Study On The Uniform Geometrical Theory Of Diffraction Method With Targets Constructed By Arbitrary Surfaces

The method of Uniform Geometrical Theory of Diffraction (GTD, UTD) is widely used when analyzing electrically large targets which are approached by typical simple geometric objects like boards, cylinders and cones traditionally. However, this method can not be used when it comes to arbitrary convex surfaces in practice, which makes the application of the method limited and makes it necessary both practically and theoretically to study UTD method based on models constructed by arbitrary surfaces; In the area of modeling, in 1991, STEP, the international standard for the geometrical definition of industrial products, was published by the International Organization for Standardization (ISO) where the Non-Uniform Rational B-Spline (NURBS) technique was accepted as the only mathematical way to define shapes of products. While the study of this technique becomes deeper and deeper, it has been already included by more and more commercial CAD/CAM softwares.Combing with supported projects, in this dissertation, the UTD method based on models constructed by arbitrary surfaces is studied, where complex models are approached by NURBS technique and a series of numerical algorithms and methods are given to solve basic problems like tracing of rays, calculating of fields, determining of occlusions, etc, aiming at achieving a numerical UTD method that can be applied to analyze electrically large targets modeled by arbitrary convex surfaces. Numerical algorithms and methods given in this dissertation are managed logically and the major work and contributions are as follows:As the basis of this dissertation, the mathematical property of NURBS surface and Bezier surface is thoroughly studied and specific method of transforming NURBS surfaces into Bezier surfaces is discussed.Before forming the kernel of algorithms, certain items which can be done beforehand and used afterward need considering first. These items include the choosing and forming of numerical optimize algorithms; uniform sampling of surfaces; determining of relationship between given point and surface and that between given surfaces. These items are not only frequently used afterward but also show one of the thoughts in this dissertation that changes can be made between precision efficiency.Tracing of various kinds of rays is considered as the basis of UTD method, the rays in the lit region where direct rays, reflected rays, diffracted rays and other rays exist are traced firstly numerically, where the tracing of reflected rays and diffracted rays take more consideration with flowchart of algorithm given. The algorithms can be applied to arbitrary surfaces and numerical results are presented to prove the algorithms.Among those rays UTD method managed, the more complex and important one is the surface diffracted rays, that is, the creeping rays which play the most important role in the shadow region. The tracing of rays in the shadow region is done numerically after that is finished in the lit region. Two aspects are taken into account due to the fact that in practice the source may be located on the surface or off the surface and corresponding flowcharts are given separately. Numerical results are presented to prove the algorithms.Within most optical methods of electromagnetic calculation, occlusions are necessary to consider to ensure the validity of results. In this dissertation, the occlusion between rays and surfaces constructed by NURBS is studied and an algorithm which is adequate in possible cases is given where simple geometrical principle is introduced. The case when the ray starts from or ends on the surface where self-shadowing is included is taken into account and also is the case when the ray intersects with the surface on the extension. The algorithm has been applied to algorithms studied in ray-tracing.As it is known that in UTD method, tracing of rays is the basis and determining of occlusions is the guarantee while the calculation of fields and pattern is the final goal. After obtaining the information of the ray-tracing, the calculation of fields radiated from the source and further computation of pattern becomes key problem to decide whether the method studied can be applied practically. According to the location of the source, two aspects are studied separately for calculating fields both in the lit region and the shadow region. The calculation of parameters by numerical means is given combining the information from ray-tracing done before and the definition of NURBS. Examples of pattern on different models are given where the results are good and reasonable.The basis of arbitrary-modeled UTD method is formed in this thesis, and it can be applied to analyze electrically large targets constructed by arbitrary surfaces in practice. As a ray-based method, UTD can perform well as long as the source point and the observer point are given in ray tracing, and in the calculating of pattern, only the initial distribution of fields around the radiating source are need but not the source itself. In practice, complex antennas are used as the radiating sources which can be analyzed by other computational electromagnetic methods independently to get the distribution of fields around them. Therefore, methods presented in this thesis can be combined with other methods to analyze electrically large targets with complex antennas as sources. Method of Moment and the popular commercial software, ANSOFT, are introduced for achieving the distribution of fields around complex antennas, combining with methods in this thesis we try to extend arbitrary-modeled UTD method into wider areas, where electrically large targets with complex antennas mounted can be handled.