[Dirichlet's Theorem].
In the introduction to Chapter II of his work L'Intégrale de Fourier et ses Applications à l'Optique, Duffieux reduces Dirichlet's Theorem to a "specific summary." Developed by a convolution where the functions of influence apply [Rev. Opt. 34, 351 (1960)], Dirichlet's Theorem immediately gives data on the form of two functions that the Fourier transform introduces in Fraunhoffer diffraction at infinity. The distribution plane, where one normally cuts off Huygens' pupils, F(x,y), is composed not of points, but of diffraction figures or correlation functions. The function f(u,v) of a spread of frequencies is also a directive function, but it shows no correlation and has discontinuities. F(x,y) is linked with the undulatory theory of light, and f(u,v) represents a corpuscular flux. Two conclusions can be drawn therefrom: (1) the limited pupils must, correctly, be defined by the directive function f(u,v); (2) Fourier's equation establishes a relation between two aspects of the propagation of the lig t crossing a plane, one of which conforms to the undulatory theory of light, the other to his corpuscular theory. We are visibly lacking a corpusculatory theory of light and its coherent images.
Duffieux
P M
PM
Université de Besançon, Faculté des Sciences, La Bouloie-Besançon, France.