Extinction coefficients for dielectric and conducting doublets of spheres

Light extinction measurements constitute a convenient method to estimate the line-of-sight average mass concentration of smoke. The mass specific extinction coefficient of smoke, /spl sigma//sub 1/, is needed to infer the mass concentration from the light extinction measurement. To determine the magnitude of the effect of the doublets an the value of /spl sigma//sub 1/, we compute the extinction cross section of a doublet of spheres and compute it with the extinction cross section of a single sphere, which is determined from the formulas for Mie scattering. We determine the fields scattered by a dielectric or conducting finite scatterer by solving Maxwell´s equations exactly, reducing the problem to the solution of a single integral equation for an unknown tangential function defined on the surface of the doublet. The fields are obtained from the surface function by integration. The extinction coefficient is related to the forward scattering amplitude by the optical theorem. We perform these calculations for polystyrene and carbon doublets, and find that the average extinction coefficient of a doublet is close to that of two spheres scattering independently. Our results agree reasonable well with others obtained by different methods.