborne particles in various size ranges has recently been discussed by Lee 1 and Whitby et al. 2 In the present work the scattering per unit mass of single spherical particles is calculated for various materials in the visible spectrum. The results indicate optically ab- sorbing particles (Fe, C) scatter light most efficiently for diameters near 0.2 μm, whereas for nonabsorbing particles (H 2 O and SiC 2 ), the scattering per unit mass peaks in the 0.4-1.0-μm diam range. The calculations are based on the rigorous Mie solutions for the diffraction of a plane monochromatic wave by a ho- Fig. 1. Optical scattering cross section per unit mass for single particles of various materials at wavelength of 0.6328 μm. mogeneous sphere. 3 The scattering cross section per unit mass of a single particle can be expressed in terms of the Mie α n and b n coefficients as where λ is the optical wavelength, D the particle diameter, ρ the material density. From this equation a computer code was written to calculateσ scat . Calculated results of the scattering per unit mass vs par- ticle diameter for iron, carbon, water, and silicon dioxide are shown in Fig. 1. The refractive indices and densities used in the calculations are: iron (m = 1.51-1.63i, ρ = 7.86); carbon (m = 2.5-0.75i, ρ = 2.25); water (m = 1.33, ρ = 1.0); and silicon dioxide (m = 1.55, ρ = 2.66). 4 The wave- length used is λ = 0.6328 m. Calculations for a 0.4416-μm wavelength using these same indices of refraction and den- sities exhibit the same general features. The particle di- ameter for maximum cross section per unit mass is found to scale proportional to wavelength, while the maximum cross section per unit mass scales inversely proportional with wavelength. Therefore, for materials whose indices of refraction do not vary appreciably over the visible spec- trum the results of Fig. 1 will only change in proportion to the wavelength shift from 0.6328 m. The optically absorbing spherical particles in the 0.1- 1.0-μm diam range scatter more light per unit mass than those in the 1.0-10.0-μm diam range, which agrees with the remarks of Whitby et al. 2 However, for nonabsorbing particles Fig. 1 shows that the scattering per unit mass can be comparable in these two size ranges. In addition to these calculations, the extinction and absorption cross sec- tions per unit mass were calculated for these materials and, for carbon and silicon dioxide, were found to agree with the results of Bergstrom. 5 Calculations of this type, especially for the particulate compounds found in the atmosphere (once their complex indices of refraction are available), along with measure- ments of airborne particle mass vs size should prove useful in analyzing atmospheric particle scattering and absorption phenomena. February 1975 / Vol. 14, No. 2 / APPLIED OPTICS 269
