Calculation of the scalar diffraction field from curved surfaces by decomposing the three-dimensional field into a sum of Gaussian beams

Erdem Şahin, Levent Onural

    Research output: Contribution to journalArticleScientificpeer-review

    11 Citations (Scopus)

    Abstract

    We present a local Gaussian beam decomposition method for calculating the scalar diffraction field due to a twodimensional field specified on a curved surface. We write the three-dimensional field as a sum of Gaussian beams that propagate toward different directions and whose waist positions are taken at discrete points on the curved surface. The discrete positions of the beam waists are obtained by sampling the curved surface such that transversal components of the positions form a regular grid. The modulated Gaussian window functions corresponding to Gaussian beams are placed on the transversal planes that pass through the discrete beam-waist position. The coefficients of the Gaussian beams are found by solving the linear system of equations where the columns of the system matrix represent the field patterns that the Gaussian beams produce on the given curved surface. As a result of using local beams in the expansion, we end up with sparse system matrices. The sparsity of the system matrices provides important advantages in terms of computational complexity and memory allocation while solving the system of linear equations.

    Original languageEnglish
    Pages (from-to)527-536
    Number of pages10
    JournalJournal of the Optical Society of America A: Optics Image Science and Vision
    Volume30
    Issue number3
    Publication statusPublished - 2013
    Publication typeA1 Journal article-refereed

    ASJC Scopus subject areas

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

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