US 2875439 A Description (OCR text may contain errors) 5 Sheets-Sheet 1 Filed Jan. 26, 1956 INVENTOR Z M M n Mn m m Ma ma Feb. 24, 1959 B. BERKOWITZ 2,875,439 CENTER-FED ANNULAR SCANNING ANTENNA Filed Jan. 26, 1956 5 shegts shee'p INVENTO R BERNARD BER/(OW/TZ WJZMW Feb. 24, 1959 B. BERKOWlTZ CENTER-FED ANNULAR SCANNING ANTENNA 3 Sheets-Sheet 3 Filed Jan. 26, 1956 W m WW mfim MM w m/ m BB CENTER-FED ANNULAR SCANNING ANTENNA Bernard Berkowitz, New Hyde Park, N. Y., assignor to Sperry Rand Corporation, a corporation of Delaware Application January 26, 1956, Serial No. 561,966 Claims. (Cl. 343-754) This invention relates to improvements in scanning antennas and more particularly to antenna structures employing a fixed lens and a rotatable radiator. In early scanning antennas both the lens and radiating structures were rotated as a unit about a common axis. The driving mechanism for accomplishing scanning was bulky and complex because of the massive structure to be moved. In a group of improved scanning antennas generically related to that suggested by R. K. Luneberg, Mathematical Theory of Optics, Brown University, 1944; pages 208-213, the radiating structure rotates about the periphery of a stationary lens structure. El'ectro magnetic energy is directed from the radiator through the periphery of the lens and emerges as a collimated beam diametrically opposite the point of entrance. Although the rotating portions of this group of antennas had lower moments of inertia than early scanning antennas, further improvements were still desirable. Thus, the large radius of rotation of the radiating structure created an unnecessarily large moment of inertia. Furthermore, any protecting radome had to be built of suflicient dimensions to allow movement of the rotating radiator about the periphery of the stationary lens. I. E. Eaton, in Transactions of the I. R. E., Professional Group on Antennas and Propagation, December 1952, pages 66-71, suggests a modified scanning antenna in which the radiating structure rotates within a stationary lens structure, although a full scan of 360 is precluded by the slot necessary for passage of the radiating structure. It is therefore an object of the present invention to provide an improved scanning antenna. It is a further object of this invention to provide an improved scanning antenna structure employing a fixed lens and a rotatable radiator. It is a further object of this invention to provide a scanning antenna employing a fixed annular lens and a radiator rotating within said lens. It is a further object of this invention to provide an improved antenna for scanning through a complete circle employing a fixed annular lens and a radiator rotating within said lens. These and other objects of this invention which will become apparent as the description proceeds are achieved by the employment of a stationary annular collimating lens whose effective index of refraction decreases as a function of the radius, becoming equal to that of free space at the outer boundary of the lens. Disposed within the lens structure is a rotatable radiator. The radiator consists of a section of rectangular waveguide bent into a circular shape about an axis parallel to one of its broad walls. The outer broad wall of the waveguide is apertured and disposed adjacent the inner boundary of the lens. The positions of the apertures are so determined that energy entering the waveguide structure will flow out of the apertures and through the lens, emerging from the lens as a plane wave. Other objects and advantages of the present invention will become apparent from the specification taken nited States Patent ice in connection with the accompanying drawings wherein: Fig. 1 is a perspective drawing, partly in cross-section, of the scanning antenna of this invention; Fig. 2 is an elevational view, partly in cross-section of the antenna of Fig. 1. Fig. 3 is a schematic diagram useful in explaining the theory of operation of this invention; Fig. 4 is a schematic diagram of the lens of this invention; Fig. 5 is a graph of the radiator phase distribution; Fig. 6 is a schematic diagram illustrating the amplitude distribution of the lens of this invention; Fig. 7 is a graph of the amplitude distribution modification function; Fig. 8 is a graph of the radiator field distribution for a selected beam pattern. Referring now to Figs. 1 and 2, there is shown partly in cross-section the preferred embodiment of the scanning antenna of this invention. The antenna comprises a stationary lens 11 and a rotatable radiator 12 disposed concentrically within lens 11. Lens 11 comprises a pair of parallel metallic annular plates 13 and 14 and a dielectric member 15 disposed between plates 13, 14. The transverse area of dielectric member 15 decreases with increasing radius in order that the effective index of refraction of lens 11 varies with the radius, r, according to the following equation: where R is the radius of the outer boundary of the lens 11. Radiator 12 comprises a rectangular waveguide section 16 bent into a circular shape about an axis parallel to one of its broad walls. A plurality of radiating apertures, such as slots 17, are spaced about a portion of the periphery of outer wall 18 of radiator 12. Outer wall 18 is disposed adjacent the inner circumferential boundary of lens 11. A spider-like member 19 is afiixed to and supports radiator 12. Member 19 is mounted on a gear-like plate 20, driven by a scanning mechanism 21, which is adapted to rotate radiator 12 through 360, or to cause the radiator to oscillate oyer'a predetermined arc. Electromagnetic energy is delivered to radiator 12 through a waveguide section 22, which is aflixed to the inner broad wall of waveguide section 16. Waveguide section 22 is connected to a fixed waveguide section 23 by means of a rotatable waveguide joint 24. Slots 17 are disposed anti-symmetrically with respect to the axis of waveguide section 22 around the outer wall 18 of radiator 12. A radome 25 is provided for covering the lens. A cover 26 provides an air-tight housing for the moveable mechanism. In operation electromagnetic energy is directed through waveguide section 23, rotatable joint 24, and waveguide section 22 to waveguide section 16. The energy flows in both directions from the juncture of waveguide section 22 with waveguide section 16, through slots 17, and across the adjacent boundary of lens 11. In flowing through lens 11 the rays of electromagnetic energy follow predetermined paths and emerge from the outer circumferential boundary as a collimated beam whose axis is collinear with that of waveguide section 22. Although radiator 12 has been described as a source of electromagnetic energy for an antenna which is transmitting electromagnetic waves, it also functions as a receptor of electromagnetic waves received by the antenna from a remote source of radiation. Furthermore, it is not necessary to the operation of this invention that lens 11 be a complete annulus, but instead, the lens may be a segment of an annulus. In such instance movement of radiator 12 will be confined to oscillatory motion through a maximum arc. Radiator phase distribution In his article, Eaton derives certain design relationships for a scanning antenna having a stationary lens and a rotatable radiator. The radiator rotates within the lens, the lens being divided into two regions. A schematic diagram of Eatons antenna is shown in Fig. 3, wherein a radiator 31 is shown directing electromagnetic energy across an inner region 32 of the lens defined by an outer circumferential boundary r=R and then through an outer lens region 33, defined by the boundaries r=R and r=R. By constructing the regions 32, 33 according to certain relationships, arbitrary rays emerging from the radiator will follow different paths through the two regions but will emerge from the outer boundary of region 33 making such an angle To with the radius vector that the emergent phase-front is plane. Eatons relationships for the elfective index of refraction and for the ray path P2'P3 in the outer region 33 of the lens are respectively: and In the antenna of this invention, the entire inner region 32 is removed and a radiator, such as an apertured waveguide bent into a circle of outside radius r=R is disposed therein. The waveguide radiator duplicates the phase relationships over the circle r=R which were necessary in order to obtain the desired plane Wavefront in the antenna of Fig. 3. To determine the phase relationships over this circle it is necessary to evaluate the electrical path length over the ray path P P P as shown in Fig. 4, which is a schematic diagram of the lens of this invention. The phase delay d for a differential path length a'l is given by where )t is the free-space wavelength of the electromagnetic propagating ray and 97 is the effective index of refraction of the medium through which the wave is propagating. The phase angle at the R circle referred to a zero reference phase at the reference line LL is The second integral term in Equation 5 may be reduced to the following expression: The expression it. dr may be determined from Equation 3. 1a dr Substituting for 4 Equation 7 becomes, Substituting Equations 2 and 8 in Equation 5, the first integral of Equation 5 becomes Substituting the two integrals of Equations 6 and 10 in Equation 5, there results where C is an arbitrary constant. Thus in Equation 11, the phase delay for the various ray paths emerging from the lens at an angle To with respect to the radius vector is determined. The position of the ray path at the radiator may be determined from Equation 3 in which r=R The resulting angle 0 is measured along the radiator, as shown in Fig. 4. Fig. 5 shows graphs of the radiator phase distribution for two values of lens inner diameter. Radiating slots may be cut into the waveguide radiator at points where the phase of the energy radiated from each slot coincides with the required phase determined from Equation 11. This condition is satisfied approximately every half guide-wavelength if the prescribed phase function varies slowly in comparison with the phase variation along the radiator. Radiator amplitude distribution The distribution of radiated energy per unit arc length of the radiator is not linearly related to the energy per unit arc length crossing the outer circumference of the lens. The amplitude distribution radiated from the lens is at the discretion of the designer. An amplitude distribution modification function P may be derived which relates the amplitude distribution at the rotatable radiator to the amplitude distribution at the outer circumference r=R of the lens. Fig. 6 shows a tube of differential cross-section enclosing a ray path such that no power flows through the walls of the tube. Equating the power flowing into the tube at surface s to that flowing out of the tube at surface s said surfaces being respectively selected at the inner and outer radii of the lens, there results 11oEo COS dodA =111E COS cud/1 Now, cos a== and substituting in Equation 13 (d 01 as developed from Equation 3, there results cos sin 0 cos a= (14) sin 1' 2-- "'V R Substituting Equation 2 in Equation 14 cos a= Substituting the value of Equation 15 at surfaces s and s, in Equation 12, there is obtained E dA1 sin T0 E dA3 sin 0 Converting the incremental area terms to polar coordinates, Equation 16 becomes E f R sin Tgdm E1 R0 sin 001100 Differentiating Equation 3 and substituting in Equation 17 there is obtained, finally E cos 1 E 72? cos T0+1 "R Since the rays from surfaces s; to s are all parallel, F =1, an overall amplitude distribution modification may be written as where y is the linear distance of the ray along plane L-L from radius O-M. A graph of the amplitude distribution modification function as a function of 0 is shown in Fig. 7. This graph is for a lens whose Selecting a field distribution at the radiating plane L-L for a desired beam pattern; such as 1 E C cos V Lens structure Several structural designs may be employed to realize the radially varying effective index of refraction required by the lens as specified in Equation 2. Since the desired index of refraction is a monotonic function of the radius; that is, it has no maxima or minima, it is most easily synthesized in a lens by the use of smoothly varying contoured boundaries or by the use of smoothly varying dielectric structures. One method of construction of such a lens is by compression of a polystyrene foam dielectric, such as described in The Luneburg Lens of Continuously Varying Dielectric Constant, by R. W. Corkum et al., October 1954, Air Force Cambridge Research Center, Publication AFCRC-TR-54-103. The lens may be also constructed of a pair of annular plates 13, 14, Fig. 2, and a dielectric member 15 disposed between said annular plates. The thickness of the dielectric member between the annular plates is tapered to achieve the varying index of refraction. N. Marcuvitz in his Waveguide Handbook, by McGraw-Hill Book Company, 1951, pages 391-393, describes propagation characteristics of a rectangular waveguide with dielectric slabs perpendicular to the electric field. By extending his analysis to a waveguide consisting of a pair of parallel plates, the desired-variable effective index of refraction may be obtained for this antenna. Selecting corresponds to a maximum index of refraction of 1.53 and a relative dielectric constant of 2.35. By dispersing pellets of titanium dioxide in Teflon a desirable low loss dielectric having a relative dielectric constant of 2.35 can be achieved. By then tapering the thickness of the dielectric material toward the radius r==R, the radially varying effective index of refraction of Equation 2 is obtained. Since many changes could be made in the above construction and many apparently widely different embodiments of this invention could be made without departing from the scope thereof, it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense. What is claimed is: 1. An antenna comprising an annular lens having a radially varying effective index of refraction and a radiator having a substantially convex apertured portion, said apertured portion being disposed adjacent the inner circumferential boundary of said lens and adapted to direct electromagnetic energy across said boundary. 2. An antenna as in claim 1, wherein the effective index of refraction of said lens is a monotonic function of the radius. 3. An antenna as in claim 1, wherein the effective index of refraction of said lens is a monotonically decreas ing function of the radius. 4. A scanning antenna comprising an annular lens having a radially varying effective index of refraction, and a radiator having a substantially convex apertured portion, said apertured portion substantially registering with the inner circumferential boundary of said lens, said radiator being adapted to rotate about the center of said lens. 5. An antenna comprising an annular lens having an effective index of refraction n that varies according to where R is the radius of the outer boundary of the lens and r is the radius of an arbitrary point between the inner and outer boundaries of the lens, and a radiator having a substantially convex apertured portion, said apertured portion being disposed adjacent the inner circumferential boundary of said lens and adapted to direct electromagnetic energy across said boundary. 6. An antenna as in claim 5, wherein said radiator is adapted to rotate about the center of said lens. 7. An antenna as in claim 1, wherein said lens comprises a pair of parallel metallic annular plates and a tapered dielectric wedge disposed between said plates. 8. An antenna comprising an annular lens having an effective index of refraction 1 that varies according to where R is the radius of the outer boundary of the lens and r is the radius of an arbitrary point between the inner and outer boundaries of the lens and a radiator comprising a rectangular waveguide section bent into a circular shape about an axis parallel to one of its broad walls, the outer broad Wall of said waveguide section being apertured and substantially registering with the inner circumferential boundary of said lens, whereby electromagnetic energy is directed from said waveguide section across said boundary. 9. A scanning antenna comprising an annular lens having an effective index of refraction a that varies according to where R is the radius of the outer boundary of the lens and r is the radius of an arbitrary point between the inner and outer boundaries of the lens and a radiator comprising a rectangular waveguide section bent into a circular shape about an axis parallel to one of its broad walls, the outer broad wall of said Waveguide section having a plurality of radiating apertures and substantially registering with the inner circumferential boundary of said lens, said apertures being adapted to transfer to said lens microwave energy which is polarized with its electric vectors parallel to said axis. 10. An antenna as in claim 8, wherein said lens comprises a pair of parallel metallic annular plates and a tapered dielectric wedge disposed within said plates. 11. A scanning antenna designed to scan a concentrated beam of electromagnetic energy through an angle of 360 around an axis normal to the plane of scan comprising, an annular lens having an effective index of refraction which varies as a montonic function between its inner and outer boundaries, a waveguide radiator having a plurality of radiating slots distributed along one broad wall of the waveguide, said slots being disposed adjacent the inner boundary of said lens for transferring microwave energy to the lens, an input waveguide section extending radially from said axis and being joined to said radiating waveguide on the broad wall opposite said radiating solts, said slots being positioned anti-symmetrically with respect to the longitudinal axis of said input waveguide, the microwave energy transferred to said lens by said slots being polarized parallel to said axls. 12. A microwave antenna system comprising a rectangular waveguide section adapted to be connected to a source of electromagnetic energy, a radiating waveguide section bent into a circular shape about an axis parallel to its broad wall and joined to said first waveguide by means of a junction on its inner broad wall, a plurality of radiating apertures located on the opposite broad wall of said radiating waveguide and positioned anti-symmetrically with respect to the longitudinal axis of said first waveguide, an annular lens structure surrounding said waveguide radiator comprised of a pair of spaced conductive plates, and means separating said plates providing an effective refractive index which varies as a monotonically decreasing function of the radius of said lens, said radiating apertures adapted to launch into said lens waves of electromagnetic energy which are polarized perpendicular to said conductive plates, the phase of the energy emitted by said apertures and the index of refraction of said lens being proportioned so that said energy follows predetermined ray paths through said lens and is collimated in a plane phase front upon emergence from said lens. 13. A microwave antenna system adapted to scan a concentrated beam of electromagnetic energy through an angle of 360 around an axis normal to the plane of scan comprising, a lens structure comprised of an annular dielectric member having a tapered cross-sectional area adapted to provide an effective index of refraction which is a monotonically decreasing function of the radius of said lens, waveguide radiating means positioned coaxially within said lens and adapted to rotate around the inner boundary of the lens, said radiating means comprised of a curved waveguide section having a plurality of radiating apertures disposed along a broad wall of said waveguide and adapted to transfer to said lens microwave energy which is polarized with its electric vectors normal to said axis, the energy radiated by the individual slots having a phase which is determined according to the relationship where is the phase with respect to energy in a plane phase front at the outer boundary of the lens, C is an arbitrary constant, R and R are the radii of the outer and inner boundaries respectively of the lens, and To is the angle that a ray of energy energizing from the lens makes with an extension of a radius drawn through the point of emergence. 14. An antenna system comprising a lens structure having a pair of spaced annular-shaped conductive surfaces, means positioned between said surfaces and coextensive with the boundaries of said surfaces providing an efiective index of refraction n which varies according to the relation COS To where R is the radius of the outer boundary of said lens, and r is the radius of an arbitrary point between the outer and inner boundaries of said lens, a waveguide radiator extending parallel to the inner boundary of said lens and having a plurality of radiating apertures distributed along a wall of said waveguide for transferring to said lens structure microwave energy which is polarized normal to said conductive surfaces, the phase relationship of the microwave energy emitted from said radiators and the index of refraction of said lens being so proportioned that points of equal phase in the ray paths of the energy radiated by said lens structure lie in a common plane normal to the direction of radiation of said energy. 15. An antenna system of the type designed to scan a concentrated beam of electromagnetic energy through an angle of 360 around an axis normal to the plane of scan comprising, an annular lens structure providing an effective index of refraction which decreases as a monotonic function of the distance from the inner boundary to the outer boundary of said lens, a waveguide radiator comprising a rectangular waveguide section bent into a circular shape about said axis, one broad wall of said waveguide having a plurality of radiating apertures substantially registering with the inner boundary of said lens, an input waveguide extending radially from said axis and joined to the opposite broad wall of said radiating waveguide, said radiating apertures being located anti-symmetrically with respect to the longitudinal axis of said input waveguide, said apertures launching waves of energy into said lens with the electric field polarized parallel to said first axis. References Cited in the file of-this patent UNITED STATES PATENTS Southworth Feb. 1, 1949 Iams Oct. 24, 1950 Wilkinson Nov. 27, 1951 Clark et al June 10, 1952 Lyman et al Dec. 29, 1953 UNITED STATES PATENT OFFICE Certificate of Correction Patent No. 2,875,439 February 24, 1959 Bernard Berkowitz It is hereby certified that error appears in the printed specification of the above numbered patent requiring correction and that the said Letters Patent should read as corrected below. Column 5, lines 35 to 38, Equation 19 should appear as shown below instead of as m the patent COS 7'0 column 7, line 58, for solts read -slots; column 8, line 23, for normal read -pa,rnllel-. Signed and sealed this 3rd day of May 1960. [sun] Attest: KARL H. AXLINE, ROBERT C. WATSON, Attestz'ng Officer, vmmiseioner of Patents. Patent Citations
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