Abstract

In the introduction to Chapter II of his work L‘Intégrale de Fourier et ses Applications à I’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,y); (2) Fourier’s equation establishes a relation between two aspects of the propagation of the light 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.

© 1967 Optical Society of America

Full Article  |  PDF Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (8)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Tables (1)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (37)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription