An inversion technique has been developed to determine volume fractions of an atmospheric aerosol composed primarily of ammonium sulfate and ammonium nitrate and water combined with fixed concentration of elemental and organic carbon. It is based on measured aerosol backscatter obtained with 9.11- and 10.59-¿m wavelength continuous wave CO2 lidars and modeled backscatter from aerosol size distribution data. The technique is demonstrated during a flight of the NASA DC-8 aircraft over the Sierra Nevada Mountain Range, California, on 19 September 1995. Volume fraction of each component and effective complex refractive index of the composite particle were determined assuming an internally mixed composite aerosol model. The volume fractions were also used to recompute aerosol backscatter, providing good agreement with the lidar-measured data. The robustness of the technique for determining volume fractions was extended with a comparison of calculated 2.1-¿m backscatter from size distribution data with the measured lidar data converted to 2.1-¿m backscatter using an earlier derived algorithm, verifying the algorithm as well as the backscatter calculations.