### Abstract

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 X 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.

Original language | English (US) |
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Pages (from-to) | 593-600 |

Number of pages | 8 |

Journal | Journal of the Optical Society of America A: Optics and Image Science, and Vision |

Volume | 7 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1990 |

### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Atomic and Molecular Physics, and Optics
- Computer Vision and Pattern Recognition

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## Cite this

*Journal of the Optical Society of America A: Optics and Image Science, and Vision*,

*7*(4), 593-600. https://doi.org/10.1364/JOSAA.7.000593