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

M.J. Bastiaans

doi:10.1007/978-3-642-67687-1_4

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

M.J. Bastiaans

Signal Processing Systems

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

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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.

Originele taal-2	Engels
Titel	Erzeugung und Analyse von Bildern und Strukturen, Informatik-Fachberichte, Band 29, 81. Jahrestagung der Deutsche Gesellschaft für angewandte Optik, Essen, Germany
Redacteuren	S.J. Pöppl, H. Platzer
Plaats van productie	Berlin
Uitgeverij	Springer
Hoofdstuk	4
Pagina's	23-32
ISBN van elektronische versie	978-3-642-67687-1
ISBN van geprinte versie	978-3-540-10130-7
DOI's	https://doi.org/10.1007/978-3-642-67687-1_4
Status	Gepubliceerd - 1980

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10.1007/978-3-642-67687-1_4

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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 (editors), Erzeugung und Analyse von Bildern und Strukturen, Informatik-Fachberichte, Band 29, 81. Jahrestagung der Deutsche Gesellschaft für angewandte Optik, Essen, Germany (blz. 23-32). Springer. https://doi.org/10.1007/978-3-642-67687-1_4

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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.",

author = "M.J. Bastiaans",

year = "1980",

doi = "10.1007/978-3-642-67687-1\_4",

language = "English",

isbn = "978-3-540-10130-7",

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booktitle = "Erzeugung und Analyse von Bildern und Strukturen, Informatik-Fachberichte, Band 29, 81. Jahrestagung der Deutsche Gesellschaft f{\"u}r angewandte Optik, Essen, Germany",

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The expansion of an optical signal into a discrete set of Gaussian beams. / Bastiaans, M.J.
Erzeugung und Analyse von Bildern und Strukturen, Informatik-Fachberichte, Band 29, 81. Jahrestagung der Deutsche Gesellschaft für angewandte Optik, Essen, Germany. reds. / S.J. Pöppl; H. Platzer. Berlin: Springer, 1980. blz. 23-32.

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

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PY - 1980

Y1 - 1980

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-642-67687-1_4

DO - 10.1007/978-3-642-67687-1_4

M3 - Conference contribution

SN - 978-3-540-10130-7

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EP - 32

BT - Erzeugung und Analyse von Bildern und Strukturen, Informatik-Fachberichte, Band 29, 81. Jahrestagung der Deutsche Gesellschaft für angewandte Optik, Essen, Germany

A2 - Pöppl, S.J.

A2 - Platzer, H.

PB - Springer

CY - Berlin

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

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