UTD Theory

This part will only give basic elements on Uniform Theory of Diffraction (UTD). There is a book found to be particularly useful and comprehensive on the subject of UTD : Introduction to the Uniform Geometrical Theory of Diffraction, by McNamara, Pistorius and Malherbe.

Compared with other methods, the UTD has some interesting advantages. It is an efficient tool to understand the phenomenology because the global field results from geometrically localised contributors (rays). In addition, the computational time is reduced. It is frequency independent and enables the method to handle electrically large structures.

IDRA is a electromagnetic computation software based on the UTD. Basically, the software performs a two step steps calculation :

The first is ray tracing. Most of the computation time is spend during this step. Given a source point S and an observation point P, the software has to find the interaction point Q on the structure element. This step is repeated for each structure element. In addition, a visibility test is performed to exclude rays intercepted by another structure element.

Once the interaction point is found, information about angles and curvatures are gathered to compute the UTD coefficients and the corresponding electric field. The details of the UTD coefficients will not be explained here. They are directly derived from classical results.

The following simple ray contributions are taken into account in the computation :

incident ray
reflected ray
diffracted from edges or corners
diffracted from curved surfaces, or also called creeping rays

Higher order contributions are also computed :

doubly reflected
doubly diffracted from edges
reflected and diffracted from edges, or diffracted from edges and then reflected by surfaces, the same with corner diffraction, doubly diffracted
creeping rays reflected or diffracted

For simple shapes, the ray tracing is straightforward. The Descartes-Snell laws can be directly applied to find the reflection point on a plate surface. The Keller’s cone properties are used to compute the position of the diffraction point on a straight edge. The laws are still true for any shape, but they aren’t easy to implement on arbitrary geometries. In these cases, a minimization of the ray path is used to satisfy the Fermat’s Principle.

In contrary to the integral techniques, UTD is a local method. That's why, the field computation at one point is independent from the other observation points. As a result, the computation time is directly related to the number of observation. In addition, the computation time increases significantly when higher order contributions are taken into account. The computation can be 10 times longer with multiple interactions. Since these rays generally have a lower intensity, it is recommended to launch a first run with only simple contributions.