Radiative properties of small particles: extension of the Penndorf model

Explicit analytical expressions to represent the radiative properties of sp herical particles in the small size-parameter range were obtained. These ex pressions were deduced following Penndorf's approach of expanding the Mie c oefficients in power series on the size parameter. However, in opposition t o Penndorf's original work-in which some errors were found and corrected-th e Mie coefficients were expanded to the eighth power of the size parameter, which results in a five-term approximation to the extinction and scatterin g efficiencies. Also, expressions for the evaluation of the asymmetry facto r and both polarized and unpolarized phase functions were deduced and prese nted. The results so obtained have proved to be very accurate, even for siz e parameters beyond the limit of validity of the approach utilized. (C) 200 1 Optical Society of America.