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Les fonctions ponctuées et l’optique corpusculaire

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Abstract

A distribution of complex amplitude F(x), x being a linear variable, has a Fourier transform f(u), directed, since u is a direction cosine and limited to the region φ. F(x) is f(u) developed in a Fourier integral, which is a continued function. But f(u) also has a development in Fourier series inside φ. In this series we call F0(x) the summation of the terms. F(x) and F0(x) are related by a simple convolution. Let φ(u) be the function representing the region φ, having a value unity inside φ at zero elsewhere. Φ(x) will be its transform in x space. Then F(x) = F0(x) × Φ(x). F(x) was a diffracted and redundant function; F0(x) is neither; it is euclidian like f(u), and the cycle of corpuscular optics is thus closed. We term information points the points of F0(x); the function we call a punctuated function. If φ is spread over its maximum field 2/λ, the distance between the points is λ/2, and in coherent as well as incoherent imagery they are at the limit of the resolving power for the wavelength used. It is therefore impossible to distinguish the photons in a linear diffracted distribution, but its spectrum, being euclidian directed and consequently dispersive, always isolates the photons in space and in time. (This spectrum, function of the direction cosines u, v, w, is the basic function of the corpuscular geometric optics presently developed.) The author outlines without experiment or new calculations work published at the end of 1944; that was corrected in 1966 by L. C. Martin, in his Theory of the Microscope.

© 1968 Optical Society of America

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