Abstract

A new approach is presented for converting the surface integral, representing the Kirchhoff diffracted field of an aperture on a plane screen, to a line integral. It has the advantages that it is mathematically rigorous and explicit and that it results in a representation that has exactly the same properties as the original Kirchhoff formula, i.e., it admits arbitrary source distributions and it is continuous everywhere in the source-free half-space, including the geometric-optics shadow boundary. Moreover, this new representation involves a unit vector whose direction can be adjusted so as to allow for accurate machine computations.

© 1985 Optical Society of America

Line integrals and physical optics. Part I. The transformation of the solid-angle surface integral to a line integral

John S. Asvestas
J. Opt. Soc. Am. A 2(6) 891-895 (1985)

Boundary Diffraction Wave in the Domain of the Rayleigh–Kirchhoff Diffraction Theory*

E. W. Marchand and E. Wolf
J. Opt. Soc. Am. 52(7) 761-767 (1962)

Young-Kirchhoff-Rubinowicz theory of diffraction in the light of Sommerfeld's solution

Yusuf Z. Umul
J. Opt. Soc. Am. A 25(11) 2734-2742 (2008)

Generalization of the Maggi-Rubinowicz Theory of the Boundary Diffraction Wave—Part II†

Kenro Miyamoto and Emil Wolf
J. Opt. Soc. Am. 52(6) 626-636 (1962)

Modified diffraction theory of Kirchhoff

Yusuf Z. Umul
J. Opt. Soc. Am. A 25(8) 1850-1860 (2008)