Title of Invention	"AN APPARATUS AND METHOD FOR OBTAINING CORRECTED ANTENNA DATA IN A COMPACT RANGE WITH A COOPERATING PROCESSOR"
Abstract	An apparatus for obtaining corrected antenna data includes a processor and a compact range, the corrected antenna data containing co-polarization and cross-polarization properties of an antenna. The compact range defines a quiet zone and has a reflector and a feed, the reflector being characterized by a paraboloidal shape having a vertex point and a focus point, the feed being located at the focus point and being characterized by a feed boresight pointed at the vertex point. The compact range further has a transmitter coupled to the feed and a receiver coupled between the antenna and the processor to provide a received signal to the processor. The processor determines aperture field data from the received signal, the aperture field data containing values based on properties of the compact range and the co-polarization and cross-polarization properties of the antenna. The processor further calculates theoretical field data, the theoretical field data characterizing the properties of the compact range. The processor further combines the aperture field data and the theoretical field data to provide the corrected antenna data.

Title of Invention

"AN APPARATUS AND METHOD FOR OBTAINING CORRECTED ANTENNA DATA IN A COMPACT RANGE WITH A COOPERATING PROCESSOR"

Abstract

An apparatus for obtaining corrected antenna data includes a processor and a compact range, the corrected antenna data containing co-polarization and cross-polarization properties of an antenna. The compact range defines a quiet zone and has a reflector and a feed, the reflector being characterized by a paraboloidal shape having a vertex point and a focus point, the feed being located at the focus point and being characterized by a feed boresight pointed at the vertex point. The compact range further has a transmitter coupled to the feed and a receiver coupled between the antenna and the processor to provide a received signal to the processor. The processor determines aperture field data from the received signal, the aperture field data containing values based on properties of the compact range and the co-polarization and cross-polarization properties of the antenna. The processor further calculates theoretical field data, the theoretical field data characterizing the properties of the compact range. The processor further combines the aperture field data and the theoretical field data to provide the corrected antenna data.

Full Text	A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by any one of the patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever. BACKGROUND OF THE INVENTION Field of the Invention The present invention relates to test methods to measure co-polarization and cross-polarization properties of an antenna. In particular, the invention relates to an apparatus and method to measure these properties in a compact range facility having a feed and reflector system that provides quiet zone in which a radiation field is uniformly polarized. Description Of Related Art The principals of compact ranges for the measurement of antenna properties is known, for example see U.S. Patent No. 3,302,205 to R. C. Johnson, incorporated herein by reference, and Johnson, Ecker and Moore, "Compact Range Techniques and Measurements", IEEE Transactions On Antennas and Propagation. September 1969, pages 568-576, also incorporated herein by reference, and "The Compact Range" by Scientific-Atlanta, Inc., The Microwave Journal. October 1974, volume 17, number 10, pages 30 and 32, also incorporated herein by reference. A property of antennas that is frequently measured is the antenna gain pattern as a function of azimuth and elevation angles relative to a vector normal to a predetermined plane that passes through the phase center of the antenna. Usually, the predetermined plane is the aperture plane of the antenna when the normal vector is co-parallel with the boresight axis of the main lobe of the antenna. Other antenna properties that are of interest include co- and cross-polarization properties of the antenna. Ideally, an antenna fed with a signal to produce a vertically polarized emission will produce only the vertically polarized emission. However, in a real world antenna, the signal will also produce some horizontally polarized emission. The degree to which the antenna produces the intended vertically polarized emission when excited to produce the vertically polarized emission may be referred to as a co-polarization property of the antenna. The degree to which the antenna produces the unintended horizontally polarized emission when excited to produce the vertically polarized emission may be referred to as a cross-polarization property of the antenna. Arthur C. Ludwig developed a more rigorous definition of cross-polarization in his paper "The Definition Of Cross Polarization", IEEE Transactions On Antennas And Propagation. January 1973, pages 116-119, incorporated herein by reference. To be precise herein, Ludwig's third definition of cross-polarization is used throughout this disclosure. Polarization is a property of a single-frequency electromagnetic wave; it describes the shape and orientation of the locus of the extremity of the field vectors as a function of time. In antenna engineering, we are primarily interested in the polarization properties of plane waves or of waves that can be considered to be planar over the local region of observation. For plane waves, we need only specify the polarization properties of the electric field vector since the magnetic field is simply related to the electric field vector. The plane containing the electric and magnetic fields is called the plane of polarization and is orthogonal to the direction of propagation. In the general case, the tip of the electric field vector moves along an elliptical path in the plane of polarization. The polarization of the wave is specified by the shape and orientation of the ellipse and the direction in which the electric field vector traverses the ellipse. In antenna measurements Ludwig's third definition of polarization is appropriate. For a transmitted field polarized in the ly direction at θ = 0, the co-polarized and cross-polarized components are given by: (Equation Removed) where the coordinates correspond to equations 8a and 8b and Ludwig's Fig. 2. For evaluating primary feed patterns for paraboloidal reflectors a logical requirement is that a perfect feed cause a perfect surface current distribution. A necessary and sufficient condition for zero cross-polarized surface currents is Eθ cos = E+ sin which is identically equivalent to Ludwig's third definition. It is possible to show that a Huygen's source satisfies this condition as well as a physically circular feed with equal E-plane and H-plane amplitude and phase patterns. Accurate cross-polarization measurements require an incident field on the antenna under test that has uniform amplitude and phase, as well as a low cross-polarization equivalent extraneous signal level. Compact ranges are well suited to provide uniform amplitude and phase over a quite zone region into which the antenna under test fits. However, to obtain low cross-polarization equivalent extraneous signal levels has required considerable expense in the design and manufacture of dual reflector systems that theoretically produce low cross-polarization, but in practice, due to manufacturing tolerances, assembly and alignment inaccuracies, etc., produce cross-polarization equivalent extraneous signal levels in the -35 to -45 dB range relative to the co-polarization signal level. A compact range typically has a feed with an asymmetric reflector. The feed boresight axis is pointed toward the center of the reflector, more or less, to produce an incident field that has substantially uniform amplitude and phase on the antenna under test. However, such arrangements also produce a cross-polarization equivalent extraneous signal that detracts from the ability to use the compact range to measure both co- and cross-polarization properties of the antenna under test. Such cross- polarization detriments are discussed by Johannes Jacobson in his paper "On the Cross Polarization of Asymmetric Reflector Antennas for Satellite Applications", IEEE Transactions On Antennas And Propagation. March 1977, pages 276-283, incorporated herein by reference. SUMMARY OFTHE INVENTION It is an object of the present invention to provide an apparatus and method to obtain high accuracy cross-polarization measurements with prime focus, single reflector, compact ranges. It is yet another object of the present invention to provide an apparatus and method to reduce cross-polarization extraneous signals to levels that rival or exceed the much more expensive dual reflector systems, with the associated cost and simplicity of a single reflector system. These and other objects are achieved in an apparatus for obtaining corrected antenna data that includes a processor and a compact range, the corrected antenna data containing co-polarization and cross-polarization properties of an antenna. The compact range defines a quiet zone and has a reflector and a feed, the reflector being characterized by a paraboloidal shape having a vertex point and a focus point, the feed being located at the focus point and being characterized by a feed boresight pointed at the vertex point. The compact range further has a transmitter coupled to the feed and a receiver coupled between the antenna and the processor to provide a received signal to the processor. The processor determines aperture field data from the received signal, the aperture field data containing values based on properties of the compact range and the co-polarization and cross-polarization properties of the antenna. The processor further calculates theoretical field data, the theoretical field data characterizing the properties of the compact range. The processor further combines the aperture field data and the theoretical field data to provide the corrected antenna data. BRIEF DESCRIPTION OF DRAWINGS The invention will be described in detail in the following description of preferred embodiments with reference to the following figures wherein: FIG. 1 is a schematic diagram of a compact range according to the present invention; FIG. 2 is a graph showing an antenna radiation pattern of a feed used in the present invention; FIGS. 3A and 4A are schematic diagrams of portions of conventional compact ranges; FIGS. 3B and 4B are graphs showing radiation patterns produced by the arrangement of FIGS. 3A and 4A, respectively; FIG. 5A is a plot showing representative Az, El positions in a raster scan according to the present invention; FIG. SB is a schematic diagram showing a positioner with mounted antenna under test according to the present invention; FIG. 6 is a flow chart showing steps used to collect data according to the present invention; FIG. 7 is a block diagram showing major processes according to the present invention; FIGS. 8-14 are data flow diagrams showing the processing of data according to the present invention; FIGS.15A and 15B are graphs showing the coordinate systems used in angle transformation according to the present invention; FIG. 16 is a mechanical schematic diagram showing dimensions used in moment arm phase corrections according to the present invention; FIGS. 17A and 17B are graphs showing the coordinate systems used in moment arm phase corrections according to the present invention; FIGS. 18A and 18B are graphs showing polarizations that will be considered co- and cross-polarized for an antenna under test according to the present invention; FIGS. 19A and 19B are graphs showing polarizations considered to be co- and cross-polarized by Ludwig's third definition as used in processing according to the * present invention; FIGS. 20A, 20B and 20C are graphs showing interpolation of raw data onto a regular, rectangular lattice according to the present invention; FIG. 21A is a schematic diagram of an antenna under test; FIGS. 2IB, 21C and 2ID are graphs in the aperture plane showing representative antenna weightings of the antenna in FIG. 21A according the present invention; FIG. 22A is a schematic diagram of a portion of the compact range of FIG. 1 to illustrate the process of calculating theoretical illumination according the present invention; and FIG. 22B is a graph showing the amplitude taper of the illumination of FIG. 22A. DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS In a single reflector compact range system, the dual requirements for (1) low cross-polarization equivalent extraneous signal level and (2) small amplitude taper in the defined test zone are mutually exclusive for antenna under test displaced from or large with respect to the defined test zone of the compact range. Low cross-polarization requires that the compact range feed be pointed at the vertex of the offset reflector's parent parabola shape, which produces significant amplitude taper in the quiet zone. Scientific-Atlanta has designed a series of compact range feeds that when pointed at the vertex of the reflector's parent parabola shape, produce cross- • polarization in the quiet zone that is negligible. However, this produces a significant asymmetric amplitude taper in the quiet zone. When a far field antenna pattern for the antenna under test is measured, the measured pattern is significantly altered by the amplitude taper of the incident field from the compact range. The effects of the induced amplitude taper on the antenna under test measured far field patterns is then removed by the use of a new algorithm based on the Fourier transform properties and the reaction between the incident field and the aperture distribution of the antenna under test. This new microwave holography technique involves the measurement of the response of the antenna under test over a solid angular region to two orthogonal polarizations. The holography algorithm manipulates these measurements to obtain the co-and cross-polarized aperture field distributions of the antenna under test. The known amplitude taper of the incident field from the compact range is removed from the co-and cross-polarized aperture distributions to form a corrected aperture distribution for the antenna under test. Then, the corrected far field patterns are calculated from the corrected aperture distribution. FIG. 1 illustrates a compact range according the present invention. In FIG. 1, reflector 12 is formed out of a portion of paraboloidal surface 14. Feed 16 is located at the focus of the paraboloidal surface. In the present invention, boresight 44 of feed 16 is pointed at vertex point VP. Vertex point VP is located at the vertex of paraboloidal surface 14. Transmitter 20 is coupled to feed 16. Feed 16 radiates a broad beam pattern, preferably having 60 to 80 degrees of beam width, to produce rays 22, 24 and 26. Rays 22, 24 and 26 • reflect from reflector 12 to form collimated rays 32, 34 and 36, respectively. The radiation from collimated rays 32, 34, 36 presents a uniform phase front 38 to the antenna under test, antenna 18. Antenna 18 is located within quite zone QZ of the compact range. Antenna 18 receives the incident radiation and provides received signal REC. Signal REG is coupled to receiver 30. Persons skilled in the art will appreciate that an equivalent configuration is where receiver 30 is coupled to feed 16 instead of antenna 18 and transmitter 20 is coupled to antenna 18 instead of feed 16 due to the reciprocal nature of antenna transmission and reception. By pointing feed boresight 44 at vertex point VP, the radiation across phase front 38 is only co-polarized and not cross-polarized with respect to the radiation from feed 16. If the radiation emitted by feed 16 were only vertically and linearly polarized, then the radiation across phase front 38 is also only vertically and linearly polarized. Similarly, horizontally polarized radiation emitted from feed 16 results in only horizontally polarized radiation across phase front 38. Transmitter 20 preferably generates a continuous wave source providing transmit signal XMTT coupled to feed 16 and reference signal REF coupled to receiver 30. Receiver 30 preferably includes a quadrature synchronous down converter coupled through a pair of analog to digital converters to processor 40. The quadrature related output of the analog to digital converters are labeled I,Q. The amplitude of the signal received by antenna 18 is proportional to the square root of I2 + Q2. The phase of the signal received by antenna 18 is given by arctan(Q /I). Processor 40 then carries out further digital processing. In its simplest form, processor 40 may simply record the received data. In FIG. 2, feed antenna pattern 42 is shown with respect to feed boresight 44 and feed 16. Feed 16 is preferably a feed with a well behaved (i.e., characterized) feed antenna pattern 42 such as a corrugated, circular waveguide horn of small aperture. In prior art compact ranges similar to the compact range shown in FIG. 1, feed boresight 44 is directed from feed 16 toward a center point of reflector 12 as shown in FIG. 3A. This produces a near uniform amplitude and phase front 38. By aiming feed boresight 44 at a central part of reflector 12, the amplitude of co-polarized illumination from rays 32, 34 and 36 are approximately symmetric across the quiet zone so as to form pattern 50 as indicated in FIG. 3B. Fringe regions 46 of pattern 50 show pattern 50 rapidly attenuating outside of the quiet zone. Fringe regions 46 are the result of carefully controlled edge treatments of reflector 12 so as to provide a high quality quite zone. If, in the conventional compact range, feed boresight 44 were to be re-aimed (from being aimed at a central portion of reflector 12 to being aimed at a point other than the central point on reflector 12, e.g., a lower edge as shown in FIG. 4A), the illumination pattern 50 would be characterized by an amplitude taper as shown in FIG. 4B. Since this is considered to be undesirable, conventional compact ranges aim the feed boresight at a central portion of reflector 12 so as to produce a symmetric, almost flat, illumination pattern 50 as shown in FIG. 3B. The amplitude taper 50, shown in FIG. 4B, corresponds to vertical polarized radiation when feed 16 emits vertically polarized radiation. The same applies for horizontally polarized emissions from feed 16. This means that, for example, linearly polarized radiation from feed 16 oriented in a vertical direction produces vertically * oriented linearly polarized radiation in the quiet zone having an amplitude taper as shown in pattern 50 and also a small horizontally polarized radiation component in the quiet zone (i.e., horizontal radiation when feed 16 emits vertical radiation due to the aim of feed boresight 44). Vertically polarized radiation from feed 16, when employed in a configuration corresponding to FIG. 3A or 4A, will result in a non¬zero horizontally polarized radiation in the quiet zone due to cross-polarization effects of the geometry of conventional compact ranges. In general, feed 16 is capable of emitting two orthogonal linear polarizations (e.g., vertical and horizontal). However, with conventional compact ranges, the polarization of the illuminating radiation in the quiet zone includes an undesired component orthogonal to the intended polarization. While conventional compact ranges are able to accurately measure co-polarized antenna patterns, they are unable to accurately measure cross-polarized antenna patterns due to the geometry of the range without additional features. For example, in compact ranges designed to more accurately measure cross-polarization properties of an antenna, a second reflector, one in addition to reflector 12, may be employed to cancel the effects of mixing the two orthogonal components of the radiation pattern. Antenna 18 is scanned in a raster pattern while data measurements are collected. Antenna 18 is articulated to a desired elevation EL and scanned in azimuth AZ while measurements are recorded (e.g., measurements of I,Q recorded by processor 40) as shown in Fig. 5A. In order to scan antenna 18, antenna 18 is mounted on positioner 60 as shown in FIG. SB. Positioner 60 includes an AZ axis articulator and an EL axis articulator and sometimes a roll axis articulator. In • practice, radiation absorbers are packed around positioner 60 which is located within and below the quiet zone of the compact range. Processor 40 controls positioner 60, transmitter 20 and receiver 30 so as to collect the required data. For example, in the program shown in FIG. 6, processor 40 controls positioner 60 to point its elevation to first elevation in step S2 then causes positioner 60 to scan in azimuth between a minimum azimuth and an a maximum azimuth in step S4. During the scan, transmitter 20 is preferably tuned in steps to a sequence of frequencies of interest in step S6. During the time each frequency is tuned, the polarization (e.g., vertical polarization or horizontal polarization) emitted from feed 16 is alternately set in step S8. While the positioner is pointed at a particular elevation and azimuth, while transmitter 20 is tuned to a particular frequency and set at a particular polarization, received signal REC from antenna 18 is down converted in receiver 30 to base band and sampled by processor 40 (e.g., in the form of digital words I,Q). Processor 40 causes the azimuth and elevation position of samples I,Q together with the associate frequency and transmitter polarization to be recorded in step S10. Processor 40 determines whether data has been collected for both alternate polarizations in step S12, determines whether data has been collected for all frequencies of interest in step S14, determines whether the azimuth scan has been completed in step S16, and determines whether all elevations of interest have been measured in step SI8. In practice, antenna 18 is mounted on positioner 60 and boresighted into the compact range reflector so that, in most instances, the maximum amplitude signal is received. The I,Q values for such a position is recorded and becomes a reference against which all other data is measured. As discussed above, the I,Q data values may be easily converted to amplitude and phase format (e.g., reference values VR and 0n). Processor 40 further processes the received data in accordance with FIG. 7. As described with reference to FIG. 1, the present invention aims feed boresight 44 at vertex point VP of paraboloidal surface 44 (normally, vertex point VP is beyond the surface of reflector 12). This has a desirable effect in that vertical polarized radiation emitted from feed 16 illuminates antenna 18 in the quiet zone with only vertically polarized radiation, and horizontally polarized radiation emitted from feed 16 illuminates antenna 18 in the quiet zone with only horizontally polarized radiation. Similarly, right circular radiation from feed 16 produces only left circular radiation in the quiet zone (the polarization reverses is due to the reflection at reflector 12). This simplifies the cross-polarization measurements; however, due to the amplitude taper of the illuminating radiation (e.g., such as is shown in FIG. 4B), the measured data will include the effects of both the antenna pattern of antenna 18 and the amplitude taper from the compact range in both the co-polarized and the cross-polarized measured data. The present invention processes the data so as to remove the effects of the amplitude taper that is generated by the compact range when feed boresight 44 is pointed at vertex point VP. In FIG. 7, processor 40 determines aperture field data from received signal REC, the aperture field data containing values based on both the amplitude taper of illumination from the compact range and the co-polarization and cross-polarization properties of antenna 18. The aperture field data is produced by processor portion 100. In processor 40, the aperture field data is processed in processor portion 150 to convert the aperture field into corrected antenna data by eliminating the influence of the compact range amplitude taper from the aperture field data, the corrected • antenna data being representative of both the co-polarized and cross-polarized properties of antenna 18 with the effects of compact range 10 removed. The processing carried out in processor portion 100, generally referred to as microwave holography, includes part 102 for collecting, recording and pre-conditioning the received signal so as to generate an array of a co-polarized values and an array of cross-polarized values. In processor portion 100, part 104 performs a Fourier transform on each of the arrays of co- and cross-polarized values to produce the aperture field data. In processor portion 150 of processor 40, part 152 calculates the theoretical field data that characterizes the amplitude taper of the illumination in the quiet zone by the combination of feed 16 and reflector 12 (see FIG. 1), the theoretical field data characterizing the influence of compact range 10 that is contained in the aperture field data generated by part 104. In processor portion 150 of processor 40, part 154 combines the aperture field data with the theoretical field data to provide the corrected antenna data using a novel variation of the reaction theorem (Richmond, J.H., "A Reaction Theorem And Its Application To Antenna Impedance Calculation", IRE Transactions On Antenna And Propagation. November 1961, pages 515-520, incorporated herein by reference). In essence, part 154 performs an inverse reaction theorem process. Processor portion 100 is described further in FIGS. 8-11, and processor portion 150 is described further in FIGS. 12-14. A set of data having been collected as described herein includes an AZ position and an EL position for each data sample taken. An array of such pairs of AZ, EL positions are denoted in FIG.8 as [AZIJ, ELIJ]. As used herein, brackets (i.e., [ ]) denote an array or matrix. This array is processed through angle transform 106 to produce an array denoted [θU, U]. In FIG. 15A, there is shown the horizontal, vertical and roll axes of rotation of positioner 60. Each measurement is characterized by a particular elevation, and azimuth as indicated in FIG. 18A. This exact same position is re-expressed in terms of theta and phi as indicated in FIG. 1SB using a conventional angle transformation technique. The array of θ, values is further transformed in a K-space transform 108 to produce a corresponding array [KX'U, KY'M] as follows: (Equation Removed) This K-space array is used later in interpolation. In FIG. 9, an array of values [D1V] represents the measured complex data values (either I,Q or amplitude, phase) as measured when feed 16 emits vertically polarized radiation, and an array of values [D1H] represents the array of measured values as measured when feed 16 emits horizontally polarized radiation. In process 110, the array of data values are normalized to the reference value as described during boresighting operations. The normalized data arrays, [D2V] and [D2H], are input into phase correction process 112. Phase correction process 112 removes from the data the effects of phase errors generated due to the non-coincident location of the phase center of antenna 18 and the intersection of the roll, azimuth and elevation axes of positioner 60. In FIG. 16, the phase center of antenna 18 (i.e., the antenna under test, AUT) is characterized with respect to the intersection of the roll and azimuth axes by X-offset, Y-offset and Z-offset, and the intersection of the roll and azimuth axes is characterized by a displacement from the elevation axis denoted Z-EL. The phase compensation is calculated as follows. First, align the antenna boresight axis parallel to the range axis. In a coordinate system having the elevation axis of the positioner as the horizontal axis and the roll axis of the positioner as the antenna boresight axis parallel to the range axis, express the position of the phase center (x,y,z) as an angle (etal, psil). Next, for a particular raster scan sample point of interest, add the elevation angle of the sample point to etal to obtain eta2, and let psi2 equal psil. Next, re-express eta2, psi2 as AZ2, EL2 in the coordinate system having the azimuth axis as the vertical axis. Next, for the particular raster scan sample point of interest, add the azimuth angle of the sample point to AZ2 to obtain AZ3, and let EL3 equal EL2. The phase error experienced by the particular raster scan sample point of interest is given by 2πZ3/λ, where Z3 is the Z axis component of the point defined by AZ3, EL3 in the coordinate system of FIG. 17B. Thus, as the antenna scans the phase center changes its phase relationship with respect to the compact range when the phase center of the antenna 18 is different than the axes of rotation of antenna 18. Phase correction process 112 either adds or subtracts a suitable phase for each data point in the input data arrays to compensate for this moment arm displacement of the phase center of antenna 18. Next the co- and cross-polarization components of phase corrected data [D3V] and [D3H] from phase correction process 112 are calculated in process 114. To calculate these polarization components it is first necessary to define what is meant by co-polarization and cross-polarization. These terms are well known to practitioners of the art, for example, as described by Arthur C. Ludwig, "The Definition Of Cross Polarization". FIGS. 18A and 18B show AZ, EL measurement positions at the intersection of gridlines depicted thereon. Compact range 10 illuminates antenna 18 with vertically polarized radiation shown by arrows in FIG.18A and with horizontally polarized radiation shown by arrows in FIG. 18B. The arrows at the grid intersections in FIG. ISA show the orientation of the vertically polarized illuminating radiation, and the arrows at the grid intersections in FIG. 18B show the orientation of the horizontally polarized illuminating radiation. These directions are to be expressed as co- and cross-polarized components as defined by Ludwig and depicted in FIGS. 19A and 19B, respectively. In particular, [D4VC], [D4vx],[D4HC] and [D4HX] are computed as follows. First, for each AZ, EL point in FIG. 18A, the depicted arrow is a measured value expressed as a vector (e.g., in polar coordinates). At the same AZ, EL measurement point, the arrow of FIG. 19A (a unit vector expressed in Ludwig's definition of co-polarization) is expressed as a vector in the same coordinate system, and a dot product is computed between these vectors for each AZ, EL measurement point to form data array [D4VC]. Second, for each AZ, EL point in FIG.18A at which the depicted arrow has been expressed as a vector in the coordinate system, the corresponding arrow of FIG. 19B (a unit vector expressed in Ludwig's definition of cross-polarization) is expressed as a vector in the same coordinate system, and a dot product is computed between these vectors for each AZ, EL measurement point to form data array [D4VX]. Third, for each AZ, EL point in FIG. 18B, the depicted arrow is a measured value expressed as a vector in the coordinate system. At the same AZ, EL measurement point, the arrow of FIG. 19A (a unit vector expressed in Ludwig's definition of co-polarization) is expressed as a vector in the same coordinate system, and a dot product is computed between these vectors for each AZ, EL measurement point to form data array [D4HC]. Fourth, for each AZ, EL point in FIG. 18B at which the depicted arrow has been expressed as a vector in the coordinate system, the corresponding arrow of FIG. 19B (a unit vector expressed in Ludwig's definition of cross-polarization) is expressed as a vector in the same coordinate system, and a dot product is computed between these vectors for each AZ, EL measurement point to form data array [D4HX]. Thus, for each raster scan sample point of interest, process 114 calculates the dot product of the raster scan data with the polarization vectors according to Ludwig's third definition of co-polarization to yield the co-polarized measured field [D4VC] and PWL and process 114 calculates the dot product of the raster scan data with the polarization vectors according to Ludwig's third definition of cross-polarization to yield the cross-polarized measured field [D4VX] and [D4HX]. This process is repeated for each of the measured data points, for each of the alternate polarizations emitted by feed 16. To provide two arrays of co-polarized measured data (i.e., corresponding to the vertically and horizontally oriented source emission) and two arrays of cross-polarized measured data (i.e., corresponding to the vertically and horizontally orient source emission). Even though, the several measured data points may be taken at fixed azimuth step sizes and fix elevation step sizes, the data is not expressed in a regular lattice suitable for Fourier transform. As discussed with respect to FIG. 8, each data point has been re-described as to its position in K-space by the array [KX'IJ, KYIJ]. FIG. 20A shows a regular lattice in two dimensions with small circles representing the irregular points in K'-space. The next step is to interpolate each data point in each of the four arrays produced by process 114 into a regular spaced lattice shown in FIG. 10 as [KXIJ, KYIJ]. As shown in FIG. 20B, the first interpolation (in the KX direction) computes interpolated data points in the X direction that lies on a regular lattice line. As shown in FIG. 20C, the data is re-interpolated so as to compute interpolated data points in the Y direction that lies on a regular lattice point (in the KY direction). The raster scan of sample points may reside in a regular, rectangular grid in AZ,EL space. The transformation to K-space expresses the sample points in KX,KY space. The raster scan of sample points expressed in KX,KY space lie on an irregular, quasi-rectangular lattice. The discrete Fourier transform preferably operates on a regular, rectangular lattice of input points. Therefore, the interpolation process produces arrays of interpolated points that lie on a regular, rectangular lattice. There are many conventional interpolation routines, for example, see "POLINT" in Numerical Recipes. William H. Press, et aL, Cambridge University Press, 1992, pages 102-104, incorporated by reference. In FIG. 10, after all four arrays have been interpolated, co-polarization array [D5vc] and co-polarization array [D5Hc] are added, point by point, in summer 118 to produce array [D6c]. Similarly, cross-polarization arrays [D5VX] and [D5Hx] are added, point by point, in summer 118 to produce array [D6X]. In FIG. 11, arrays [D6c] and [D6X] are first conditioned in Fourier conditioner 120 and then transformed in Fourier transform 122 to produce aperture field data [D8c] and [D8x]. Fourier conditioners 120 merely re-label the indices into the array so as to conform with conventional Fourier transform notation: (Equation Removed) as may be found in available software libraries. Because of the Fourier transform shift property, an angular shift of the main beam off axis in the far field domain causes (or is a result of) a phase taper across the aperture distribution in the aperture domain. Therefore, since the Fourier transform requires that the indices start at 0 and go to n = N-l and m=M-l and a phase taper in the aperture domain will be caused if the main beam peak does not have indices of n=0 and m=0, the Fourier conditioning process takes advantage of the periodic nature of the far-field and aperture domains to reorder the data to be compatible with the Fourier transform. The sample data is measured at spacings that satisfy the Nyquist criteria as a minimum (e.g., twice the antenna half-power angle). In order to ensure that a sufficient number of data points are computed in the x-y coordinates, preferably an array of 501 points by 501 points, the data points into the Fourier transform may be additionally sampled or zero padded. FIG. 21A shows antenna 18 as a paraboloidal reflector with a feed horn at the focus of the paraboloidal shape. Obviously, there are many other types of antennas that may be tested in compact range 10. Antenna 18 may be uniformly weighted across its aperture. Such uniform weighting is shown in FIG. 21B. For example, a rectangular antenna would have an antenna pattern that is in the form of sin(u)/u, and thereby have first side lobes in the principal planes approximately 13 dB below the main lobe. Sometimes, antennas are designed so as to have a weighting function applied across the antenna aperture, for example, as shown in FIGS. 21C and 21D. Antennas with these weighting functions are usually designed for minimum side lobes or perhaps particularly shaped radiation patterns. The data array [D8c] produced by Fourier transform 122 represents the weighting function of the antenna under test, antenna 18, in the two dimensional aperture plane. Thus, this output array would reproduce the antenna weighting function (e.g., FIG. 21B, FIG. 21C, FIG. 21D, or other weighting function) of antenna 18 based on the measured data. The output of Fourier transform 122 is an array of data points on a regular, rectangular lattice. These XY coordinate points on the regular, rectangular lattice are referred to as [XYIJ] in FIG. 12. In FIG. 12, process 156 transforms the X,Y position of each of these data points in the plane of the aperture of antenna 18 (also the X,Y position of the aperture of reflector 12 since rays 32, 34 and 36 are all co-parallel) into an array of azimuth and elevation values denoted [AZFIJ, ELFIJ] in FIG. 12. These azimuth and elevation positions are processed in process 158 into a calculated value for the feed antenna pattern (i.e., the gain of the feed), denoted [GIJ]. Feed 16, preferably a circularly symmetric waveguide horn located at the origin of a Cartesian axis, has a circularly symmetric gain pattern defined by: where k is the value of the gain in dB at angle θ 0 measured with respect to boresight 44. The angle, θ , can be defined as a function of x, y by: (Equation Removed) Therefore, the feed gain pattern can be expressed as: (Equation Removed) where a and b are the coordinates of the position where the feed boresight is pointed and θ 0 is the angle between the feed boresight and direction where the feed gain has been measured to be -k dB with respect to the feed boresight. For example, assuming a = b = 0 and k = -3, there is at least one point (x, y, z) where the gain has been measured to be -3 dB with respect to the gain along the boresight axis; therefore, the angle between the z axis and the vector [x, y, z] is θ0. Gain d(x, y) is the feed voltage gain and is given by: (Equation Removed) The function d(x,y) is used to compute a value for data array [Gu] for each element of [XYIJ] in FIG. 12. Next, process 160 traces the line from the feed, located at the focus, to the reflector for each ray, and computes the space dispersion factor, most often referred to as space loss, based on a R-2 function to provide an array of loss data points shown as [LIJ] in Fig. 12. Power loss is based on R'-2, but voltage loss is proportional to R-1. For the purposes of analysis and simplicity, assume that the rays obey geometrical optics and the distance from feed 16 to the surface of reflector 18 can be expressed as: (Equation Removed) where a(x,y) is the inverse of the distance from feed 16 to the surface of reflector 18, the vertex of which is located at the origin of a cartesian coordinate system, the z axis of the coordinate system is the axis of symmetry of the paraboloidal surface, F is the focal length and feed 16 is located at z = F. The space loss is due to the substantially spherically dispersive emission from feed 16 (e.g., rays 22, 24 and 26). Upon reflection at reflector 12, the rays become collimated and are no longer dispersive. Thus, only space loss between feed 16 and reflector 18 is to be computed. Data array [LIj] is the array of voltage loss values that corresponds to data array [XYIJ] in FIG. 12. Data arrays [GIJ] and [LIj] are used to calculate the illumination levels of compact range 10. The array of gains and the array of losses are then multiplied (i.e., their values expressed in dB are added) in multiply operation 162 to produce data array [D9], By examining illumination contours for various feed beam widths and pointing angles it is evident that the test zone apertures are essentially circular and their diameters have only a small dependence on the feed pointing angle. For example, the test zone diameter (normalized to the reflector focal length) for 0.5 dB and 1.0 dB tapers vary from about 0.44 to 0.45 and 0.60 to 0.65, respectively, as the tilt of the feed varies from 0° to 40° for a feed pattern whose 3 dB beam width is 66°. An interesting observation on conventional compact ranges (i.e., FIG. 3A) is that the correct feed pointing angle is dependent on the feed beam width. Since the space attenuation increases from the center to the outer edge in the elevation plane, the feed's beam peak must be pointed above the center of the reflector to equalize amplitude taper in that plain (e.g., FIG. 4B). The broader the beam width of the feed, the more it should be pointed toward the upper portion of the range reflector. In FIG. 22A, feed 16 is characterized by boresight 44 pointed at vertex point VP. Ray 24 is directed from feed 16 to reflector 12 at angle A22. Similarly, ray 24 is directed from feed 16 to reflector 12 at angle A24 and ray 26 is directed from feed 16 to reflector 12 at angle A26. Process 158 (FIG. 12) calculates the falloff of feed antenna pattern gain as a function of angle A22, A24 and A26. Process 160 (FIG. 12) calculates the space loss due to the differing lengths of rays 22, 24 and 26 (FIG. 22A). In FIG. 22A, rays 22, 24 and 26 correspond to aperture plane X, Y offsets denoted XY1,1 and XYI,J and XY10,10, respectively, the correspondence being defined by process 156 (FIG. 12). Thus, data array (D9) defines the amplitude taper produced in the illuminating field provided by compact range 10 (FIG. 1, and is shown in FIG. 22B. It is therefore necessary and desirable to de-embed the influence of the amplitude taper from compact range 10 as shown in Fig. 22B from the aperture field data [D6c] and [D6x]. In FIG. 13, Fourier conditioner process 164 re-orders the indices of data array [D9] in the same way Fourier conditioner process 120 orders data (FIG. 11). The conditioned Fourier data [D10] produced by Fourier conditioner process 164 represents the amplitude taper (FIG. 22B) produced by compact range 10 in a lattice arrangement with lattice indices identical to those used in aperture plane data [D6c] and [D6X]. De-embed process 166 divides, on a point by point basis, each value in array [D6c] by a corresponding value in array [D10], and similarly divides each value in array [D6X] by a corresponding value in array [D10]. The de-embedded resulting arrays [D11c] and [Dnx] are further processed in inverse Fourier process 168 to provide corrected co-polarized far field array [D12C] and corrected cross-polarized far field array [D12X]. The de-embedded, corrected, co- and cross-polarized far field data is further Fourier de-conditioned in process 170 (the reverse of processes 120 and • 164). The de-conditioned data arrays [D13C] and [D13x] are re-interpolated in process 172 to effect the reverse of process 116, and then the angles corresponding to the resulting re-interpolated data arrays [D14C] and [D14X] are reverse angle transformed in process 174 to effect the reverse of processes 106, 108 (FIG. 8) so that the output data arrays [D15C] and [D15x] provide a corrected antenna pattern for antenna 18 for both co-polarized and cross-polarized data at the angles of the original measurements; however, the influence of the amplitude taper (FIG. 22B) produced by compact range 10 (FIG. 1) is absent from the antenna patterns. Persons skilled in the art will be able to derive the microwave holography computations performed in processor portion 100 (FIG. 7) from Maxwell's laws with a high frequency approximation and a small angle approximation. The high frequency approximation is based on a sufficiently high frequency so that the field of antenna 18 is contained in the quiet zone of compact range 10. This means that for angles near the aperture plane normal of antenna 18, fields outside the aperture can be neglected because (1) outside the aperture, antennas with diameters larger than a few wavelengths have fields that fall off rapidly, and (2) the phase of the field outside the aperture changes rapidly so that energy directed there is not well collimated. A circular aperture antenna of diameter D has its field substantially contained in a cylindrical pattern having the same diameter as the antenna for a distance B in front of the antenna where: (Equation Removed) In antennas of only 10 wavelengths in diameter, energy will remain substantially collimated for nearly 40 wavelength. The small angle approximation is based on cos( θ ) being approximately equal * to unity. To the extent that either the high frequency approximation or the small angle approximation are violated, the accuracy of cross-polarization measurements will be eroded. For example, an antenna specification might require that the cross-polarized extraneous signal level be no more than -30 dB with respect to the co-polarized signal level. The antenna test procedure may require that the measurement process be accurate to -20 dB with respect to the measured quantity (e.g., the cross-polarized extraneous signal level); therefore, the measurement process must be such that processing noise errors be no more -SO dB with respect to the co-polarized signal level. This is a level that is difficult to achieve in a two reflector range. However, with the present invention, the high frequency approximation and the small angle approximation are controlled so that this accuracy is achievable. The test procedures would merely determine the lowest permitted frequency and largest permitted scan angle that achieves the specified measurement accuracy. Having described preferred embodiments of a novel apparatus and method to measure co-polarization and cross-polarization properties of an antenna (which are intended to be illustrative and not limiting), it is noted that modifications and variations can be made by persons skilled in the art in light of the above teachings. For example, transmitting from antenna to feed instead of from feed to antenna, or arbitrary pointing of the feed boresight with cooresponding processing adjustments are expressly contemplated. It is therefore to be understood that changes may be made in the particular embodiments of the invention disclosed which are within the scope and spirit of the invention as defined by the appended claims. Having thus described the invention with the details and particularity required by the patent laws, what is claimed and desired protected by Letters Patent is set forth in the appended claims. We Claim:- 1. An apparatus for obtaining corrected antenna data, the apparatus comprising: a processor; and a compact range, the compact range defining a quiet zone and having a reflector and a feed, the reflector being characterized by a paraboloidal shape having a vertex point and a focus point, the feed being located at the focus point and being characterized by a feed boresight pointed at the vertex point, the compact range further having one of a receiver and a transmitter coupled to the feed and another of the receiver and the transmitter to an antenna, the receiver being coupled to the processor to provide a received signal to the processor. 2. The apparatus of claim 1, wherein the corrected antenna data includes data based on co-polarization and cross-polarization properties of the antenna. 3. The apparatus of claim 1, wherein: the corrected antenna data includes data based on co-polarization and cross-polarization properties of the antenna; the processor determines aperture field data from the received signal, the aperture field data containing values based on properties of the compact range and the co-polarization and cross-polarization properties of the antenna; the processor further calculates theoretical field data, the theoretical field data characterizing the properties of the compact range; and the processor further combines the aperture field data and the theoretical field data to provide the corrected antenna data. 4. A processor for use with a compact range to obtain corrected antenna data, the compact range defining a quiet zone and having a reflector and a feed, the reflector being characterized by a paraboloidal shape having a focus point, the feed being located at the focus point, the compact range further having one of a receiver and a transmitter coupled to the feed and another of the receiver and the transmitter coupled to an antenna, the receiver being coupled to the processor to provide a received signal to the processor, the processor comprising: means for measuring aperture field data, the aperture field data containing values based on properties of the compact range and properties of the antenna; means for calculating theoretical field data, the theoretical field data characterizing the properties of the compact range; and means for combining the aperture field data and the theoretical field data to provide the corrected antenna data. 5. The processor of claim 4, wherein: the paraboloidal shape of the reflector has a vertex point; and the feed is characterized by a feed boresight pointed at the vertex point. 6. The processor of claim 4, wherein: the corrected antenna data includes data based on co-polarization and cross-polarization properties of the antenna; and the means for measuring aperture field data includes measuring data that is based on the co-polarization and cross-polarization properties of the antenna. 7. A computer readable medium for use with a processor, the processor being for use with a compact range to obtain corrected antenna data, the compact range defining a quiet zone and having a reflector and a feed, the reflector being characterized by a paraboloidal shape having a focus point, the feed being located at the focus point, the compact range further having one of a receiver and a transmitter coupled to the feed and another of a receiver and a transmitter coupled to an antenna, the receiver being coupled to the processor to provide a received signal to the processor, the computer readable medium comprising: a first module of program logic stored in said computer readable medium for controlling the processor to transform the received signal into aperture field data, the aperture field data containing values based on properties of the compact range and properties of the antenna; a second module of program logic stored in said computer readable medium for controlling the processor to calculate theoretical field data, the theoretical field data characterizing the properties of the compact range; and a third module of program logic stored in said computer readable medium for controlling the processor to combine the aperture field data and the theoretical field data to provide the corrected antenna data. 8. The computer readable medium of claim 7, wherein: the corrected antenna data contains co-polarization and cross-polarization properties of an antenna; and the first module controls the processor so that the aperture field data transformed from the received signal 9. A method to obtain corrected antenna data in a compact range with a cooperating processor, the compact range defining a quiet zone and having a reflector and a feed, the reflector being characterized by a paraboloidal shape having a focus point, the feed being located at the focus point, the compact range further having one of a receiver and a transmitter coupled to the feed and another of the receiver and the transmitter coupled to the antenna, the receiver being coupled to the processor to provide a received signal to the processor, the method comprising steps of: measuring aperture field data, the aperture field data containing values based on properties of the compact range and properties of the antenna; calculating theoretical field data, the theoretical field data characterizing the properties of the compact range; and combining the aperture field data and the theoretical field data to provide the corrected antenna data. 10. The method of claim 9, wherein: the corrected antenna data incudes data containing co-polarization and cross-polarization properties of an antenna; and the step of measuring the aperture data measures data that includes the co-polarization and cross-polarization properties of the antenna. 11. The method of claim 9, wherein: the paraboloidal shape of the reflector has a vertex point; and the feed is characterized by a feed boresight pointed at the vertex point. 12. A apparatus for obtaining co-polarization and cross-polarization properties of an antenna comprising: means for determining aperture field data, the aperture field data containing values based on the apparatus for measuring and the co-polarization and cross-polarization properties of the antenna; and means for converting the aperture field data into corrected antenna data by eliminating an influence of the apparatus for measuring from the aperture field data, the corrected antenna data being representative of the co-polarization and cross-polarization properties of the antenna. 13. The apparatus of claim 12, wherein the means for converting comprises: means for calculating theoretical field data, the theoretical field data characterizing the influence of the apparatus for measuring; and means for combining the aperture field data and the theoretical field data to provide the corrected antenna data. 14. The apparatus of claim 12, wherein: the means for determining includes a compact range, the compact range having a feed and reflector system defining a quiet zone and a range field pattern within the quiet zone, the influence of the apparatus for measuring including an amplitude taper that characterizes the range field pattern; the antenna is disposed within the quiet zone; and the means for converting removes from the aperture field data effects of the amplitude taper that characterizes the range field pattern. 15. The apparatus of claim 12, wherein: the means for determining includes a compact range, the compact range having a feed and only one reflector; the reflector in cooperation with the feed defines a quiet zone and a range field pattern within the quiet zone, the influence of the apparatus for measuring including an influence of the range field pattern; and the antenna is disposed within the quiet zone, the antenna providing a received signal, the means for determining processing the received signal to determine the aperture field data. 16. The apparatus of claim 12, wherein: • the means for determining includes a compact range, the compact range having a feed and a reflector, the reflector having a paraboloidal shape so as to define a vertex point of the paraboloidal shape of the reflector; the feed radiates in a predetermined feed radiation pattern oriented along a feed centerline, the feed being disposed so that the feed centerline points at the vertex point; the reflector in cooperation with the feed defines a quiet zone and a range field pattern within the quiet zone, the influence of the apparatus for measuring including an influence of the range field pattern; and the antenna is disposed within the quiet zone, the antenna providing a received signal, the means for determining processing the received signal to determine the aperture field data. 17. The apparatus of claim 12, wherein: the means for determining includes means for measuring a first array of values, each of the values of the first array representing a measured signal voltage and phase when the antenna is pointed at a corresponding Az/El position while the antenna is illumined with only vertically polarized radiation; the means for determining further includes means for measuring a second array of values, each of the values of the second array representing a measured signal voltage and phase when the antenna is pointed at a corresponding Az/El position while the antenna is illumined with only horizontally polarized radiation; the aperture field data includes a third array of values and a fourth array of values, the third array of values representing the co-polarization property of the antenna uninfluenced by the cross-polarization property of the antenna, the fourth array of values representing the cross-polarization property of the antenna uninfluenced by the co-polarization property of the antenna; and the means for determining includes means to process the first and second arrays into the third and fourth arrays. 18. An apparatus for obtaining corrected antenna data Substantially as hereinbefore described with reference to and as illustrated in the accompanying drawings. 19. A processor substantially as hereinbefore described with reference to and as illustrated in the accompanying drawings. 20. A computer readable medium for use with a processor substantially as hereinbefore described with reference to and as illustrated in the accompanying drawings. 21. Apparatus for obtaining co-polarization and cross-polarization properties of an antenna substantially as hereinbefore described with reference to and as illustrated in the accompanying drawings.

Full Text

A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by any one of the patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever.
BACKGROUND OF THE INVENTION
Field of the Invention
The present invention relates to test methods to measure co-polarization and cross-polarization properties of an antenna. In particular, the invention relates to an apparatus and method to measure these properties in a compact range facility having a feed and reflector system that provides quiet zone in which a radiation field is uniformly polarized.
Description Of Related Art
The principals of compact ranges for the measurement of antenna properties is known, for example see U.S. Patent No. 3,302,205 to R. C. Johnson, incorporated herein by reference, and Johnson, Ecker and Moore, "Compact Range Techniques and Measurements", IEEE Transactions On Antennas and Propagation. September 1969, pages 568-576, also incorporated herein by reference, and "The Compact

Range" by Scientific-Atlanta, Inc., The Microwave Journal. October 1974, volume 17, number 10, pages 30 and 32, also incorporated herein by reference.
A property of antennas that is frequently measured is the antenna gain pattern as a function of azimuth and elevation angles relative to a vector normal to a predetermined plane that passes through the phase center of the antenna. Usually, the predetermined plane is the aperture plane of the antenna when the normal vector is co-parallel with the boresight axis of the main lobe of the antenna.
Other antenna properties that are of interest include co- and cross-polarization properties of the antenna. Ideally, an antenna fed with a signal to produce a vertically polarized emission will produce only the vertically polarized emission. However, in a real world antenna, the signal will also produce some horizontally polarized emission. The degree to which the antenna produces the intended vertically polarized emission when excited to produce the vertically polarized emission may be referred to as a co-polarization property of the antenna. The degree to which the antenna produces the unintended horizontally polarized emission when excited to produce the vertically polarized emission may be referred to as a cross-polarization property of the antenna.
Arthur C. Ludwig developed a more rigorous definition of cross-polarization in his paper "The Definition Of Cross Polarization", IEEE Transactions On Antennas And Propagation. January 1973, pages 116-119, incorporated herein by reference. To be precise herein, Ludwig's third definition of cross-polarization is used throughout this disclosure.
Polarization is a property of a single-frequency electromagnetic wave; it describes the shape and orientation of the locus of the extremity of the field vectors as a function of time. In antenna engineering, we are primarily interested in the polarization properties of plane waves or of waves that can be considered to be planar over the local region of observation. For plane waves, we need only specify the polarization properties of the electric field vector since the magnetic field is simply related to the electric field vector.
The plane containing the electric and magnetic fields is called the plane of polarization and is orthogonal to the direction of propagation. In the general case, the tip of the electric field vector moves along an elliptical path in the plane of

polarization. The polarization of the wave is specified by the shape and orientation of the ellipse and the direction in which the electric field vector traverses the ellipse. In antenna measurements Ludwig's third definition of polarization is appropriate. For a transmitted field polarized in the ly direction at θ = 0, the co-polarized and cross-polarized components are given by:
(Equation Removed)
where the coordinates correspond to equations 8a and 8b and Ludwig's Fig. 2. For evaluating primary feed patterns for paraboloidal reflectors a logical requirement is that a perfect feed cause a perfect surface current distribution. A necessary and sufficient condition for zero cross-polarized surface currents is Eθ cos = E+ sin which is identically equivalent to Ludwig's third definition. It is possible to show that a Huygen's source satisfies this condition as well as a physically circular feed with equal E-plane and H-plane amplitude and phase patterns.
Accurate cross-polarization measurements require an incident field on the antenna under test that has uniform amplitude and phase, as well as a low cross-polarization equivalent extraneous signal level. Compact ranges are well suited to provide uniform amplitude and phase over a quite zone region into which the antenna under test fits. However, to obtain low cross-polarization equivalent extraneous signal levels has required considerable expense in the design and manufacture of dual reflector systems that theoretically produce low cross-polarization, but in practice, due to manufacturing tolerances, assembly and alignment inaccuracies, etc., produce cross-polarization equivalent extraneous signal levels in the -35 to -45 dB range relative to the co-polarization signal level.
A compact range typically has a feed with an asymmetric reflector. The feed boresight axis is pointed toward the center of the reflector, more or less, to produce an incident field that has substantially uniform amplitude and phase on the antenna under test. However, such arrangements also produce a cross-polarization equivalent extraneous signal that detracts from the ability to use the compact range to measure both co- and cross-polarization properties of the antenna under test. Such cross-

polarization detriments are discussed by Johannes Jacobson in his paper "On the Cross Polarization of Asymmetric Reflector Antennas for Satellite Applications", IEEE Transactions On Antennas And Propagation. March 1977, pages 276-283, incorporated herein by reference.
SUMMARY OFTHE INVENTION
It is an object of the present invention to provide an apparatus and method to obtain high accuracy cross-polarization measurements with prime focus, single reflector, compact ranges.
It is yet another object of the present invention to provide an apparatus and method to reduce cross-polarization extraneous signals to levels that rival or exceed the much more expensive dual reflector systems, with the associated cost and simplicity of a single reflector system.
These and other objects are achieved in an apparatus for obtaining corrected antenna data that includes a processor and a compact range, the corrected antenna data containing co-polarization and cross-polarization properties of an antenna. The compact range defines a quiet zone and has a reflector and a feed, the reflector being characterized by a paraboloidal shape having a vertex point and a focus point, the feed being located at the focus point and being characterized by a feed boresight pointed at the vertex point. The compact range further has a transmitter coupled to the feed and a receiver coupled between the antenna and the processor to provide a received signal to the processor. The processor determines aperture field data from the received signal, the aperture field data containing values based on properties of the compact range and the co-polarization and cross-polarization properties of the antenna. The processor further calculates theoretical field data, the theoretical field data characterizing the properties of the compact range. The processor further combines the aperture field data and the theoretical field data to provide the corrected antenna data.
BRIEF DESCRIPTION OF DRAWINGS
The invention will be described in detail in the following description of
preferred embodiments with reference to the following figures wherein:

FIG. 1 is a schematic diagram of a compact range according to the present
invention;
FIG. 2 is a graph showing an antenna radiation pattern of a feed used in the present invention;
FIGS. 3A and 4A are schematic diagrams of portions of conventional compact ranges;
FIGS. 3B and 4B are graphs showing radiation patterns produced by the arrangement of FIGS. 3A and 4A, respectively;
FIG. 5A is a plot showing representative Az, El positions in a raster scan according to the present invention;
FIG. SB is a schematic diagram showing a positioner with mounted antenna under test according to the present invention;
FIG. 6 is a flow chart showing steps used to collect data according to the present invention;
FIG. 7 is a block diagram showing major processes according to the present invention;
FIGS. 8-14 are data flow diagrams showing the processing of data according to the present invention;
FIGS.15A and 15B are graphs showing the coordinate systems used in angle transformation according to the present invention;
FIG. 16 is a mechanical schematic diagram showing dimensions used in moment arm phase corrections according to the present invention;
FIGS. 17A and 17B are graphs showing the coordinate systems used in moment arm phase corrections according to the present invention;

FIGS. 18A and 18B are graphs showing polarizations that will be considered
co- and cross-polarized for an antenna under test according to the present invention;
FIGS. 19A and 19B are graphs showing polarizations considered to be co- and
cross-polarized by Ludwig's third definition as used in processing according to the
*
present invention;
FIGS. 20A, 20B and 20C are graphs showing interpolation of raw data onto a regular, rectangular lattice according to the present invention;
FIG. 21A is a schematic diagram of an antenna under test;
FIGS. 2IB, 21C and 2ID are graphs in the aperture plane showing representative antenna weightings of the antenna in FIG. 21A according the present invention;
FIG. 22A is a schematic diagram of a portion of the compact range of FIG. 1 to illustrate the process of calculating theoretical illumination according the present invention; and
FIG. 22B is a graph showing the amplitude taper of the illumination of FIG. 22A.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
In a single reflector compact range system, the dual requirements for (1) low cross-polarization equivalent extraneous signal level and (2) small amplitude taper in the defined test zone are mutually exclusive for antenna under test displaced from or large with respect to the defined test zone of the compact range. Low cross-polarization requires that the compact range feed be pointed at the vertex of the offset

reflector's parent parabola shape, which produces significant amplitude taper in the
quiet zone.
Scientific-Atlanta has designed a series of compact range feeds that when pointed at the vertex of the reflector's parent parabola shape, produce cross-
•
polarization in the quiet zone that is negligible. However, this produces a significant asymmetric amplitude taper in the quiet zone. When a far field antenna pattern for the antenna under test is measured, the measured pattern is significantly altered by the amplitude taper of the incident field from the compact range.
The effects of the induced amplitude taper on the antenna under test measured far field patterns is then removed by the use of a new algorithm based on the Fourier transform properties and the reaction between the incident field and the aperture distribution of the antenna under test. This new microwave holography technique involves the measurement of the response of the antenna under test over a solid angular region to two orthogonal polarizations.
The holography algorithm manipulates these measurements to obtain the co-and cross-polarized aperture field distributions of the antenna under test. The known amplitude taper of the incident field from the compact range is removed from the co-and cross-polarized aperture distributions to form a corrected aperture distribution for the antenna under test. Then, the corrected far field patterns are calculated from the corrected aperture distribution.
FIG. 1 illustrates a compact range according the present invention. In FIG. 1, reflector 12 is formed out of a portion of paraboloidal surface 14. Feed 16 is located at the focus of the paraboloidal surface.

In the present invention, boresight 44 of feed 16 is pointed at vertex point VP.
Vertex point VP is located at the vertex of paraboloidal surface 14. Transmitter 20 is coupled to feed 16. Feed 16 radiates a broad beam pattern, preferably having 60 to 80 degrees of beam width, to produce rays 22, 24 and 26. Rays 22, 24 and 26
•
reflect from reflector 12 to form collimated rays 32, 34 and 36, respectively. The radiation from collimated rays 32, 34, 36 presents a uniform phase front 38 to the antenna under test, antenna 18. Antenna 18 is located within quite zone QZ of the compact range. Antenna 18 receives the incident radiation and provides received signal REC. Signal REG is coupled to receiver 30.
Persons skilled in the art will appreciate that an equivalent configuration is where receiver 30 is coupled to feed 16 instead of antenna 18 and transmitter 20 is coupled to antenna 18 instead of feed 16 due to the reciprocal nature of antenna transmission and reception.
By pointing feed boresight 44 at vertex point VP, the radiation across phase front 38 is only co-polarized and not cross-polarized with respect to the radiation from feed 16. If the radiation emitted by feed 16 were only vertically and linearly polarized, then the radiation across phase front 38 is also only vertically and linearly polarized. Similarly, horizontally polarized radiation emitted from feed 16 results in only horizontally polarized radiation across phase front 38.
Transmitter 20 preferably generates a continuous wave source providing transmit signal XMTT coupled to feed 16 and reference signal REF coupled to receiver 30. Receiver 30 preferably includes a quadrature synchronous down converter coupled through a pair of analog to digital converters to processor 40. The quadrature related output of the analog to digital converters are labeled I,Q. The

amplitude of the signal received by antenna 18 is proportional to the square root of
I2 + Q2. The phase of the signal received by antenna 18 is given by arctan(Q /I). Processor 40 then carries out further digital processing. In its simplest form, processor 40 may simply record the received data.
In FIG. 2, feed antenna pattern 42 is shown with respect to feed boresight 44 and feed 16. Feed 16 is preferably a feed with a well behaved (i.e., characterized) feed antenna pattern 42 such as a corrugated, circular waveguide horn of small aperture.
In prior art compact ranges similar to the compact range shown in FIG. 1, feed boresight 44 is directed from feed 16 toward a center point of reflector 12 as shown in FIG. 3A. This produces a near uniform amplitude and phase front 38. By aiming feed boresight 44 at a central part of reflector 12, the amplitude of co-polarized illumination from rays 32, 34 and 36 are approximately symmetric across the quiet zone so as to form pattern 50 as indicated in FIG. 3B. Fringe regions 46 of pattern 50 show pattern 50 rapidly attenuating outside of the quiet zone. Fringe regions 46 are the result of carefully controlled edge treatments of reflector 12 so as to provide a high quality quite zone.
If, in the conventional compact range, feed boresight 44 were to be re-aimed (from being aimed at a central portion of reflector 12 to being aimed at a point other than the central point on reflector 12, e.g., a lower edge as shown in FIG. 4A), the illumination pattern 50 would be characterized by an amplitude taper as shown in FIG. 4B. Since this is considered to be undesirable, conventional compact ranges aim the feed boresight at a central portion of reflector 12 so as to produce a symmetric, almost flat, illumination pattern 50 as shown in FIG. 3B.

The amplitude taper 50, shown in FIG. 4B, corresponds to vertical polarized
radiation when feed 16 emits vertically polarized radiation. The same applies for horizontally polarized emissions from feed 16. This means that, for example, linearly polarized radiation from feed 16 oriented in a vertical direction produces vertically
*
oriented linearly polarized radiation in the quiet zone having an amplitude taper as shown in pattern 50 and also a small horizontally polarized radiation component in the quiet zone (i.e., horizontal radiation when feed 16 emits vertical radiation due to the aim of feed boresight 44). Vertically polarized radiation from feed 16, when employed in a configuration corresponding to FIG. 3A or 4A, will result in a non¬zero horizontally polarized radiation in the quiet zone due to cross-polarization effects of the geometry of conventional compact ranges.
In general, feed 16 is capable of emitting two orthogonal linear polarizations (e.g., vertical and horizontal). However, with conventional compact ranges, the polarization of the illuminating radiation in the quiet zone includes an undesired component orthogonal to the intended polarization. While conventional compact ranges are able to accurately measure co-polarized antenna patterns, they are unable to accurately measure cross-polarized antenna patterns due to the geometry of the range without additional features.
For example, in compact ranges designed to more accurately measure cross-polarization properties of an antenna, a second reflector, one in addition to reflector 12, may be employed to cancel the effects of mixing the two orthogonal components of the radiation pattern.
Antenna 18 is scanned in a raster pattern while data measurements are collected. Antenna 18 is articulated to a desired elevation EL and scanned in azimuth

AZ while measurements are recorded (e.g., measurements of I,Q recorded by processor 40) as shown in Fig. 5A. In order to scan antenna 18, antenna 18 is mounted on positioner 60 as shown in FIG. SB. Positioner 60 includes an AZ axis articulator and an EL axis articulator and sometimes a roll axis articulator. In
•
practice, radiation absorbers are packed around positioner 60 which is located within and below the quiet zone of the compact range.
Processor 40 controls positioner 60, transmitter 20 and receiver 30 so as to collect the required data. For example, in the program shown in FIG. 6, processor 40 controls positioner 60 to point its elevation to first elevation in step S2 then causes positioner 60 to scan in azimuth between a minimum azimuth and an a maximum azimuth in step S4. During the scan, transmitter 20 is preferably tuned in steps to a sequence of frequencies of interest in step S6. During the time each frequency is tuned, the polarization (e.g., vertical polarization or horizontal polarization) emitted from feed 16 is alternately set in step S8.
While the positioner is pointed at a particular elevation and azimuth, while transmitter 20 is tuned to a particular frequency and set at a particular polarization, received signal REC from antenna 18 is down converted in receiver 30 to base band and sampled by processor 40 (e.g., in the form of digital words I,Q). Processor 40 causes the azimuth and elevation position of samples I,Q together with the associate frequency and transmitter polarization to be recorded in step S10. Processor 40 determines whether data has been collected for both alternate polarizations in step S12, determines whether data has been collected for all frequencies of interest in step S14, determines whether the azimuth scan has been completed in step S16, and determines whether all elevations of interest have been measured in step SI8.

In practice, antenna 18 is mounted on positioner 60 and boresighted into the compact range reflector so that, in most instances, the maximum amplitude signal is received. The I,Q values for such a position is recorded and becomes a reference against which all other data is measured. As discussed above, the I,Q data values
may be easily converted to amplitude and phase format (e.g., reference values VR and 0n). Processor 40 further processes the received data in accordance with FIG. 7.
As described with reference to FIG. 1, the present invention aims feed boresight 44 at vertex point VP of paraboloidal surface 44 (normally, vertex point VP is beyond the surface of reflector 12). This has a desirable effect in that vertical polarized radiation emitted from feed 16 illuminates antenna 18 in the quiet zone with only vertically polarized radiation, and horizontally polarized radiation emitted from feed 16 illuminates antenna 18 in the quiet zone with only horizontally polarized radiation. Similarly, right circular radiation from feed 16 produces only left circular radiation in the quiet zone (the polarization reverses is due to the reflection at reflector 12). This simplifies the cross-polarization measurements; however, due to the amplitude taper of the illuminating radiation (e.g., such as is shown in FIG. 4B), the measured data will include the effects of both the antenna pattern of antenna 18 and the amplitude taper from the compact range in both the co-polarized and the cross-polarized measured data. The present invention processes the data so as to remove the effects of the amplitude taper that is generated by the compact range when feed boresight 44 is pointed at vertex point VP.
In FIG. 7, processor 40 determines aperture field data from received signal REC, the aperture field data containing values based on both the amplitude taper of illumination from the compact range and the co-polarization and cross-polarization

properties of antenna 18. The aperture field data is produced by processor portion
100. In processor 40, the aperture field data is processed in processor portion 150 to convert the aperture field into corrected antenna data by eliminating the influence of the compact range amplitude taper from the aperture field data, the corrected
•
antenna data being representative of both the co-polarized and cross-polarized properties of antenna 18 with the effects of compact range 10 removed. The processing carried out in processor portion 100, generally referred to as microwave holography, includes part 102 for collecting, recording and pre-conditioning the received signal so as to generate an array of a co-polarized values and an array of cross-polarized values. In processor portion 100, part 104 performs a Fourier transform on each of the arrays of co- and cross-polarized values to produce the aperture field data.
In processor portion 150 of processor 40, part 152 calculates the theoretical field data that characterizes the amplitude taper of the illumination in the quiet zone by the combination of feed 16 and reflector 12 (see FIG. 1), the theoretical field data characterizing the influence of compact range 10 that is contained in the aperture field data generated by part 104. In processor portion 150 of processor 40, part 154 combines the aperture field data with the theoretical field data to provide the corrected antenna data using a novel variation of the reaction theorem (Richmond, J.H., "A Reaction Theorem And Its Application To Antenna Impedance Calculation", IRE Transactions On Antenna And Propagation. November 1961, pages 515-520, incorporated herein by reference). In essence, part 154 performs an inverse reaction theorem process. Processor portion 100 is described further in FIGS. 8-11, and processor portion 150 is described further in FIGS. 12-14.

A set of data having been collected as described herein includes an AZ
position and an EL position for each data sample taken. An array of such pairs of AZ, EL positions are denoted in FIG.8 as [AZIJ, ELIJ]. As used herein, brackets (i.e., [ ]) denote an array or matrix. This array is processed through angle transform
106 to produce an array denoted [θU, U]. In FIG. 15A, there is shown the horizontal, vertical and roll axes of rotation of positioner 60. Each measurement is characterized by a particular elevation, and azimuth as indicated in FIG. 18A. This exact same position is re-expressed in terms of theta and phi as indicated in FIG. 1SB using a conventional angle transformation technique.
The array of θ, values is further transformed in a K-space transform 108 to produce a corresponding array [KX'U, KY'M] as follows:
(Equation Removed)
This K-space array is used later in interpolation.
In FIG. 9, an array of values [D1V] represents the measured complex data values (either I,Q or amplitude, phase) as measured when feed 16 emits vertically polarized radiation, and an array of values [D1H] represents the array of measured values as measured when feed 16 emits horizontally polarized radiation. In process 110, the array of data values are normalized to the reference value as described during boresighting operations. The normalized data arrays, [D2V] and [D2H], are input into phase correction process 112. Phase correction process 112 removes from the data the effects of phase errors generated due to the non-coincident location of the phase center of antenna 18 and the intersection of the roll, azimuth and elevation axes of positioner 60. In FIG. 16, the phase center of antenna 18 (i.e., the antenna under

test, AUT) is characterized with respect to the intersection of the roll and azimuth
axes by X-offset, Y-offset and Z-offset, and the intersection of the roll and azimuth axes is characterized by a displacement from the elevation axis denoted Z-EL. The phase compensation is calculated as follows.
First, align the antenna boresight axis parallel to the range axis. In a coordinate system having the elevation axis of the positioner as the horizontal axis and the roll axis of the positioner as the antenna boresight axis parallel to the range axis, express the position of the phase center (x,y,z) as an angle (etal, psil). Next, for a particular raster scan sample point of interest, add the elevation angle of the sample point to etal to obtain eta2, and let psi2 equal psil. Next, re-express eta2, psi2 as AZ2, EL2 in the coordinate system having the azimuth axis as the vertical axis. Next, for the particular raster scan sample point of interest, add the azimuth angle of the sample point to AZ2 to obtain AZ3, and let EL3 equal EL2. The phase error experienced by the particular raster scan sample point of interest is given by 2πZ3/λ, where Z3 is the Z axis component of the point defined by AZ3, EL3 in the coordinate system of FIG. 17B.
Thus, as the antenna scans the phase center changes its phase relationship with respect to the compact range when the phase center of the antenna 18 is different than the axes of rotation of antenna 18.
Phase correction process 112 either adds or subtracts a suitable phase for each data point in the input data arrays to compensate for this moment arm displacement of the phase center of antenna 18.
Next the co- and cross-polarization components of phase corrected data [D3V] and [D3H] from phase correction process 112 are calculated in process 114. To

calculate these polarization components it is first necessary to define what is meant
by co-polarization and cross-polarization. These terms are well known to practitioners of the art, for example, as described by Arthur C. Ludwig, "The Definition Of Cross Polarization".
FIGS. 18A and 18B show AZ, EL measurement positions at the intersection of gridlines depicted thereon. Compact range 10 illuminates antenna 18 with vertically polarized radiation shown by arrows in FIG.18A and with horizontally polarized radiation shown by arrows in FIG. 18B. The arrows at the grid intersections in FIG. ISA show the orientation of the vertically polarized illuminating radiation, and the arrows at the grid intersections in FIG. 18B show the orientation of the horizontally polarized illuminating radiation. These directions are to be expressed as co- and cross-polarized components as defined by Ludwig and depicted in FIGS. 19A and 19B, respectively.
In particular, [D4VC], [D4vx],[D4HC] and [D4HX] are computed as follows. First, for each AZ, EL point in FIG. 18A, the depicted arrow is a measured value expressed as a vector (e.g., in polar coordinates). At the same AZ, EL measurement point, the arrow of FIG. 19A (a unit vector expressed in Ludwig's definition of co-polarization) is expressed as a vector in the same coordinate system, and a dot product is computed between these vectors for each AZ, EL measurement point to form data array [D4VC]. Second, for each AZ, EL point in FIG.18A at which the depicted arrow has been expressed as a vector in the coordinate system, the corresponding arrow of FIG. 19B (a unit vector expressed in Ludwig's definition of cross-polarization) is expressed as a vector in the same coordinate system, and a dot product is computed between these vectors for each AZ, EL measurement point to

form data array [D4VX]. Third, for each AZ, EL point in FIG. 18B, the depicted arrow is a measured value expressed as a vector in the coordinate system. At the same AZ, EL measurement point, the arrow of FIG. 19A (a unit vector expressed in Ludwig's definition of co-polarization) is expressed as a vector in the same coordinate system, and a dot product is computed between these vectors for each AZ, EL measurement point to form data array [D4HC]. Fourth, for each AZ, EL point in FIG. 18B at which the depicted arrow has been expressed as a vector in the coordinate system, the corresponding arrow of FIG. 19B (a unit vector expressed in Ludwig's definition of cross-polarization) is expressed as a vector in the same coordinate system, and a dot product is computed between these vectors for each AZ, EL measurement point to form data array [D4HX].
Thus, for each raster scan sample point of interest, process 114 calculates the dot product of the raster scan data with the polarization vectors according to Ludwig's third definition of co-polarization to yield the co-polarized measured field [D4VC] and PWL and process 114 calculates the dot product of the raster scan data with the polarization vectors according to Ludwig's third definition of cross-polarization to yield the cross-polarized measured field [D4VX] and [D4HX]. This process is repeated for each of the measured data points, for each of the alternate polarizations emitted by feed 16. To provide two arrays of co-polarized measured data (i.e., corresponding to the vertically and horizontally oriented source emission) and two arrays of cross-polarized measured data (i.e., corresponding to the vertically and horizontally orient source emission).
Even though, the several measured data points may be taken at fixed azimuth step sizes and fix elevation step sizes, the data is not expressed in a regular lattice

suitable for Fourier transform. As discussed with respect to FIG. 8, each data point
has been re-described as to its position in K-space by the array [KX'IJ, KYIJ]. FIG. 20A shows a regular lattice in two dimensions with small circles representing the irregular points in K'-space. The next step is to interpolate each data point in each of the four arrays produced by process 114 into a regular spaced lattice shown in FIG. 10 as [KXIJ, KYIJ]. As shown in FIG. 20B, the first interpolation (in the KX direction) computes interpolated data points in the X direction that lies on a regular lattice line. As shown in FIG. 20C, the data is re-interpolated so as to compute interpolated data points in the Y direction that lies on a regular lattice point (in the KY direction).
The raster scan of sample points may reside in a regular, rectangular grid in AZ,EL space. The transformation to K-space expresses the sample points in KX,KY space. The raster scan of sample points expressed in KX,KY space lie on an irregular, quasi-rectangular lattice. The discrete Fourier transform preferably operates on a regular, rectangular lattice of input points. Therefore, the interpolation process produces arrays of interpolated points that lie on a regular, rectangular lattice. There are many conventional interpolation routines, for example, see "POLINT" in Numerical Recipes. William H. Press, et aL, Cambridge University Press, 1992, pages 102-104, incorporated by reference.
In FIG. 10, after all four arrays have been interpolated, co-polarization array [D5vc] and co-polarization array [D5Hc] are added, point by point, in summer 118 to produce array [D6c]. Similarly, cross-polarization arrays [D5VX] and [D5Hx] are added, point by point, in summer 118 to produce array [D6X].

In FIG. 11, arrays [D6c] and [D6X] are first conditioned in Fourier conditioner
120 and then transformed in Fourier transform 122 to produce aperture field data [D8c] and [D8x]. Fourier conditioners 120 merely re-label the indices into the array so as to conform with conventional Fourier transform notation:
(Equation Removed)
as may be found in available software libraries. Because of the Fourier transform shift property, an angular shift of the main beam off axis in the far field domain causes (or is a result of) a phase taper across the aperture distribution in the aperture domain. Therefore, since the Fourier transform requires that the indices start at 0 and go to n = N-l and m=M-l and a phase taper in the aperture domain will be caused if the main beam peak does not have indices of n=0 and m=0, the Fourier conditioning process takes advantage of the periodic nature of the far-field and aperture domains to reorder the data to be compatible with the Fourier transform. The sample data is measured at spacings that satisfy the Nyquist criteria as a minimum (e.g., twice the antenna half-power angle). In order to ensure that a sufficient number of data points are computed in the x-y coordinates, preferably an array of 501 points by 501 points, the data points into the Fourier transform may be additionally sampled or zero padded.
FIG. 21A shows antenna 18 as a paraboloidal reflector with a feed horn at the focus of the paraboloidal shape. Obviously, there are many other types of antennas

that may be tested in compact range 10. Antenna 18 may be uniformly weighted
across its aperture. Such uniform weighting is shown in FIG. 21B. For example, a rectangular antenna would have an antenna pattern that is in the form of sin(u)/u, and thereby have first side lobes in the principal planes approximately 13 dB below the main lobe. Sometimes, antennas are designed so as to have a weighting function applied across the antenna aperture, for example, as shown in FIGS. 21C and 21D. Antennas with these weighting functions are usually designed for minimum side lobes or perhaps particularly shaped radiation patterns. The data array [D8c] produced by Fourier transform 122 represents the weighting function of the antenna under test, antenna 18, in the two dimensional aperture plane. Thus, this output array would reproduce the antenna weighting function (e.g., FIG. 21B, FIG. 21C, FIG. 21D, or other weighting function) of antenna 18 based on the measured data.
The output of Fourier transform 122 is an array of data points on a regular, rectangular lattice. These XY coordinate points on the regular, rectangular lattice are referred to as [XYIJ] in FIG. 12. In FIG. 12, process 156 transforms the X,Y position of each of these data points in the plane of the aperture of antenna 18 (also the X,Y position of the aperture of reflector 12 since rays 32, 34 and 36 are all co-parallel) into an array of azimuth and elevation values denoted [AZFIJ, ELFIJ] in FIG. 12. These azimuth and elevation positions are processed in process 158 into a calculated value for the feed antenna pattern (i.e., the gain of the feed), denoted [GIJ].
Feed 16, preferably a circularly symmetric waveguide horn located at the origin of a Cartesian axis, has a circularly symmetric gain pattern defined by:

where k is the value of the gain in dB at angle θ 0 measured with respect to boresight
44. The angle, θ , can be defined as a function of x, y by:
(Equation Removed)
Therefore, the feed gain pattern can be expressed as:
(Equation Removed)
where a and b are the coordinates of the position where the feed boresight is pointed and θ 0 is the angle between the feed boresight and direction where the feed gain has been measured to be -k dB with respect to the feed boresight. For example, assuming a = b = 0 and k = -3, there is at least one point (x, y, z) where the gain has been measured to be -3 dB with respect to the gain along the boresight axis; therefore, the angle between the z axis and the vector [x, y, z] is θ0. Gain d(x, y) is the feed voltage gain and is given by:
(Equation Removed)
The function d(x,y) is used to compute a value for data array [Gu] for each element of [XYIJ] in FIG. 12.
Next, process 160 traces the line from the feed, located at the focus, to the reflector for each ray, and computes the space dispersion factor, most often referred to as space loss, based on a R-2 function to provide an array of loss data points shown as [LIJ] in Fig. 12. Power loss is based on R'-2, but voltage loss is proportional to R-1. For the purposes of analysis and simplicity, assume that the rays obey geometrical optics and the distance from feed 16 to the surface of reflector 18 can be expressed as:

(Equation Removed)
where a(x,y) is the inverse of the distance from feed 16 to the surface of reflector 18, the vertex of which is located at the origin of a cartesian coordinate system, the z axis of the coordinate system is the axis of symmetry of the paraboloidal surface, F is the

focal length and feed 16 is located at z = F.
The space loss is due to the substantially spherically dispersive emission from feed 16 (e.g., rays 22, 24 and 26). Upon reflection at reflector 12, the rays become collimated and are no longer dispersive. Thus, only space loss between feed 16 and reflector 18 is to be computed. Data array [LIj] is the array of voltage loss values that corresponds to data array [XYIJ] in FIG. 12.
Data arrays [GIJ] and [LIj] are used to calculate the illumination levels of compact range 10. The array of gains and the array of losses are then multiplied (i.e., their values expressed in dB are added) in multiply operation 162 to produce data array [D9],
By examining illumination contours for various feed beam widths and pointing angles it is evident that the test zone apertures are essentially circular and their diameters have only a small dependence on the feed pointing angle. For example, the test zone diameter (normalized to the reflector focal length) for 0.5 dB and 1.0 dB tapers vary from about 0.44 to 0.45 and 0.60 to 0.65, respectively, as the tilt of the feed varies from 0° to 40° for a feed pattern whose 3 dB beam width is 66°. An interesting observation on conventional compact ranges (i.e., FIG. 3A) is that the correct feed pointing angle is dependent on the feed beam width. Since the space attenuation increases from the center to the outer edge in the elevation plane, the feed's beam peak must be pointed above the center of the reflector to equalize

amplitude taper in that plain (e.g., FIG. 4B). The broader the beam width of the
feed, the more it should be pointed toward the upper portion of the range reflector.
In FIG. 22A, feed 16 is characterized by boresight 44 pointed at vertex point VP. Ray 24 is directed from feed 16 to reflector 12 at angle A22. Similarly, ray 24 is directed from feed 16 to reflector 12 at angle A24 and ray 26 is directed from feed 16 to reflector 12 at angle A26. Process 158 (FIG. 12) calculates the falloff of feed antenna pattern gain as a function of angle A22, A24 and A26. Process 160 (FIG. 12) calculates the space loss due to the differing lengths of rays 22, 24 and 26 (FIG. 22A). In FIG. 22A, rays 22, 24 and 26 correspond to aperture plane X, Y offsets denoted XY1,1 and XYI,J and XY10,10, respectively, the correspondence being defined by process 156 (FIG. 12). Thus, data array (D9) defines the amplitude taper produced in the illuminating field provided by compact range 10 (FIG. 1, and is shown in FIG. 22B. It is therefore necessary and desirable to de-embed the influence of the amplitude taper from compact range 10 as shown in Fig. 22B from the aperture field data [D6c] and [D6x].
In FIG. 13, Fourier conditioner process 164 re-orders the indices of data array [D9] in the same way Fourier conditioner process 120 orders data (FIG. 11). The conditioned Fourier data [D10] produced by Fourier conditioner process 164 represents the amplitude taper (FIG. 22B) produced by compact range 10 in a lattice arrangement with lattice indices identical to those used in aperture plane data [D6c] and [D6X].
De-embed process 166 divides, on a point by point basis, each value in array [D6c] by a corresponding value in array [D10], and similarly divides each value in array [D6X] by a corresponding value in array [D10]. The de-embedded resulting

arrays [D11c] and [Dnx] are further processed in inverse Fourier process 168 to provide corrected co-polarized far field array [D12C] and corrected cross-polarized far field array [D12X]. The de-embedded, corrected, co- and cross-polarized far field data is further Fourier de-conditioned in process 170 (the reverse of processes 120 and
•
164). The de-conditioned data arrays [D13C] and [D13x] are re-interpolated in process 172 to effect the reverse of process 116, and then the angles corresponding to the resulting re-interpolated data arrays [D14C] and [D14X] are reverse angle transformed in process 174 to effect the reverse of processes 106, 108 (FIG. 8) so that the output data arrays [D15C] and [D15x] provide a corrected antenna pattern for antenna 18 for both co-polarized and cross-polarized data at the angles of the original measurements; however, the influence of the amplitude taper (FIG. 22B) produced by compact range 10 (FIG. 1) is absent from the antenna patterns.
Persons skilled in the art will be able to derive the microwave holography computations performed in processor portion 100 (FIG. 7) from Maxwell's laws with a high frequency approximation and a small angle approximation.
The high frequency approximation is based on a sufficiently high frequency so that the field of antenna 18 is contained in the quiet zone of compact range 10. This means that for angles near the aperture plane normal of antenna 18, fields outside the aperture can be neglected because (1) outside the aperture, antennas with diameters larger than a few wavelengths have fields that fall off rapidly, and (2) the phase of the field outside the aperture changes rapidly so that energy directed there is not well collimated. A circular aperture antenna of diameter D has its field substantially contained in a cylindrical pattern having the same diameter as the antenna for a distance B in front of the antenna where:

(Equation Removed)
In antennas of only 10 wavelengths in diameter, energy will remain substantially collimated for nearly 40 wavelength.
The small angle approximation is based on cos( θ ) being approximately equal
*
to unity. To the extent that either the high frequency approximation or the small angle approximation are violated, the accuracy of cross-polarization measurements will be eroded. For example, an antenna specification might require that the cross-polarized extraneous signal level be no more than -30 dB with respect to the co-polarized signal level. The antenna test procedure may require that the measurement process be accurate to -20 dB with respect to the measured quantity (e.g., the cross-polarized extraneous signal level); therefore, the measurement process must be such that processing noise errors be no more -SO dB with respect to the co-polarized signal level. This is a level that is difficult to achieve in a two reflector range. However, with the present invention, the high frequency approximation and the small angle approximation are controlled so that this accuracy is achievable. The test procedures would merely determine the lowest permitted frequency and largest permitted scan angle that achieves the specified measurement accuracy.
Having described preferred embodiments of a novel apparatus and method to measure co-polarization and cross-polarization properties of an antenna (which are intended to be illustrative and not limiting), it is noted that modifications and variations can be made by persons skilled in the art in light of the above teachings. For example, transmitting from antenna to feed instead of from feed to antenna, or arbitrary pointing of the feed boresight with cooresponding processing adjustments are expressly contemplated. It is therefore to be understood that changes may be
made in the particular embodiments of the invention disclosed which are within the
scope and spirit of the invention as defined by the appended claims.
Having thus described the invention with the details and particularity required by the patent laws, what is claimed and desired protected by Letters Patent is set forth in the appended claims.

We Claim:-
1. An apparatus for obtaining corrected antenna data, the apparatus comprising:
a processor; and
a compact range, the compact range defining a quiet zone and having a reflector and a feed, the reflector being characterized by a paraboloidal shape having a vertex point and a focus point, the feed being located at the focus point and being characterized by a feed boresight pointed at the vertex point, the compact range further having one of a receiver and a transmitter coupled to the feed and another of the receiver and the transmitter to an antenna, the receiver being coupled to the processor to provide a received signal to the processor.
2. The apparatus of claim 1, wherein the corrected antenna data includes
data based on co-polarization and cross-polarization properties of the antenna.
3. The apparatus of claim 1, wherein:
the corrected antenna data includes data based on co-polarization and cross-polarization properties of the antenna;
the processor determines aperture field data from the received signal, the aperture field data containing values based on properties of the compact range and the co-polarization and cross-polarization properties of the antenna;
the processor further calculates theoretical field data, the theoretical field data characterizing the properties of the compact range; and
the processor further combines the aperture field data and the theoretical field data to provide the corrected antenna data.

4. A processor for use with a compact range to obtain corrected antenna
data, the compact range defining a quiet zone and having a reflector and a feed, the reflector being characterized by a paraboloidal shape having a focus point, the feed being located at the focus point, the compact range further having one of a receiver and a transmitter coupled to the feed and another of the receiver and the transmitter coupled to an antenna, the receiver being coupled to the processor to provide a received signal to the processor, the processor comprising:
means for measuring aperture field data, the aperture field data containing values based on properties of the compact range and properties of the antenna;
means for calculating theoretical field data, the theoretical field data characterizing the properties of the compact range; and
means for combining the aperture field data and the theoretical field data to provide the corrected antenna data.
5. The processor of claim 4, wherein:
the paraboloidal shape of the reflector has a vertex point; and
the feed is characterized by a feed boresight pointed at the vertex point.
6. The processor of claim 4, wherein:
the corrected antenna data includes data based on co-polarization and cross-polarization properties of the antenna; and
the means for measuring aperture field data includes measuring data that is based on the co-polarization and cross-polarization properties of the antenna.
7. A computer readable medium for use with a processor, the processor
being for use with a compact range to obtain corrected antenna data, the compact

range defining a quiet zone and having a reflector and a feed, the reflector being
characterized by a paraboloidal shape having a focus point, the feed being located at the focus point, the compact range further having one of a receiver and a transmitter coupled to the feed and another of a receiver and a transmitter coupled to an antenna, the receiver being coupled to the processor to provide a received signal to the processor, the computer readable medium comprising:
a first module of program logic stored in said computer readable medium for controlling the processor to transform the received signal into aperture field data, the aperture field data containing values based on properties of the compact range and properties of the antenna;
a second module of program logic stored in said computer readable medium for controlling the processor to calculate theoretical field data, the theoretical field data characterizing the properties of the compact range; and
a third module of program logic stored in said computer readable medium for controlling the processor to combine the aperture field data and the theoretical field data to provide the corrected antenna data.
8. The computer readable medium of claim 7, wherein:
the corrected antenna data contains co-polarization and cross-polarization properties of an antenna; and
the first module controls the processor so that the aperture field data transformed from the received signal
9. A method to obtain corrected antenna data in a compact range with a
cooperating processor, the compact range defining a quiet zone and having a reflector
and a feed, the reflector being characterized by a paraboloidal shape having a focus

point, the feed being located at the focus point, the compact range further having one
of a receiver and a transmitter coupled to the feed and another of the receiver and the transmitter coupled to the antenna, the receiver being coupled to the processor to provide a received signal to the processor, the method comprising steps of:
measuring aperture field data, the aperture field data containing values based on properties of the compact range and properties of the antenna;
calculating theoretical field data, the theoretical field data characterizing the properties of the compact range; and
combining the aperture field data and the theoretical field data to provide the corrected antenna data.
10. The method of claim 9, wherein:
the corrected antenna data incudes data containing co-polarization and cross-polarization properties of an antenna; and
the step of measuring the aperture data measures data that includes the co-polarization and cross-polarization properties of the antenna.
11. The method of claim 9, wherein:
the paraboloidal shape of the reflector has a vertex point; and
the feed is characterized by a feed boresight pointed at the vertex point.
12. A apparatus for obtaining co-polarization and cross-polarization
properties of an antenna comprising:
means for determining aperture field data, the aperture field data containing values based on the apparatus for measuring and the co-polarization and cross-polarization properties of the antenna; and

means for converting the aperture field data into corrected antenna data
by eliminating an influence of the apparatus for measuring from the aperture field data, the corrected antenna data being representative of the co-polarization and cross-polarization properties of the antenna.
13. The apparatus of claim 12, wherein the means for converting
comprises:
means for calculating theoretical field data, the theoretical field data characterizing the influence of the apparatus for measuring; and
means for combining the aperture field data and the theoretical field data to provide the corrected antenna data.
14. The apparatus of claim 12, wherein:
the means for determining includes a compact range, the compact range having a feed and reflector system defining a quiet zone and a range field pattern within the quiet zone, the influence of the apparatus for measuring including an amplitude taper that characterizes the range field pattern;
the antenna is disposed within the quiet zone; and the means for converting removes from the aperture field data effects of the amplitude taper that characterizes the range field pattern.
15. The apparatus of claim 12, wherein:
the means for determining includes a compact range, the compact range having a feed and only one reflector;
the reflector in cooperation with the feed defines a quiet zone and a range field pattern within the quiet zone, the influence of the apparatus for measuring including an influence of the range field pattern; and

the antenna is disposed within the quiet zone, the antenna providing a
received signal, the means for determining processing the received signal to determine the aperture field data.
16. The apparatus of claim 12, wherein:
•
the means for determining includes a compact range, the compact range having a feed and a reflector, the reflector having a paraboloidal shape so as to define a vertex point of the paraboloidal shape of the reflector;
the feed radiates in a predetermined feed radiation pattern oriented along a feed centerline, the feed being disposed so that the feed centerline points at the vertex point;
the reflector in cooperation with the feed defines a quiet zone and a range field pattern within the quiet zone, the influence of the apparatus for measuring including an influence of the range field pattern; and
the antenna is disposed within the quiet zone, the antenna providing a received signal, the means for determining processing the received signal to determine the aperture field data.
17. The apparatus of claim 12, wherein:
the means for determining includes means for measuring a first array of values, each of the values of the first array representing a measured signal voltage and phase when the antenna is pointed at a corresponding Az/El position while the antenna is illumined with only vertically polarized radiation;
the means for determining further includes means for measuring a second array of values, each of the values of the second array representing a measured signal voltage and phase when the antenna is pointed at a corresponding

Az/El position while the antenna is illumined with only horizontally polarized
radiation;
the aperture field data includes a third array of values and a fourth array of values, the third array of values representing the co-polarization property of the antenna uninfluenced by the cross-polarization property of the antenna, the fourth array of values representing the cross-polarization property of the antenna uninfluenced by the co-polarization property of the antenna; and
the means for determining includes means to process the first and second arrays into the third and fourth arrays.
18. An apparatus for obtaining corrected antenna data
Substantially as hereinbefore described with reference to and as
illustrated in the accompanying drawings.
19. A processor substantially as hereinbefore described with
reference to and as illustrated in the accompanying drawings.
20. A computer readable medium for use with a processor
substantially as hereinbefore described with reference to and as
illustrated in the accompanying drawings.
21. Apparatus for obtaining co-polarization and cross-polarization
properties of an antenna substantially as hereinbefore described
with reference to and as illustrated in the accompanying drawings.

Documents:

1231-del-1996-abstract.pdf

1231-del-1996-claims.pdf

1231-del-1996-correspondence-others.pdf

1231-del-1996-correspondence-po.pdf

1231-del-1996-description (complete).pdf

1231-del-1996-drawings.pdf

1231-del-1996-form-1.pdf

1231-del-1996-form-13.pdf

1231-del-1996-form-19.pdf

1231-del-1996-form-2.pdf

1231-del-1996-form-4.pdf

1231-del-1996-form-6.pdf

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Patent Number

232833

Indian Patent Application Number

1231/DEL/1996

PG Journal Number

13/2009

Publication Date

27-Mar-2009

Grant Date

21-Mar-2009

Date of Filing

06-Jun-1996

Name of Patentee

SCIENTIFIC-ATLANTA INC.

Applicant Address

ONE TECHNOLOGY PARKWAY, SOUTH NORCROSS, GEORGIA 30092, UNITED STATES OF AMERICA

Inventors:

#	Inventor's Name	Inventor's Address
1	JAMES H. COOK, JR.	4641 WESTHAMPTON DRIVE, TUCKER, GEORGIA 30084, USA
2	DAVID C. COOK	1090 SECRET COVE DRIVE, SUGARHILL, GEORGIA 30519, USA
3	WILLIAM KEITH DISHMAN	100 SHADOW SPRINGS DRIVE, ALPHARETTA, GEORGIA 30302, USA

PCT International Classification Number

H01Q 3/00

PCT International Application Number

N/A

PCT International Filing date

PCT Conventions:

#	PCT Application Number	Date of Convention	Priority Country
1	08/672,972	1996-04-04	U.S.A.
2	PCT/US97/-3730	1997-03-14	U.S.A.