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, which is bi-orthonormal to the set of Gaussian elementary signals; this bi-orthonormality property allows an easy determination of the expansion coefficients.

To: Papers by Martin J. Bastiaans