Abstract:
An apparatus and method for testing of rotating surface based antennas arrays (regardless of their shape), with the capability of fully diagnosing and locating a failure on the face of the antenna by coherently sampling and storing the radiation in the near field and imaging the fully array complex excitation from the stored data. The rotation of the antenna is used in order to collect data for the full azimuth span required for high resolution imaging of excitation in the horizontal domain. Excitation in the vertical domain can be preformed in two ways depending on the type of antenna used. For electronically scanning antennas in elevation (phased array antennas), the phase shifter in the desired row is toggled and the row is isolated by subtracting the complex data from pairs of adjacent samples. The sampling probe is moved vertically while the antenna is rotating horizontally. The vertical movement of the probe provides the aperture necessary to resolve the vertical excitation of the array to a degree of accuracy sufficient for fault detection and isolation.

Description:
This application claims the benefit of provisional No. 60/092,799 filed Jul. 14, 1998 
    
    
     FIELD OF THE INVENTION 
     The invention relates generally to mechanically rotating surface based antennas, and more particularly to the efficient near field testing of such antennas. 
     BACKGROUND OF THE INVENTION 
     Rotating surface based antennas can be parabolic, flat plate arrays or pleased arrays (or any other arbitrary shaped antennas) which can be steered electronically in elevation. The latter two types of antennas are characterized by an array of radiating elements and an elaborate network of power distribution components. It is very difficult to diagnose these antennas, especially in field conditions, and after years of operational use. Ordinarily, modern systems include automatic on-line testing that tests most of the prime components but does not usually test the radiating elements. Any known radiating element testing which may be provided is either quite crude and does not provide accurate and high resolution fault detection and isolation, or it is very difficult to perform, especially in field conditions. 
     Known prior techniques for providing field diagnosis of the radiating elements of the antenna include near field probing and far field pattern measurement. Near field probing requires that the antenna be stopped from rotating and that a probe sample the near field across the whole aperture. This techniques requires the construction of scaffolds and precise probe guide fixtures around the antenna. As a result, operational use of the antenna is stopped for a period which may last for several days. Other known near field techniques require that the test probe be moved in a circular path near the array, requiring a complex and highly accurate mechanical apparatus. Such near field testers are expensive. 
     Far field tests include placement of a radiating element in the far field and performing radiation pattern measurements. These techniques are elaborate logistically, as they require another site with line of sight to the antenna, and higher power for the test signal due to the greater distance. In addition, multi-path signals are also usually present which contaminate the test results. 
     SUMMARY OF THE INVENTION 
     Accordingly, it is an object of the present invention to overcome the problems of the prior art described above by providing the capability of fault detecting and isolating a complete antenna without requiring construction of an elaborate test fixture around the antenna. 
     It is a further object of the present invention to provide an apparatus and a method for fault detecting and isolating a complete antenna without the power requirements and multi-path contamination of a far field measurement apparatus and method. 
     It is still further object of the present invention to provide an apparatus and a method for fault detecting and isolating a complete antenna which considerably cuts the cost and downtime for such testing. 
     Therefore, and according to a preferred embodiment of the invention, a stationary RF probe is located at a fixed arbitrary, but known point in the near field of the antenna under test. This configuration (one of several possible configurations) is suitable for testing a mechanically rotating antenna, with electronic beam-steering capability in elevation. An RF signal is transmitted from the probe to the array, and the signal from the antenna is coherently down converted and stored in the apparatus. The antenna mechanically rotates, and the phase shifter of the row under test is toggled, typically between 0 and 180 degrees. In each phase state coherent data is sampled, digitized, and stored while all other phase shifters remain fixed. After one revolution, data collection for that row is complete. The phase shifter of the next row is then toggled and the above cycle is repeated. Full data collection requires a number of scans equal to the number of rows. Operational activity of the antenna can resume immediately after the data collection cycle is complete. Analysis of the stored data is then performed. By subtracting stored vectors of two adjacent stored samples, all rows but the one with the toggled phase shifters are removed. The data from the isolated row is then used by an imaging algorithm which maps the complex excitation function of that row. This process will be referred to later as MTI (Moving Target Indicator) process. 
     According to a second embodiment of the apparatus, a moving probe is located in the near field of the antenna under test. This configuration is suitable for testing a mechanically rotating antenna without electronic steering capability. The probe is moved vertically in an arbitrary, but known set of paths, by a predetermined increment. In each location, coherent data is collected for an entire scan. The data collection is complete when the probe is scanned thorough all the vertical positions. For each position, coherent data is collected for the complete revolution. The data collection cycle will require a number of scans equal to the number of vertical positions of the probe. Although this embodiment requires a mechanical apparatus for the vertical motion of the probe, this apparatus is not restricted to a particular path and thus can be manufactured at a much lower cost with fewer restrictions on installation and use. 
     Therefore, the described apparatus and method can map one dimensional excitation (collapsed) in a specific cut of any antenna (parabolic, phase array, etc) typically, in one revolution thereof, and two dimensional excitation in several revolutions as previously discussed. 
     Other objects, features and advantages of the present invention will become apparent from the following Detailed Description of the Invention as read in conjunction with the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     For a better understanding of these and other objects of the present invention, reference will be made to the following Detailed Description of the Invention which is to be read in association with the accompanying drawings, wherein: 
     FIG. 1 is a block diagram of a typical layout of a test setup in accordance with a preferred embodiment of the invention; 
     FIG. 2 is a block diagram of a typical tester used in conjunction with the preferred embodiment; 
     FIG. 3 is a two dimensional setup for analysis purposes; 
     FIG.  3 ( a ) is a typical three dimensional setup; 
     FIG. 4 is a graphical comparison of actual versus estimated excitation amplitudes derived from a computer simulation used for verifying the imaging algorithm; 
     FIG. 5 is a graphical comparison of actual versus estimated phase excitations from the simulation of FIG. 4; and; 
     FIGS. 6-10 are processing flow charts which describe the processing of test data received from an antenna using the apparatus of FIGS.  1 - 3 . 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 1 illustrates a typical test setup in accordance with the present invention. A horn  16  of tester  12  made in accordance with a preferred embodiment of the invention is placed in the near field of an antenna  10  (Near field as defined herein is approximately 1 to 10 antenna diameters therefrom though this parameter can be suitably varied). An RF signal  24  from the antenna  10  is routed to the tester  12 , by conventional means, or alternately the tester can generate its own RF signal using the horn  16  or other suitable radiating means as appropriate for the specific antenna under test. Antenna azimuth data  36  is also routed to the tester  12 . 
     FIG.  3 ( a ) depicts a typical three dimensional setup. The relative distance between the phase center  14  of the horn  16  and the phase center of the desired point on the antenna  10  is calculated from measured trigger and azimuth data  36 , FIG. 2, which is routed to the tester  12  from an azimuth encoder  17  disposed in relation to the antenna. Details relating to the azimuth encoder itself are well known in the field and do not form an inventive part of the present invention. In addition, other known parameters including the known antenna height, dimensions between adjacent elements and rows of the antenna array, the tilt angle of the antenna plate, and other mechanical configuration data are also routed to the tester  12 , described in greater detail below. The overall calculations of each are provided as a three-dimensional motion model of the antenna array under test, the model being derived trigonometrically from the above data and stored into storage means provided in the tester  12 . 
     More particularly and referring to FIG. 2, a typical tester  12  is shown. This particular drawing uses array nonmenclature, and is clearly suitable for all other configurations described herein . The tester  12  receives a reference RF signal from the “low power Tx”  18  or from an internal reference source (not shown). The signal  18  is routed through a splitter  20  and transmitted through the horn  16  to the antenna array. The “array RF output” signal  24  arrives from the antenna  10 , FIG. 1, and is fed into a I, Q downconverter  26  in which the transmitted signal is downconverter using LO as a reference. The I, Q components  28 ,  30  of the downconverted signal are then fed to an I, Q A/D (analog to digital) converter  32  which converts the components into I, Q data  33 . The I, Q data  33  is already digital, and is stored into storage means (allocated memory  34 ) of the tester  12 . It will be readily apparent that the above schematic can be augmented such that the reference signal will be routed to tile antenna  10  and subsequently the signal received through the horn  16 . This augmentation produces the exact same results as achieved when transmitting through the horn  16  due to the reciprocity theorem which is very well known in the antenna design art. 
     The simpler embodiment is used in the case of a phased array antenna. According to this embodiment, the horn  16  of the tester  12  is stationary, and the RF signal is coherently down converted and sampled by the tester as described in the manner above. The antenna array includes a series of adjacent rows of radiating/receiving elements wherein each row includes a phase shifter uses its internal testing capabilities to, either, receive through a single row, or toggle the phase shifter of a specific row between two states (typically 0 and 180 degrees) while keeping all other rows at a fixed phase. Each of the above can be done simultaneously, depending on the specific antenna under test. The sampling period is determined such that there will be no aliasing in the array imaging domain, and the antenna motion between two adjacent pulses will be small enough to ensure good rejection of all rows in which the phase shifter was not toggled. The sampled data is stored in the memory  34 , FIG. 2, of the tester  12 . Each row of the array of antenna elements can be fully sampled in one scan, and then the next row is selected for data collection. That is to say, a row of the array is collected for data capture purposes, upon a single revolution of the antenna. Subsequent rotations of the antenna allow subsequent rows to be collected. Upon collection of all data received from the antenna  10  and all known azimuth data of the antenna elements and finally all relevant dimensional data between the antenna and the tester, further input from the antenna is no longer required. 
     As noted, the above embodiment refers to a phased array antenna. For non-phased array antennas, the horn of the tester can be moved sequentially either upwardly or downwardly in a direction which is orthogonal in relation to the antenna&#39;s axis of rotation for each revolution of the antenna. Data collection is performed for each horn position. 
     Upon receipt of the data from the antenna, the following processing steps are performed with reference to FIGS.  6 - 10 : 
     FIGS. 6-10 describe typical processing steps preformed on the data collected by the tester  12 . FIG. 6 provides a general overview of all required processing steps, while FIGS. 7-10 each illustrate details on each of the processing steps shown generally in FIG.  6 . 
     Referring first to FIG. 6, data collection  60  is performed by the tester  12 , FIG. 2, as previously described, and the data is stored in a raw data file  62  located in the memory  34 , FIG. 2, of the tester. 
     Still referring to FIG. 6, the first processing step consists of reading tile raw data file  62  and then isolating a single row of the antenna array by using the previously described MTI process or switching that particular row using existing means found on the antenna  10  as shown in step  64 . As previously noted, processing step  64  is required only for phased array antennas. The data from each isolated single row is read using the Preliminary Imaging processing step  70  in which an initial two dimensional excitation image of the antenna is created. In non phased array antennas, the MTI processing step  64  is not performed and the isolation of a single row and element is an integral part of the Preliminary Imaging processing step  70  which uses the simultaneous antenna rotation and the motion of the horn  16 , FIG. 2, to provide the full two dimensional excitation image. 
     In the subsequent processing step, identified as the Motion Correction processing step  90 , the preliminary excitation image created by step  70  is used to correct the antenna motion parameters. Final Imaging, shown as step  100 , is preformed using the improved motion parameters determined in the Motion Correction processing step  90  to create a final antenna excitation image. Finally, the final Antenna Excitation image developed under step  100  is compared to expected excitation of the antenna in order to isolate faults. This processing step is shown as step  110 . 
     Referring to FIG. 7, the Preliminary Imaging processing steps comprising step  70  are herein discussed. First, the input parameters (e.g. the measured input data  72  and the physical data  73  stored at the memory  34 , FIG. 2, of the tester  12 , FIG. 2) are read (step  71 ). As shown in FIG.  3 ( a ), the physical data typically includes, but is not limited to, the array azimuth data from the Azimuth Encoder  17 , array tilt  6 , array height h 2 , horn height h 1 , and distance from the array rotation center to the horn  16 . Additional parameters may be included in order to enable the full trigonometric calculation of the location of each array element relative to the horn phase center  14 . 
     Next, a reference vector of each element location is calculated using the physical data  73 , according to step  74 . The known distance of each element of the array is then used to calculate the electric parameters (e.g. the field reference) of this reference function according to step  75 , therefore transforming the physical trigonometric data into electric field data. 
     The measured data  72  is multiplied by the electric reference parameters and tile resulting product is summed for each element location according to step  76 . The effects of element pattern, polarization and hone pattern are also accounted for, per step  77 , as part of the calculations of step  76 . In step  78 , the process is repeated for each element location in the image plane. When the horn  16  is stationary, (for phased array antennas or a collapsed azimuth out of any antenna), this step is performed for elements placed on a single row, and the resulting two dimensional excitation is obtained by repeating the above steps for each isolated row. In apparatus using a moving horn, (not shown- for non phased array antennas) processing steps  76  and  77  are performed for each element on the array as a two dimensional imaging summation. The summation of each imaging location uses weighting functions in order to reduce image sidelobes. Details relating to such weighting functions are well known in the art and do not require further discussion. 
     The resulting excitation is checked for validity, processing step  79 , by performing coarse comparison to a reference function. If the deviations are large across the whole image plane, then another weighting function is selected, step  81 , and steps  75  through  79  are repeated. If the excitation is valid, step  79 , then it is outputted to the next processing step  80 . 
     Referring to FIG. 8, details relating to the Motion Correction processing step  90  are herein described. First, preliminary image data  92  of some of the reference elements in the image (excitation) plane is selected, step  94 . Step  96  essentially repeats steps  74 - 78  for these reference locations with perturbations being applied to the parameters of the physical data  73 . Each of the physical data parameters are separately perturbed, and the effect on the image at the reference points of step  94  are examined. When the best image response is obtained, according to maximum response of contrast (by methods known in the radio frequency imaging art), the physical data is updated with the perturbations yielding the best image response, step  98 , as a corrected motion model. 
     Referring to FIG. 9, the final processing step  100  includes each of the steps  101 - 109 , each of these steps being essentially described in FIG. 7 as steps  74 - 81  but using the corrected physical data parameters (or motion model)  98 ,  101 . 
     FIG. 10 illustrates the details of the Analysis Processing step  110  in which the final image  112  resulting from step  108  is compared to a known nominal excitation  118  of the antenna which is stored in the memory  34 , FIG. 2, of the tester  12 , FIG. 2 according to step  114 . This comparison can be preformed directly, to the nominal excitation parameters or alternately to far field patterns calculated from the excitation. The final output is a display of estimated excitation and faults, step  116  and related far field parameters. 
     A specific description for an antenna is flow presented, for the case of a typical two dimensional setup. The three dimensional model, including motion of the horn in the vertical direction, is not shown here. The analysis of this simplified case discusses the theory of operation of the present invention. Computer simulation results for a more complex case are shown in FIGS. 4 and 5 illustrating typical comparisons of designed versus estimated excitation amplitude and phase. Measured data (not shown) produces similar results. FIG. 3 depicts the physical data for this simplified case. 
     Notation: 
     r 0 —Distance from horn phase center to row feed center 
     x n —Distance of nth element in row feed from row feed center 
     n—Element number on the row feed 
     d—Interelement spacing 
     D—Aperture size of the antenna 
     N—Total number of elements on row feed 
     r n —Distance from horn phase center to the nth element on row feed 
     r i —Distance from row feed center to the point of image focus 
     r focus —Distance from horn phase center to the point of image focus 
     w n —Complex weighting of the nth element of the row feed 
     N—Total number of elements in a row feed 
     θ—Mechanical rotation angle of the row feed 
     λ—Wavelength 
     v n —Field density at the nth dipole on the row feed 
     crad—Complex output voltage of the row feed 
     cv out —Complex output voltage at the image domain 
     ref—Complex reference function 
     k—Wave number        k   =       2   ·   π     λ                            
     u—Sine of the rotation angle (sine space). u=sin (θ). 
     For the purpose of this analysis, it is assumed that the horn radiates towards the row, and that the complex voltage is measured at the output of the row. It is obvious that due to reciprocity, the same results will be obtained when radiation is performed through the row and reception through the born, as previously noted above. 
     For a given rotation angle the radiation field at the ports of the nth dipole on the row can be expressed as follows:                v   n     =       1     r   n       ·     exp        (     j   ·   k   ·     r   n       )                 (   1   )                                
     r n  can be expressed, according to the cosine theorem, as:                r   n     =         r   0   2     +       (     n   ·   d     )     2     -     2   ·     r   0     ·     (     n   ·   d     )     ·     sin        (   θ   )                     (   2   )                                
     Assuming an isotropic element pattern, the voltage at the output of a row element is proportional to the field. The proportionality scale factor is ignored in tile analysis because its effect is not material to the analysis. 
     The output voltage of the row at this specific angle is:                crad        (   θ   )       =       ∑     n   =   1     N            w   n     ·     1     r   n       ·     exp        (     j   ·   k   ·         r   0   2     +       (     n   ·   d     )     2     -     2   ·     r   0     ·     (     n   ·   d     )     ·     sin        (   θ   )               )                   (   3   )                                
     where w n  is the complex weighting of the no element of the row feed. 
     In order to appropriately perform an image of the complex excitation function, the output voltage of the row is multiplied by a reference function to create a zero resultant phase and to normalize the effect of the distance of a specific element to the horn. 
     The appropriate reference function for the row complex excitation at a distance r 1  is assumed to have a phase which is the complex conjugate of the radiation field at that point, and an amplitude which is proportional to the distance from tile horn in order to correctly normalize the free space propagation loss. In mathematical terms:                r   focus     =         r   0   2     +     r   1   2     -     2   ·     r   0     ·     r   1     ·     sin        (   θ   )                     (   4   )                                
     and the complex reference function is:                ref        (   θ   )       =       r   focus     ·     exp        (       -   j     ·   k   ·         r   0   2     +     r   1   2     -     2   ·     r   0     ·     r   1     ·     sin        (   θ   )               )                 (   5   )                                
     To obtain the image, each output is multiplied by the reference function, summed over all values of the mechanical rotation angle. 
     The continuous imaging integral is:              cimage   =       ∫     θ   1       θ   2              crad        (   θ   )       ·     ref        (   θ   )       ·                   θ                 (   6   )                                
     In order to analyze the performance, the impulse response of the imaging integral is determined. The impulse response is obtained by assuming a single element on the row feed, and imaging the entire row by selecting all possible values of the reference function. It is not possible to analytically calculate the imaging integral in the near field in a closed form. Numerical integration or computer simulation are required. However, it is possible to calculate the far field impulse response. This is an exact analysis which will give a good visibility to the phenomena observed in the near field. The results for near field are shown in the simulation and can also be demonstrated by test. 
     Equation (6) represents the imaging integral for the complete row. In order to calculate the impulse response, one specific element n=n 1 , is selected. We shall also express the square root terms assuming we are in the far field; i.e. r 0 &gt;&gt;r 1 . Under these assumptions, the approximation of the square root terms is: 
     Rewriting equation (3) as:                crad        (   θ   )       =       w     n   1       ·     1     r   0       ·     exp        (     j   ·   k   ·     (       r   0     -       n   1     ·   d   ·     sin        (   θ   )           )       )                 (   7   )                                
     and equation (5) can be written as: 
     
       
         ref(θ)=r 0 ·exp(−j·k·(r 0 -r 1 ·sin (θ)))  (8) 
       
     
     It is convenient to perform the integral in sine space rather than in angle space. The far field approximation of the imaging integral in sine space is:                cimage        (     r   1     )       =         W     n   1           u   2     -     u   1         ·       ∫     u   1       u   2              exp        (       -   j     ·   k   ·     (         n   1     ·   d     -     r   1       )     ·   u     )       ·                   u                   (   9   )                                
     Equation (9) is the Fourier transform of the measurements taken from the various aspect angles. When r 1 =n 1 ·d, the integral equals w n1 , which is tile desired result. Without any windowing, tile response image is a sinc function multiplied by a phase term. The phase term is immaterial if u 1  and u 2  are not symmetric. 
     The mainlobe width of the image is:                B                 W     =     0.88   ·     λ       u   2     -     u   1                   (   10   )                                
     which is tile resolution of the image in the excitation domain. The angle in sine space, can extend from no more than +1 to −1. A substitution in equation (10) to obtain tile best possible resolution of the image yields:                B                   W   min       =     0.88   ·       λ   2     .               (   11   )                                
     This is a known resolution limit in coherent RF imaging. 
     The sidelobe level of a sinc function is known, and the peak level is −13 dB relative to the peak. To obtain a higher image quality, it is desirable to apply some weighting to tile imagining integral. The weighted impulse response is:                cimage        (     r   1     )       =         w     n   1         (       u   2     -     u   1       )       ·       ∫     u   1       u   2              a        (   u   )       ·     exp        (       -   j     ·   k   ·     (         n   1     ·   d     -     r   1       )     ·   u     )       ·                   u                   (   12   )                                
     where a(u) is the weighting function for lowering tile side lobes of the imaging impulse response. Properties of weighted transform are vastly covered in the literature and will not be discussed here. 
     It is not necessary to continuously measure the radiation field at any angle. Discrete sampling is also possible. Let Us assume that we periodically measure the field at the output of the antenna at regular intervals of u 0 . Substituting a periodic series of delta function in equation (12) yields:                cimage        (     r   1     )       =         w     n   1         (       u   2     -     u   1       )       ·       ∑     m   =   1     M            a        (     m   ·     u   o       )       ·     exp        (       -   j     ·   k   ·     (         n   1     ·   d     -     r   1       )     ·   m   ·     u   o       )                     (   13   )                                
     From equation (13), tile anti-aliasing condition is derived for the angular sampling. No aliasing conditions mean that there is only one imaging mainlobe in the entire region covered by the physical aperture. Aliasing occurs when the argument of the reference function term in equation (13) is a multiple integer of 2π, or mathematically: 
     
       
         k·r 1 ·m·u 0 =2·π. 
       
     
     If D is the aperture size of the antenna, then the angular sampling interval should be:                u   0     ≤     λ   D             (   14   )                                
     This is a marginal condition, and in practice a factor of at least 1.3 should be taken in order to avoid aliasing. 
     For small angles the sine approximately equals the angle, and periodic sampling in the angle domain yields the same results as in sine space. The simulation was performed in angle space and not in sine space, because it is more convenient to use periodic azimuth data from the antenna. If we calculate tile minimal spacing period in sine space and convert it to angle space, a conservative number is taken, as we are over sampling at the larger angles. 
     The analytical approach shown here is, basically, a matched filter to the phase/amplitude history of each particular element on the array. An alternate way of viewing can be preformed through the Doppler shift of each element on the array. As the antenna rotates, each element has a different radial velocity relative to the tester antenna. As the system is coherent (the same reference phase is used for transmit and receive) each radial velocity produces a different Doppler shift, which can be measured by a filter tuned to that frequency. A bank of such filters (not shown) would be required in order to cover the entire array. The motion model has to be accounted for in this approach as well: motion model Doppler has to be removed before an attempt is made to estimate the excitation in a specific point. In mathematical terms, it is easy to see that substituting the angular rate of change in equations (7) and (8) as a function of time (assuming that only θ changes as a function of time) obtains an alternate formula, which contains the instantaneous Doppler shift. It is understood that conceptually the Doppler method is identical to what has been described above, and that motion model Doppler will have to be removed just as the reference vector described here. 
     Finally, a note regarding an alternate embodiment which involves vertical motion of the horn All the preceding equations apply to show the principle of the invention. However, the single summation for the radiation pattern will change to a double summation representing the elements in the vertical domain. The reference function will therefore include excitation in two dimensions, and the angular motion will include two angles; one angle representing the horizontal rotation of the antenna, and the other angle representing the vertical mechanical motion of the probe. As a typical example, equation (7) will be rewritten for the two dimensional case:                crad        (     θ   ,   α     )       =       w     m     n   1         ·     1     r   o       ·     exp   (     j   ·   k   ·     (       r   o     -         n   1     ·   d                     x   ·   sin          (   θ   )       -         m   1     ·   d                     y   ·     sin        (   α   )             )                   (   15   )                                
     In which m and n represent the element number in the horizontal and vertical locations, dx and dy represent the interelement spacing in the horizontal and vertical locations respectively, and θ and α represent the angles in the horizontal and vertical directions. It is evident that for this case, that the motion model correction portion of the processing has to be preformed in both dimensions. 
     A computer simulation was performed in order to verify the performance of the algorithm in near field conditions. The computer simulation uses the exact formulas previously described. 
     The results presented here were run based upon the following data: 
     
       
         
               
               
             
           
               
                   
               
             
             
               
                 Row size: 
                 7 meters 
               
               
                 Total number of elements 
                 36 
               
               
                 Wavelength: 
                 0.23 meters 
               
               
                 Scanning angle: 
                 −90 degrees to +90 degrees 
               
               
                 Angular sampling interval: 
                 0.375 degrees 
               
               
                 Image sampling interval: 
                 0.1 wavelength 
               
               
                 Distance of horn from row feed center: 
                 10 meters 
               
               
                 Array amplitude weighting: 
                 Taylor, n = 5. 
               
               
                 Imaging window: 
                 Taylor, n = 5, squared 
               
               
                 Phase errors: 
                 −45 dB sidelobes 
               
               
                   
               
             
          
         
       
     
     FIGS. 4 and 5 show that for measurements taken from a distance of only twice the array size, the amplitude and the phase can be constructed with a very high degree of accuracy. 
     It should also be noted that the invention is not restricted to the simple motion model described here. In fact, no restrictions apply and the only requirement is to know the antenna elements location. In addition, any arbitrary shape antenna can be tested and testing is not necessarily restricted to flat plate or parabolic antennas, for the same reason, i.e. location of any element can be arbitrary but known. 
     While the present invention has been particularly shown and described with reference to the preferred embodiments as illustrated in the drawings, it is to be understood that the invention is not limited to those embodiments and that various changes and modifications may be effected therein without departing from the scope of the invention.