UTD analysis of a shaped subreflector in a dual offset-reflectorantenna system

The geometrical theory of diffraction (GTD) is known as an efficient high-frequency method for the analysis of electrically large objects such as a reflector antenna. However it is difficult to obtain geometrical parameters in order to apply GTD to an arbitrary shaped reflector, especially a subreflector. The geometrical parameters of an arbitrary shaped subreflector for the uniform theory of diffraction (UTD) analysis are derived based on differential geometry. The radiation patterns of various subreflector types, including hyperboloidal and a shaped subreflector, are evaluated by UTD. The computed result for the hyperboloidal reflector agrees well with that obtained by uniform asymptotic theory (UAT)     

附加相位修正副面的多波束环面天线方向图

首先利用等光程条件导出了抛物环面上的点与副面上的点的关系公式；其次，巧妙地利用微波光学强度定律、几何光学法和物理光学法给出了计算“附加相位校正副面的多波束抛物环面天线”的辐射方向图公式；最后，利用所得的辐射方向图公式对一个实际天线进行了理论计算，理论计算值和实验测试值吻合异常良好。     

Subreflector extension for improved efficiencies in Cassegrain antennas--GTD/PO analysis

Both offset and symmetric Cassegrain reflector antennas are used in satellite and ground communication systems. It is known that the subreflector diffraction can degrade the performance of these reflectors. A geometrical theory of diffraction/physical optics (GTD/PO) analysis technique is used to investigate the improving effects of the extended subreflector, beyond its optical rim, on the reflector efficiency and farfield patterns. Representative numerical results are shown for an offset Cassegrain reflector antenna with different feed illumination tapers and subreflector extensions. It is observed that for subreflector extensions as small as1 lambdanoticeable improvements in the overall efficiencies can be expected. Useful design data are generated for the efficiency curves and far-field patterns.     

Subreflector shaping for antenna distortion compensation: an efficient Fourier-Jacobi expansion with GO/PO analysis

Technological demands have brought a renewed interest in the application of large reflector antennas with steadily increasing operating frequencies and antenna dimensions. The high surface accuracy of the main reflector required by these antennas can often not be achieved with available manufacturing technologies. The utilization of a shaped subreflector for main reflector-distortion compensation is considered an effective measure to enhance the overall radiation performance of an antenna system. In the process of evaluating the suitability of the subreflector shaping, however, it is crucial to accurately assess the most suitable subreflector shape within a reasonable amount of computational time. This is especially true for electrically large reflectors, where simple analysis of the radiation characteristics already creates a serious computational burden, moreover, since reflector shaping is a synthesis process that necessitates repeated computation of the radiation characteristics. In this paper, the development of an efficient computational tool for subreflector shaping is presented. The subreflector shaping is performed through a combination of geometrical optics (GO) and physical optics (PO) on the subreflector and the main reflector, respectively. To significantly limit the number of parameters subject to optimization, the subreflector surface is parameterized by the coefficients of a global, orthogonal Fourier-Jacobi set (related to Zernike polynomials), which allows us to accurately represent a surface with only a small number of coefficients. The incorporation of this surface expansion into a GO/PO synthesis technique is detailed, representative results are given for a computationally challenging reflector configuration, and the tolerances for the shaped subreflector surface are studied.     

An offset-fed reflector antenna with an axially symmetric main reflector

A design method for an offset-fed, dual reflector antenna (Cassegrain type or Gregorian type) system with an axisymmetric main reflector is presented. Geometrical optics (GO) and the geometrical theory of diffraction (GTD) are used to find the surface-current density on the main reflector. A modified Jacobi-Bessel series (JBS) method is used to find the far-field pattern for the physical optics (PO) integral. In the defocused mode of operation, a new technique is developed to find the reflection point on the subreflector corresponding to the defocused feed and a general field point on the main reflector. Two sample systems are designed.     

La synthèse d’antennes à deux réflecteurs conformés à alimentation décalée

A potentially economic method for upgrading the gain of the large earth reflector antenna Cassegrain system to a gain comparable to that obtainable with a dualshaped reflector antenna system is presented herein. It involves a redesign of only the subreflector portion of a Cassegrain antenna or the introduction of a subreflector feed system for a paraboloid. A pair of offset subreflectors are synthesized which will give a controllable high gain amplitude distribution in the aperture of the large paraboloid. The synthesis method that is used is based on an approximate formulation for an offset dual shaped high gain antenna where the geometrical optics energy was scattered from a subreflector and then from a second large reflector which reflected a uniform phase distribution. In the present offset dual shaped subreflector (DSS) antenna, the second reflection is from a smaller subreflector and it scatters a spherical wave that feeds a hyperboloid or feeds a large paraboloid directly. Excellent results are shown for the approximate synthesis of the DSS.     

Asymptotic transition region theory for edge diffraction. I.Tracing transition regions via reflectors

A new edge-diffraction theory for multireflector antennas is presented. It is based on the uniform geometrical theory of diffraction (UTD) and other well-known asymptotic techniques, but is simplified and extended to cover edge diffraction in the presence of several reflector surfaces. The main emphasis of the theory is placed on the transition region around the boundary of the geometrical optics (GO) field. The theory describes the field near the GO boundary in terms of a standard function and a wavelength-dependent parameter Δρ, where Δρ represents the lateral extent of the transition region. The field around the GO boundary can thereby be constructed solely from knowledge of the single parameter Δρ. Formulas are presented for tracing Δρ along the GO boundary from a diffraction point at a certain edge via other possible reflectors. Existing diffraction theories do not allow such tracing of transition region fields via several reflectors     

Focused aperture antenna using a spherical main reflector with (Cassegrain) convex feed

A focused aperture antenna has been realised using a (Cassegrain) convex subreflector with a spherical main reflector. The design was based on geometrical optics, and good agreement was obtained between the measured and calculated field in the focal region.     

Synthesis of offset dual shaped subreflector antennas for control of Cassegrain aperture distributions

Many existing large ground reflector antennas have been designed as Cassegrain systems-i.e., paraboloid/hyperboloid combinations. Other large ground antennas are simply paraboloid designs. Upgrading the gain of these systems to a gain comparable to that obtainable with a dual shaped reflector antenna system has been an important and costly objective of many such ground stations. A potentially economic method for such an antenna upgrade is presented herein. It involves a redesign of only the subreflector portion of a Cassegrain antenna or the introduction of a subreflector feed system for a parabaloid. A pair of offset subreflectors are synthesized which will give a controllable high gain amplitude distribution in the aperture of the large paraboloid. The synthesis method that is used is based on an approximate formulation for an offset dual shaped high gain antenna that was first presented by Galindo-Israel and Mittra in 1977. In that approximate formulation, the geometrical optics (GO) energy was scattered from a subreflector and then from a second large reflector which reflected a uniform phase distribution. In the present offset dual shaped subreflector (DSS) antenna, the second reflection is from a smaller (sub) reflector and it scatters a spherical wave that feeds a hyperboloid or feeds a large paraboloid directly. Excellent results are shown for the approximate synthesis of the DSS.     

Diffraction of high-frequency electromagnetic waves by curvedstrips

The authors describe the construction of a high-frequency solution in the geometrical theory of diffraction (GTD) format for the generation of edge-diffracted space rays and edge-excited surface waves by an electromagnetic wave normally incident on the edge of a curved impedance strip. The transformation coefficients necessary for the analysis of the diffraction on curved surfaces with equal vanishing face impedances are tabulated in a form appropriate for numerical applications. The procedure for evaluating the diffracted field excited by the edge of a cylindrically curved strip, which can be associated with a reflector antenna or an aperture on a curved surface, is presented for both perfectly and nonperfectly conducting cases     

Analysis of near-field Cassegrain reflector: plane wave versuselement-by-element approach

A near-field Cassegrain reflector (NFCR) is an effective way to magnify a small phased array into a much larger aperture antenna for limited scan applications. Traditionally the pattern wave approach, i.e. the field from the feed array incident on the subreflector is approximated by a truncated collimated beam with planar phase and tapered amplitude distribution. This approach simplifies the computation tremendously, but fails to provide design information about the most critical component of the whole antenna system, namely, the feed array. With the help of today's computers, it is now feasible to calculate the pattern of a NFCR by a more exact element-by-element approach. Each element in the feed array is considered individually and the diffraction pattern from the subreflector is calculated by the geometrical theory of diffraction (GTD). The field contributions from all elements are superimposed at the curved main reflector surface, and a physical optics integration is performed to obtain the secondary pattern     

A study of three techniques used in the diffraction analysis ofshaped dual-reflector antennas

An examination is presented of three techniques used for the efficient computation of fields diffracted by a subreflector that has been shaped by geometrical optics synthesis. It is found that these techniques, which are based on the geometrical theory of diffraction (GTD), produce errors in the computed fields that are specific to shaped reflectors. These errors are examined for a reflector system shaped to produce maximum gain from a tapered feed illumination. The discrepancies are directly related to the caustic being located near an observation point of the GTD calculations. The errors found are localized, and they increase in magnitude as the caustic approaches the main reflector. In a general offset geometry, the location of the caustic may be located arbitrarily close to the main reflector given a prescribed output aperture distribution. For the specific case considered here-the common situation of shaping to produce maximum gain-the caustic is located near the edge of the main reflector and on the reflection shadow boundary. A local correction is derived which creates a uniform solution through the caustic and across the reflection shadow boundary. Away from this point the calculation recedes to the standard GTD solution     

Application of the geometrical theory of diffraction to Cassegrain subreflectors with laterally defocused feeds

The geometrical theory of diffraction (GTD) as formulated by R. G. Kouyoumjian has been applied to predict the radiation characteristics of hyperboloidal subreflectors with laterally defocused feeds. In caustic or multicaustic directions the scattered fields are determined using an equivalent ring current placed along the edge of the subreflector. The theoretical results are compared to measured amplitude and phase data. In order to improve the agreement, the blocking effects of the feed horn have been accounted for using the geometrical theory of diffraction. The calculated subreflector fields have been used to illuminate a paraboloid from which the scattered field is determined by physical optics. The results are compared to those obtained using a laterally defocused equivalent paraboloid.     

Diffraction par le réflecteur secondaire d’une antenne Cassegrain de révolution

Diffraction by the subreflector of a revolution dual reflector antenna is studied as contribution to the side-lobe radiation of the antenna; a better knowledge of this sidelobe radiation is necessary in order to satisfy more and more difficult specifications. Calculation of the subreflector diffracted field is made with geometrical theory of diffraction and more precisely with the uniform asymptotic theory. The antenna is made of two revolution surfaces generated by two meridian curves which are not necessarily the set hyperbola-parabola of the classical Cassegrainian antenna. Computation results are compared to measurements made on the subreflector of an existing antenna. The agreement is satisfying particularly in the angular zone corresponding to the primary feed spill-over.     

G/T maximization of a paraboloidal reflector fed by a dipole-diskantenna with ring by using the multiple-reflection approach and themoment method

A 1.8-m paraboloidal reflector fed by a dipole-disk antenna with a beamforming ring is optimized for high G/T at L-band by using the moment method (MM) and the multiple reflection (MR) approach. The MR approach is based on using MM to calculate the radiation and scattering patterns of the feed, using physical optics plus uniform geometrical theory of diffraction (UTD) to include the reflector, and in addition to include the mutual interaction (multiple reflections) between the reflector and the feed by using the expression for the sum of an infinite geometric series. The MR approach is shown to be equally accurate as a MM solution of the complete antenna with reflector, provided the reflector is in the far field of the feed, and the MR approach is much faster. As a result of the calculations using the MR approach, design curves are presented showing how the G/T varies as a function of antenna geometry, size, and elevation angle, all for a given noise profile of the surrounding sky and ground. The computed radiation patterns and G/Ts are compared with measurements for several elevation angles and surrounding terrain     

Cross polarization in dual reflector antennas--A PO and PTD analysis

A physical optics (PO) and physical theory of diffraction (PTD) analysis of symmetric and offset dual reflector antennas is performed. It is shown that in most cases PO gives sufficient accuracy, but the PTD correction can be of importance to determine the depolarization, especially if the subreflector edge taper is low.     

Analysis of blended rolled edge reflectors using numerical UTD

The uniform geometrical theory of diffraction (UTD) concept is used to predict the scattered fields in the target zones of compact-range reflectors. Since the necessary diffraction coefficients are not known in a closed form, a numerical method to calculate the diffraction coefficients is described. In the numerical method, the problem is reduced to two dimensions, and physical optics line integration is used to compute the diffraction coefficients. Thus, the method is computationally efficient. The method is used to analyze two compact-range reflectors. The results obtained using the numerical UTD show good agreement with the scattered fields obtained using a corrected physical optics surface integration     

Diffraction by an arbitrary subreflector: GTD solution

The high-frequency asymptotic solution of diffraction by a conducting subreflector is studied. By using Keller's geometrical theory of diffraction and the newly developed uniform asymptotic theory of diffraction, the scattered field is determined up to an including terms of orderk^{-1/2}relative to the incident field. The key feature of the present work is that the surface of the subreflector is completely arbitrary. In fact, it is only necessary to specify the surface at a set of discrete points over a random net. Our computer program will fit those points by cubic spline functions and calculate the necessary geometrical parameters of the subreflector. In a companion paper by Y. Rahmat-Samii, R. Mittra, and V. Galindo-Israel, the scattered field from the submflector is used to calculate the secondary pattern of an arbitrarily shaped reflector by a series expansion method. Thus, in these two papers, it is hoped that we have developed a "universal" computer program that can analyze most dual-reflector antennas currently conceivable. It should also be added that our method of calculation is extremely numerically efficient. In many cases, it is one order of magnitude faster than the conventional integration method based on physical optics.     

用UTD方法评估一种紧凑场反射器的目标区特性

讨论了一种紧凑场反射器的边缘绕射情况,并用一致性几何绕射方法(UTD)对该反射器的目标区准平面波指标作了评估,给出了目标区大小与工作频率之间的关系.     

Analytical solution for early-time transient radiation frompulse-excited parabolic reflector antennas

A closed-form analytical solution is developed for predicting the early-time transient electromagnetic fields which are generated by a perfectly conducting parabolic reflector antenna when it is illuminated by a transient step spherical wave due to an elemental Huygen's source located at the focus. This closed-form time-domain solution, which is valid both near and far from the reflector (and anywhere in the forward region) can be used via the convolution theorem to efficiently obtain the early-time transient fields generated by the same parabolic reflector antenna when it is illuminated by a realistic finite-energy pulse which emanates as a spherical wave from the focus. The transient solution is developed here by analytically inverting, in closed form, the corresponding frequency-domain solution in terms of a radiation integral that employs an asymptotic high-frequency geometrical optics (GO)-based approximation for the fields in the aperture. Numerical results are presented for the transient fields both near and far from the reflector. The fields on boresight exhibit an impulse-like behavior similar to that of the impulse radiating antenna (IRA) introduced by Baum et al. (1989, 1993)