The digitized Green's function (DGF) algorithm and the underlying theory are described. This finite element algorithm models dielectric particles of arbitrary shape and arbitrary optical structure. DGF predictions of differential and total cross sections are compared with predictions of Mie and EBCM algorithms for several homogeneous spheres and spheroids. Results of tests of convergence of the DGF calculation as the number of elements are increased are presented. Computer time and storage requirements as functions of wavelength and particle size, shape, and optical structure are discussed.

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Stochastic inversion is a well known technique for the solution of inverse problems in tomography. It employs the idea that the propagation medium may be represented as random with a known spatial covariance function. In this paper, a generalization of the stochastic inverse for acoustic travel-time tomography of the atmosphere is developed. The atmospheric inhomogeneities are considered to be random, not only in space but also in time. This allows one to incorporate tomographic data ͑travel times͒ obtained at different times to estimate the state of the propagation medium at any given time, by using spatial-temporal covariance functions of atmospheric turbulence. This increases the amount of data without increasing the number of sources and/or receivers. A numerical simulation for two-dimensional travel-time acoustic tomography of the atmosphere is performed in which travel times between sources to receivers are calculated, given the temperature and wind velocity fields. These travel times are used as data for reconstructing the original fields using both the ordinary stochastic inversion and the proposed time-dependent stochastic inversion algorithms. The time-dependent stochastic inversion produces a good match to the specified temperature and wind velocity fields, with average errors about half those of the ordinary stochastic inverse.

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