Overview of Novel Post-Processing Techniques to Reduce Uncertainty in Antenna Measurements <s> Application of source reconstruction techniques to reduce the effect of the noise, leakage and scattering <s> In many cases, it is impractical or impossible to make antenna pattern measurements on a conventional far-field range; the distance to the radiating far field may be too long, it may be impractical to move the antenna from its operating environment to an antenna range, or the desired amount of pattern data may require too much time on a far-field range. For these and other reasons, it is often desirable or necessary to determine far-field antenna patterns from measurements made in the radiating near-field region; three basic techniques for accomplishing this have proven to be successful. In the first technique, the aperture phase and amplitude distributions are sampled by a scanning field probe, and then the measured distributions are transformed to the far field. In the second technique, a plane wave that is approximately uniform in amplitude is created by a feed and large reflector in the immediate vicinity of the test antenna. And in the third technique, the test antenna is focused within the radiating near-field region, patterns are measured at the reduced range, and then the antenna is refocused to infinity. Each of these techniques is discussed, and the various advantages and limitations of each technique are presented. <s> BIB001 </s> Overview of Novel Post-Processing Techniques to Reduce Uncertainty in Antenna Measurements <s> Application of source reconstruction techniques to reduce the effect of the noise, leakage and scattering <s> After a brief history of near-field antenna measurements with and without probe correction, the theory of near-field antenna measurements is outlined beginning with ideal probes scanning on arbitrary surfaces and ending with arbitrary probes scanning on planar, cylindrical, and spherical surfaces. Probe correction is introduced for all three measurement geometries as a slight modification to the ideal probe expressions. Sampling theorems are applied to determine the required data-point spacing, and efficient computational methods along with their computer run times are discussed. The major sources of experimental error defining the accuracy of typical planar near-field measurement facilities are reviewed, and present limitations of planar, cylindrical, and spherical near-field scanning are identified. <s> BIB002 </s> Overview of Novel Post-Processing Techniques to Reduce Uncertainty in Antenna Measurements <s> Application of source reconstruction techniques to reduce the effect of the noise, leakage and scattering <s> An alternative method is presented for computing far-field antenna patterns from near-field measurements. The method utilizes the near-field data to determine equivalent magnetic current sources over a fictitious planar surface that encompasses the antenna, and these currents are used to ascertain the far fields. Under certain approximations, the currents should produce the correct far fields in all regions in front of the antenna regardless of the geometry over which the near-field measurements are made. An electric field integral equation (EFIE) is developed to relate the near fields to the equivalent magnetic currents. The method of moments is used to transform the integral equation into a matrix one. The matrix equation is solved with the conjugate gradient method, and in the case of a rectangular matrix, a least-squares solution for the currents is found without explicitly computing the normal form of the equation. Near-field to far-field transformation for planar scanning may be efficiently performed under certain conditions. Numerical results are presented for several antenna configurations. > <s> BIB003 </s> Overview of Novel Post-Processing Techniques to Reduce Uncertainty in Antenna Measurements <s> Application of source reconstruction techniques to reduce the effect of the noise, leakage and scattering <s> A new antenna diagnostics technique has been developed for the DTU-ESA Spherical Near-Field Antenna Test Facility, which is operated by the Technical University of Denmark (DTU) for the European Space Agency (ESA). The technique is based on the transformation of the spherical-wave expansion (SWE) of the radiated field, obtained from a spherical near-field measurement, to the plane-wave expansion (PWE). It allows an accurate reconstruction of the field in the extreme near-field region of the antenna under test (AUT), including the aperture field. The fundamental properties of the SWE-to-PWE transformation, as well as the influence of finite measurement accuracy, have been reported previously. We validate here the new antenna diagnostics technique through an experimental investigation of a commercially available offset reflector antenna, where a tilt of the feed horn and surface distortions were intentionally introduced. The effects of these errors were detected inthe antenna's far-field pattern, and the accuracy and ability of the diagnostic technique to subsequently identify them were investigated. Real measurement data were employed for each test case. <s> BIB004
A sources reconstruction technique is a method to obtain the extreme near-field or the equivalent currents distribution of an antenna from the knowledge of its radiated field (near or far field). This information can be employed to detect errors, and also identify which are the causes of such errors, for example, electrical errors in arrays or mechanical errors in reflectors. Apart from its classic application, a diagnostic process also gives a complete electromagnetic characterization of the antenna, which is the basis of other applications, like near-to far-field transformations, radome applications, radioelectric coverage, etc. In this work, that additional information is employed to reduce the effect of common errors in antenna measurements. Basically, diagnostic techniques can be divided into two types. The first of them is based on the equivalence principle and the integral equations relating fields and sources (integral equation methods), and the second one on modal expansions (modal expansion methods). Integral equation methods have general characteristics, but from a numerical point of view they are more complex than modal expansion methods because it is necessary to solve a system of integral equations. Several approaches to obtain a solution of such a system (sources from the radiated field) have been studied in (Alvarez, 2007) and BIB003 for different measurement setup geometries. In these studies, a system of integral equations (1) is solved by using a numerical method like the Finite Difference Time Domain (FDTD) method, the Finite Element Method (FEM), or the Method of Moments (MoM). On the other side, modal expansion methods require lower computational complexity, but due to the fact that the measured field has to be expressed as a superposition of orthogonal functions (vector wave solutions), they can only be used in particular situations, i.e., when the measurement is performed over canonical surfaces; planar, cylindrical and spherical are normally used because complex mechanical scannings are not required. Depending on the coordinate system, one particular kind of expansion (plane wave expansion, cylindrical wave expansion or spherical wave expansion) is carried out BIB002 and BIB001 . Then, the plane wave spectrum (PWS) is calculated from the corresponding expansion, and the field over the antenna aperture can be directly obtained once the PWS is known, as shown in (2). where P(k x ,k y ) stands for the electric field PWS in the (k x ,k y ) direction. The last step is to explain how to obtain the PWS from the modal expansions. In planar near-field measurements, the PWS is directly obtained from the modal expansion of the samples. However, this PWS is referenced to the measurement plane, and a back-propagation to the AUT plane  has to be used to determine the appropriate PWS. For the spherical near-field case, a transformation from a spherical wave expansion to a plane wave expansion (SWE-to-PWE) is required. This transformation was recently developed in BIB004 and relates spherical and plane coefficients. If a measurement is to be performed in a cylindrical near-field system, up to now there have been no publications explaining the approach to calculate the PWS from the cylindrical coefficients. In this case, the only solution is to apply a cylindrical near-field to far-field transformation BIB002 and BIB001 . Next, the PWS components are obtained by solving the system of equations specified in (3).  This information provided can be used as the basis of methods to suppress certain errors when measuring an antenna. In this work, the next three methods are proposed.