الفهرس 
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Abstract
The fine of art of synthesizing, analyzing and designing surface reflector antennas of many various geometries did not really advance until the days of World War 11, when numerous ’applications evolved to satisfy diverse technical demands. Subsequent demands for surface reflectors for use in radio astronomy, microwave communications, satellite communications and tracking, and the like have resulted in both development of sophisticated reflector configurations and analytical and experimental design techniques.
Reflector antennas may take many configurations, some of the most popular ones being plane, corner, cliE-ved reflectors and so on. In this thesis, only the curved reflectors such as Cassegrain and Gregorian will be discussed. In chapter 1, an introduction to the shaped reflectors is demonstrated. The concept of wave reflection is discussed and compared with the reflection of light. Surface reflector antennas have the same function of light mirrors. The shape of antenna beam may be controlled by different methods. One of these methods is the surface shaping of a single or dual reflectors. The need of this shaping is briefed in several points. Some applications that require beam/surface shaping are summarized in the same chapter. Also the use of Geometrical Optics technique in reflector analysis is shown wi th its validi ty requirement on the operating wavelength relative to the reflector dimensions. Dealing with the mathematics of reflector antennas is not an easy task so that many approximation techniques are used to make the problem easier. Exact Maxwell’s wave quations were used in some reflector analysis with pecial conditions in very limi ted papers. The shaped eflector synthesis problem is used to be treated using technique and then analyzed by less approximate . echniques such as GTD and PO. Since this thesis is ~oncerned with the dual reflectors synthesis problem, lonly GO is used. The physical definition of the dual reflectors ynthesis problem states that for a given feeder power ttern and a specified aperture power pattern that ~tisfies the required optimum performance for the ntenna system, the surfaces of both the subreflec~9r an~ :he main reflector surfaces are wanted. There are two thods to define the dual reflectors synthesis problem thematically. The first one expresses the problem in second order rtial differential Monge Ampere equations (MA PDE’s). he production of the MA PDE’ s using complex variables nd stereographic projection is introduced in chapter 2. he different types of the MA PDE’s for different flector systems are included with the aid of previous rk of many researchers. We comment on the difficulties ,le in solving the elliptic type of MA PDE. The second mathematical defini tion for the same roblem is introduced in chapter 3. Using real variables nstead of complex variables, a set of first order PDE’s sdeveloped from Snell’s law, energy conservation rinciple and total derivative condition for the ubreflector surface. A comparison between the two thematical definitions shows that the second method is uch easier than the first one. The ease o~~ first rder PDE’s comes from its progressive and non-iterative ~t:ype of solution while the second order PDE’ s needs Jteration and simultaneous type of solution. Hence, much less time and memory capacity are needed when the first ~rder PDE’s are solved. The algorithm of the method of
line are described in detail on the same chapter.
After discussion of some numerical and programming nsiderations, design of offset Cassegrain and Gregorian ual shaped reflectors are presented in chapter 4. Effect 1 f changing ini tial points and di fferent design rameters such as offset parameter and tilt angle is Iso discussed.
o reduce subreflector and main reflector._ edge’~ iffraction, tapering of both feeder and aperture power tterns are made.
Smooth reflector surfaces are obtained except for a all region inside the reflector where some numerical rors appear. These errors can be avoided if an initial entral point is chosen. However, the specified main eflector rim is lost. A technique based on surface nterpolation is proposed in chapter 5. One dimension, ~o dimensions and cubic spline interpolation are made. flectors system is divided into two wings to enable the ystem symmetry to play an important role in the nterpolation process. Lagrangian polynomials are chosen for interpolation cause of non uniform domain over which interpolation is ade. Another problem appears during the interpolation rocess is called slabs intersection. Why does this roblem appear and how can we overcome it, are discussed ith a demonstrative example showing the success of the omplete interpolation procedures.