Lidar remote sensing of clouds provides direct measurement of the radar backscatter coefficient but not the extinction coefficient, which is needed for any calculations involving optical depth. The relationship between these quantities for single spheres is very complicated but becomes simpler for poly-dispersions or illumination by radiation with a broad spectrum. The accuracy of estimating the extinction coefficient from measured radar backscatter coefficients of thin clouds is examined for single- and multiple-wavelength lidar systems. The stability of the ratio of the coefficients is examined for radii between 1 and 100 µm for a poly-dispersion of 5-µm width. The results show that the extinction coefficients of a broad selection of thin clouds may be obtained from lidar measurements with errors of ~15% by visible and near visible lidar systems. Multiple lidar wavelengths permit a reduction of the error to ~9%.
V. E. Derr, "Estimation of the extinction coefficient of clouds from multiwavelength lidar backscatter measurements," Appl. Opt. 19, 2310-2314 (1980)