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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References
D. Gabor, “Theory of communication”, J. IEE (London) 93 (III) (1946) 429–457.
C.W. Helstrom, “An expansion of a signal in Gaussian elementary signals”, IEEE Trans. Inf. Theory IT-12 (1970) 81–82.
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M.J. Bastiaans, “Gabor’s expansion of a signal into Gaussian elementary signals”, Proc. IEEE 68 (1980) in press.
M.J. Bastiaans, “A sampling theorem for the complex spectrogram, and Gabor’s expansion of a signal in Gaussian elementary signals”, to be published in the Proceedings of the International Optical Computing Conference, Washington, D.C., 8–11 April, 1980.
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© 1980 Springer-Verlag Berlin · Heidelberg
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Bastiaans, M.J. (1980). The Expansion of an Optical Signal into a Discrete Set of Gaussian Beams. In: Pöppl, S.J., Platzer, H. (eds) Erzeugung und Analyse von Bildern und Strukturen. Informatik-Fachberichte, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-67687-1_4
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DOI: https://doi.org/10.1007/978-3-642-67687-1_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10130-7
Online ISBN: 978-3-642-67687-1
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