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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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 language	English
Title of host publication	Erzeugung und Analyse von Bildern und Strukturen, Informatik-Fachberichte, Band 29, 81. Jahrestagung der Deutsche Gesellschaft für angewandte Optik, Essen, Germany
Editors	S.J. Pöppl, H. Platzer
Place of Publication	Berlin
Publisher	Springer
Chapter	4
Pages	23-32
ISBN (Electronic)	978-3-642-67687-1
ISBN (Print)	978-3-540-10130-7
DOIs	https://doi.org/10.1007/978-3-642-67687-1_4
Publication status	Published - 1980

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Cite this

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title = "The expansion of an optical signal into a discrete set of Gaussian beams",

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.",

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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. ed. / S.J. Pöppl; H. Platzer. Berlin: Springer, 1980. p. 23-32.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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T1 - The expansion of an optical signal into a discrete set of Gaussian beams

AU - Bastiaans, M.J.

PY - 1980

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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

ER -

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

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