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Goodman, JJ, Draine BT, Flatau PJ.  1991.  Application of Fast-Fourier-Transform Techniques to the Discrete-Dipole Approximation. Optics Letters. 16:1198-1200.   10.1364/ol.16.001198   AbstractWebsite

We show how fast-Fourier-transform methods can be used to accelerate computations of scattering and absorption by particles of arbitrary shape using the discrete-dipole approximation.

Draine, BT, Flatau PJ.  2008.  Discrete-dipole approximation for periodic targets: theory and tests. Journal of the Optical Society of America a-Optics Image Science and Vision. 25:2693-2703.   10.1364/josaa.25.002693   AbstractWebsite

The discrete-dipole approximation (DDA) is a powerful method for calculating absorption and scattering by targets that have sizes smaller than or comparable to the wavelength of the incident radiation. The DDA can be extended to targets that are singly or doubly periodic. We generalize the scattering amplitude matrix and the 4 x 4 Mueller matrix to describe scattering by singly and doubly periodic targets and show how these matrices can be calculated using the DDA. The accuracy of DDA calculations using the open-source code DDSCAT is demonstrated by comparison with exact results for infinite cylinders and infinite slabs. A method for using the DDA solution to obtain fields within and near the target is presented, with results shown for infinite slabs. (C) 2008 Optical Society of America

Draine, BT, Flatau PJ.  1994.  Discrete-Dipole Approximation for Scattering Calculations. Journal of the Optical Society of America a-Optics Image Science and Vision. 11:1491-1499.   10.1364/josaa.11.001491   AbstractWebsite

The discrete-dipole approximation (DDA) for scattering calculations, including the relationship between the DDA and other methods, is reviewed. Computational considerations, i.e., the use of complex-conjugate gradient algorithms and fast-Fourier-transform methods, are discussed. We test the accuracy of the DDA by using the DDA to compute scattering and absorption by isolated, homogeneous spheres as well as by targets consisting of two contiguous spheres. It is shown that, for dielectric materials (Absolute value of m less than or similar to 2), the DDA permits calculations of scattering and absorption that are accurate to within a few percent.

Flatau, PJ, Draine BT.  2012.  Fast near field calculations in the discrete dipole approximation for regular rectilinear grids. Optics Express. 20:1247-1252.   10.1364/OE.20.001247   AbstractWebsite

A near-field calculation of light electric field intensity inside and in the vicinity of a scattering particle is discussed in the discrete dipole approximation. A fast algorithm is presented for gridded data. This algorithm is based on one matrix times vector multiplication performed with the three dimensional fast Fourier transform. It is shown that for moderate and large light scattering near field calculations the computer time required is reduced in comparison to some of the other methods. (C) 2012 Optical Society of America

Lelieveld, J, Berresheim H, Borrmann S, Crutzen PJ, Dentener FJ, Fischer H, Feichter J, Flatau PJ, Heland J, Holzinger R, Korrmann R, Lawrence MG, Levin Z, Markowicz KM, Mihalopoulos N, Minikin A, Ramanathan V, de Reus M, Roelofs GJ, Scheeren HA, Sciare J, Schlager H, Schultz M, Siegmund P, Steil B, Stephanou EG, Stier P, Traub M, Warneke C, Williams J, Ziereis H.  2002.  Global air pollution crossroads over the Mediterranean. Science. 298:794-799.   10.1126/science.1075457   AbstractWebsite

The Mediterranean Intensive Oxidant Study, performed in the summer of 2001, uncovered air pollution layers from the surface to an altitude of 15 kilometers. In the boundary layer, air pollution standards are exceeded throughout the region, caused by West and East European pollution from the north. Aerosol particles also reduce solar radiation penetration to the surface, which can suppress precipitation. In the middle troposphere, Asian and to a lesser extent North American pollution is transported from the west. Additional Asian pollution from the east, transported from the monsoon in the upper troposphere, crosses the Mediterranean tropopause, which pollutes the lower stratosphere at middle latitudes.

Flatau, PJ, Draine BT.  2014.  Light scattering by hexagonal columns in the discrete dipole approximation. Optics Express. 22:21834-21846.   10.1364/oe.22.021834   AbstractWebsite

Scattering by infinite hexagonal ice prisms is calculated using Maxwell's equations in the discrete dipole approximation for size parameters x = pi D/lambda up to x = 400 (D = prism diameter). Birefringence is included in the calculations. Applicability of the geometric optics approximation is investigated. Excellent agreement between wave optics and geometric optics is observed for large size parameter in the outer part of the 22 degree halo feature. For smaller ice crystals halo broadening is predicted, and there is appreciable "spillover" of the halo into shadow scattering angles < 22 degrees. Ways to retrieve ice crystal sizes are suggested based on the full width at half-maximum of the halo, the power at < 22deg, and the halo polarization. (C) 2014 Optical Society of America

Flatau, PJ, Stephens GL, Draine BT.  1990.  Light-Scattering by Rectangular Solids in the Discrete-Dipole Approximation - a New Algorithm Exploiting the Block-Toeplitz Structure. Journal of the Optical Society of America a-Optics Image Science and Vision. 7:593-600.   10.1364/josaa.7.000593   AbstractWebsite

The discrete-dipole approximation is used to study the problem of light scattering by homogeneous rectangular particles. The structure of the discrete-dipole approximation is investigated, and the matrix formed by this approximation is identified to be a symmetric, block-Toeplitz matrix. Special properties of block-Toeplitz arrays are explored, and an efficient algorithm to solve the dipole scattering problem is provided. Timings for conjugate gradient, Linpack, and block-Toeplitz solvers are given; the results indicate the advantages of the block-Toeplitz algorithm. A practical test of the algorithm was performed on a system of 1400 dipoles, which corresponds to direct inversion of an 8400 × 8400 real matrix. A short discussion of the limitations of the discrete-dipole approximation is provided, and some results for cubes and parallelepipeds are given. We briefly consider how the algorithm may be improved further.