Les fonctions ponctuées et l'optique corpusculaire.
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 phi. 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 phi. In this series we call F(0)(x) the summation of the terms. F(x) and F(0)(x) are related by a simple convolution. Let phi(u) be the function representing the region phi, having a value unity inside phi at zero elsewhere. Phi(x) will be its transform in x space. Then F(x) = F(0)(x) x Phi(x). F(x) was a diffracted and redundant function; F(0)(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 F(0)(x); the function we call a punctuated function. If phi is spread over its maximum field 2/lambda, the distance between the points is lambda/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.
Duffieux
P M
PM