Studies of the Focal Region of a Spherical Reflector: Polarization Effects

The polarization of the reflection of a uniform plane wave incident on a spherical reflector is analyzed using the current distribution method for scattered fields. The current distribution on the reflector is derived. For reflectors subtending about60degor less, the radiation scattered in the direction of the circle of least confusion has essentially the same polarization as that reflected specularly from the tangent plane. The effective current, the component of surface current density radiating toward the focal region, is derived in several representations. Assuminghat{i}incident polarization, contour plots are provided forhat{i},hat{j}, andhat{k}components in spherical coordinates. Next, general formulas are derived for thehat{i},hat{j},hat{k}components of the reflected fields, in terms of the direction cosines of the normal to the reflecting surface. These are displayed in terms of projections, and apply directly to the spherical reflector.     

Synthesis of the fields of a transverse feed for a spherical reflector

The problem of designing a transverse feed for a spherical reflector is considered and a method is presented for synthesizing the fields on a surface of a sphere enclosing a feed that will produce a specified reflected field at the surface of a spherical reflector. The method identifies the reflector and a spherical surface enclosing the feed as a boundary value problem and uses a finite set of spherical waves to approximate the boundary conditions. A feed designed to excite this field will in turn produce the desired reflected field at the surface of the reflector, under the condition that that portion of the reflected field which is scattered by the feed may be neglected. It is shown that the feed need produce only a small part of the synthesized field to obtain an antenna efficiency of more than 70 percent. Some typical field distributions will be shown so as to indicate a method for designing a feed and to point out the correlation between the polarization of the synthesized field and the polarization of the reflected field at the surface of the reflector.     

Efficient solution for backscattered field of a dihedral cornerreflector

The problem of transverse magnetic (TM) plane wave scattering from a dihedral corner reflector is investigated. Using the mode matching technique (MMT), the transmitted and scattered fields are expressed in the angular spectral domain in terms of radial waveguide modes. The boundary conditions are enforced to obtain simultaneous equations for the transmitted and scattered fields. The simultaneous equations are then solved to represent the fields in a series form. Numerical results obtained by this method compare favourably with those obtained by other methods     

An efficient plane wave spectral analysis to predict the focalregion fields of parabolic reflector antennas for small and wide anglescanning

An efficient approach is described for calculating the field distribution in the focal region of an electrically large, symmetric or offset parabolic reflector antenna with an arbitrary rim contour, when the concave reflector surface is fully illuminated by an obliquely incident arbitrary electromagnetic plane wave. The dominant contribution to the focal-region fields is found by transforming the physical-optics integral over the reflector surface into a plane-wave spectral (PWS) integral. The PWS integral is evaluated rapidly via the fast Fourier transform (FET) algorithm to furnish, in only a single computation, the field for every place in the focal plane (or any plane parallel to it) within the focal region for a given direction of the incident wave. The correction to the physical-optics field is relatively small in the focal region and may therefore be neglected. Numerical results based on this PWS approach are presented, and their accuracy is established by comparison with results based on other approaches     

An analysis of the elliptical reflector

The distribution of the electromagnetic fields diffracted by an elliptical reflector which is fed by a line source at or near one of its two foci is studied. For the elliptic cylinder the magnitude of the fields near the foci, the size of the focal region, the displacement of the focal spot as a function of the source displacement, and the application of the method of stationary phase in calculating the fields at points distant from either focus are calculated. Explicit results are presented for the fields as a function of the eccentricity of the ellipse and the angles subtended by the reflector edges.     

The analysis of deployable umbrella parabolic reflectors

The radiation characteristics of an umbrella-type reflector are studied in detail. When the supporting ribs of the quasiparabolic reflector are parabolic in shape and the surface between any two adjacent ribs is the surface of a parabolic cylinder, the deviation of the surface from the true parabolic shape has the effect of spreading the focal point of the parabolic reflector into a focal region, the limits of which can be calculated from the knowledge of the reflector parameters. The best feed position can be accurately determined by requiring that the phase error over the surface be minimized. For the cosine to the powernillumination, numerical results showing the gain degradation, the shift in optimum focal point, and the change in secondary patterns, due to the deviation of the reflector surface from the true parabolic surface, are presented.     

Full-wave investigation of a corner reflector proposed as referenceline target for automotive applications

The backscattering property of the 90° dihedral corner reflector is exploited to define a distributed target for automotive applications. In the analysis, the scatterer is described as a junction among three radial waveguides and the problem is solved by applying the mode-matching technique in a convenient matrix form. Once the structure is characterized in terms of a multimodal scattering matrix, the evaluation of the scattered fields at any observation point is straightforward     

Some important geometrical features of conic-section-generated offset refelector antennas

Geometrical characteristics of conic-section-generated offset reflectors are studied in a unified fashion. Some unique geometrical features of the reflector rim constructed from the intersection of the reflector surface and a cone or cylinder are explored in detail. It is found that the intersection curve (rim) of the rotationally generated conic-section reflector surface and a circular cone with its tip at the focal point is always a planar curve and has a circular projection on the focal plane only for the offset parabolic reflector. Furthermore, in this case, the line going through the center of the circle, parallel to the focal axis, and the central axis of the cone do not intersect the reflector surface at the same point. Numerical results are presented to demonstrate some unique features of offset parabolic reflectors.     

An equivalent focused reflector feed in place of any generalised defocused or extended feed

A procedure is presented whereby generalised reflector feeds with near-field and/or defocused properties can be replaced by an equivalent point-source feed located at the origin. The equivalent feed induces identical reflector currents and consequently yields identical scattered fields. Thus all physical optics reflector analysis can be carried out in terms of a focused point-source illumination function.     

Diffraction analysis of frequency selective reflector antennas

A unified computational technique which allows the incorporation of the curved frequency selective surface (FSS) geometry in the computation of a dual-reflector-antenna radiation pattern is presented. The scattered fields from a illuminated FSS reflector are formalized using Huygens' principle in such a way that the `reflecting' and the `transparent' FSS subreflector cases are treated identically and the thickness of the FSS subreflector remains arbitrary. The analysis utilizes local surface coordinates to describe the reflection/transmission matrices of the FSS subreflector, assuming that these matrices are available. In most cases the local tangent plane may be used to approximate the plane of the FSS in the local coordinate surface of the reflector. The way in which the local curved coordinate system can be introduced in the diffraction modeling of FSS reflectors and its importance in accurately predicting the sidelobe and cross-polarization levels are demonstrated. Results of numerical simulations are presented for several FSS subreflector configurations     

Studies of the focal region of a spherical reflector: Stationary phase evaluation

The geometric optics and polarization properties of a spherical reflector are used to develop an integral representation of its focal region fields. These integrals are evaluated by the extended method of stationary phase for field points off the caustics, on the axial caustic, on the caustic surface, and at the paraxial focus. The contributions to the field at a field point are shown to arise respectively from three ordinary stationary points: a stationary ring and a stationary point at the vertex; an ordinary stationary point and a caustic type stationary point; and a fourth-order stationary point. The resulting formulas are used to compute the value of the focal region fields. The computed results are then compared to measured data.     

Offset parabolic reflector antennas

The paper provides a tutorial review of a number of offset parabolic reflector configurations including both single and double-reflector geometries. The author commences by describing some basic techniques which can be applied to predict the vector radiation fields and provides some indication of the validity of these methods. The formulation of a relatively simple analytical model for the offset reflector antenna is described based upon the physical-optics approximation. The electrical performance of the single-offset reflector is examined by comparison of predicted and measured data. The particular problems arising from the choice of polarisation and reflector dimensions are highlighted, and some practical applications involving multiplebeams, shaped and contoured beams, monopulse tracking and low sidelobes are briefly reviewed. Practical primary-feeds for offset-reflector antennas are discussed and the matched-feed concept is outlined, the matching of the electric fields in the primary-feed aperture to the reflector focal fields being illustrated. The advantages and disadvantages of dual-reflector antennas are then examined, with particular emphasis upon the open Cassegrainian configuration and the optimised doubleoffset configuration which offers, in principle, both freedom from blockage and low levels of cross-polarised radiation.     

A note on antennas: Definitions and methods

Definitions of scattered and diffracted fields, originally given by R. F. Millar, are reviewed and supplemented. The definitions are used to discuss relations between results obtained by commonly used pattern prediction methods for reflector antennas.     

Equivalence of surface current and aperture field integrations for reflector antennas

The "extinction theorem" is used to prove that the fields of reflector antennas determined by integration of the current on the illuminated surface of the reflector are identical to the fields determined by aperture field integration with the Kottler-Franz formulas over any surfaceS_{a}that caps the reflector. As a corollary to this equivalence theorem, the fields predicted by integration of the physical optics (PO) surface currents and the Kottler-Franz integration of the geometrical optics (GO) aperture fields onS_{a}agree to within the locally plane-wave approximation inherent in PO and GO. Moreover, within the region of accuracy of the fields predicted by PO current or GO aperture field integration, the far fields predicted by the Kottler-Franz aperture integration are closely approximated by the far fields obtained from aperture integration of the tangential electric or magnetic field alone. In particular, discrepancies in symmetry between the far fields of offset reflector antennas obtained from PO current and GO aperture field integrations disappear when the aperture of integration is chosen to cap (or nearly cap) the reflector.     

Secondary pattern and focal region distribution of reflector antennas under wide-angle scanning

A new numerical method, Fourier-Bessel series techniques, has been developed to investigate the far-field pattern and focal region distribution of reflector antennas under wide-angle scanning. In this Fourier-Bessel series technique, the current on the reflector surface is first expanded in terms of elementary sinusoidal functions via the well established fast Fourier transform (FFT) algorithm and the surface integration involved in physical optics integration is then carried out analytically. The derivation of Fourier-Bessel series and its convergence as applied to parabolic reflectors are described. The secondary patterns and focal region distributions of a parabolic reflector withF/D = 0.48and scanning up to 48 beamwidths are presented.     

Microwave holographic technique for reflector antenna profile measurement

A short-range microwave holographic technique for the measurement of reflector antenna surface profile is described. The technique uses a linearly scanned transmit/receive CW probe located on-axis at approximately two focal lengths from the reflector vertex. Rotation of the reflector provides a plane-polar data set which can be reconstructed by a fast algorithm to provide a surface profile error map. No special precautions are required with regard to the reflectivity of the environment. Practical results are provided to illustrate the performance of the system.     

Reflector surface deviations in large parabolic antennas

One of the important factors affecting the efficiency of parabolic reflector antennas is the degree to which the surface of the reflector deviates from the true parabolic shape. For a given reflector surface it is also important to locate the focal point of the best-fit paraboloid relative to the existing feed support structure. A simple method is presented for making these measurements, and results are given for a particular 60-ft diameter reflector. Static measurements were made with the antenna axis pointed vertically upwards, and changes were also measured as a function of elevation angle and wind. When the surface errors have a Gaussian distribution relative to the focal point, simple theory indicates that the received power relative to that from a perfect reflecting surface isP/P_{0} = exp -(2pi sigma / lambda)^{2}wheresigmais the standard deviation of the surface errors andlambdais the operating wavelength.     

Zooming and Scanning Gregorian Confocal Dual Reflector Antennas

The zooming and scanning capabilities of a Gregorian confocal dual reflector antenna are described. The basic antenna configuration consists of two oppositely facing paraboloidal reflectors sharing a common focal point. A planar feed array is used to illuminate the subreflector allowing the antenna to scan its beam. The resulting quadratic aberrations can be compensated by active mechanical deformation of the subreflector surface, which is based on translation, rotation and focal length adjustment. In order to reduce the complexity of the mechanical deformation, least squares fit paraboloids are defined to approximate the optimal correction surface. These best fit paraboloids considerably reduce scanning losses and pattern degradation. This work also introduces two different zooming techniques for the Gregorian confocal dual reflector antenna: the first consists of introducing a controlled quadratic path error to the main reflector aperture; and the second is based on reducing the size of the radiating aperture of the feeding array.      

Moment method analysis of the magnetic shielding factor of aconducting TM shield at ELF

This paper presents an integral equation and method of moments (MoM) solution to the problem of TM transmission by a metallic conducting shield at extremely low frequencies (ELF). In order to accurately compute the total fields interior to the shield, equivalent problems are formulated which avoid the numerically difficult problem of computing the total fields as the sum of the incident plus scattered fields. In particular, the total electric field on the interior surface of the shield is obtained by a volume current equivalent problem, and then the total magnetic field interior to the shield is formulated in terms of equivalent magnetic surface currents flowing on the interior surface of the shield replaced by a perfect conductor     

Microwave technique for reflector antenna profile measurement

A method for microwave measurement of the reflector antenna surface profile is described. The technique uses a focused monostatic secondary reflector located on axis at approximately two focal lenths from the reflector under test. Measurement of the two-ways phase change provides profile error information over a set of annular sections. Practical results are provided to illustrate the spatial resolution and sensitivity of the technique.