Application of a particular class of integrals in the theory of diffraction

A particular class of integrals appearing in the problems of diffraction is treated in this paper. For the analysis of the classical sources or lasers, Kirchhoff's integral can be used only for apertures of a determined shape. So far, the problems are solved and analyzed completely, whenever the geomtry of apertures creates the possibility of using Kirchhoff's integral, namely for the so-called geometry of rectangular apertures. Other apertures exist for which Kirchhoff's integral cannot be applied, because of difficulties of mathematical character. In this group of apertures belong all the apertures which are bounded with an inclined line, such as those with triangular form. In this paper, the application of a particular class of integrals is shown to give satisfying results in two problems of diffraction theory: double-diffraction phenomena consisting on separating the interferential-diffractional field from the diffractional field, and the case of near-zone of diffraction in the triangular aperture.