THE DIFFRACTION TRANSFORMATION OF ELECTROMAGNETIC FIELDS BETWEEN TWO PARALLEL PLANES,
Abstract
The problem of inverse diffraction between two parallel planes is: given the diffracted field over some area of the second plane, find the field in the aperture of the first plane. In the infinite version both the aperture and the area in the second plane are assumed infinite in extent. For the finite problem these regions are considered finite with known dimensions and the field on the first plane is assumed zero outside the aperture. An exact inverse transformation is given for the infinite problem. However, this inverse is shown to be numerically ill-conditioned, and approximate inverses based on a consideration of the field's spectrum are given. The finite problem of inverse diffraction is formulated using the Hilbert-Schmidt theory of integral equations. The kernel of the direct finite transformation is shown to be diagonalized by the eigenfunctions of the first iterates of the kernel. Thus an exact expression for the inverse kernel is given in terms of an infinite series of these eigenfunctions. However, the series is shown to be numerically unstable beyond a certain term, which is predicted by the norm of the direct kernel. Truncation of the series at this term provides numerically stable solutions to the finite inverse problem. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1969
- Accession Number
- AD0697766
Entities
People
- Georges A. Deschamps
- Preston Lee Ransom
Organizations
- University of Illinois Urbana–Champaign