The expansion of an optical signal into a discrete set of Gaussian beams

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Abstract

It is shown how an optical signal can be expanded in Gaussian beams. The expansion is essentially the one suggested by Gabor in 1946, when he proposed to expand a signal into a discrete set of properly shifted and modulated Gaussian elementary signals; determining the expansion coefficients, however, seemed difficult, since the set of Gaussian elementary signals is not orthogonal. A set of functions is described, wnich is bi-orthonormal to the set of Gaussian elementary signals; this bi-orthonormality property allows an easy determination of the expansion coefficients.
Original languageEnglish
Title of host publicationErzeugung und Analyse von Bildern und Strukturen, Informatik-Fachberichte, Band 29, 81. Jahrestagung der Deutsche Gesellschaft für angewandte Optik, Essen, Germany
EditorsS.J. Pöppl, H. Platzer
Place of PublicationBerlin
PublisherSpringer
Chapter4
Pages23-32
ISBN (Electronic)978-3-642-67687-1
ISBN (Print)978-3-540-10130-7
DOIs
Publication statusPublished - 1980

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    Bastiaans, M. J. (1980). The expansion of an optical signal into a discrete set of Gaussian beams. In S. J. Pöppl, & H. Platzer (Eds.), Erzeugung und Analyse von Bildern und Strukturen, Informatik-Fachberichte, Band 29, 81. Jahrestagung der Deutsche Gesellschaft für angewandte Optik, Essen, Germany (pp. 23-32). Springer. https://doi.org/10.1007/978-3-642-67687-1_4