## Abstract

A specially developed method is proposed to retrieve the particle volume
distribution, the mean refractive index, and other important physical parameters,
e.g., the effective radius, volume, surface area, and number concentrations of
tropospheric and stratospheric aerosols, from optical data by use of multiple
wavelengths. This algorithm requires neither *a priori* knowledge of
the analytical shape of the distribution nor an initial guess of the distribution. As
a result, even bimodal and multimodal distributions can be retrieved without any
advance knowledge of the number of modes. The nonlinear ill-posed inversion is
achieved by means of a hybrid method combining regularization by discretization,
variable higher-order B-spline functions and a truncated singular-value
decomposition. The method can be used to handle different lidar devices that work
with various values and numbers of wavelengths. It is shown, to my knowledge for the
first time, that only one extinction and three backscatter coefficients are
sufficient for the solution. Moreover, measurement errors up to 20% are allowed. This
result could be achieved by a judicious fusion of different properties of three
suitable regularization parameters. Finally, numerical results with an additional
unknown refractive index show the possibility of successfully recovering both
unknowns simultaneously from the lidar data: the aerosol volume distribution and the
refractive index.

© 2001 Optical Society of America

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