Estimating the effect of higher order azimuthal modes in spherical near-field probe correction

The standard numerical analysis used for efficient processing of spherical near-field data requires that the far-field pattern of the probe can be expressed using only azimuthal spherical modes with indices of μ = ±1 [1, 2, 3]. In this commonly used approach, the probe is assumed to have only modes for μ = ±1, and if the probe has higher order modes, errors will be present within the calculated AUT spherical mode coefficients and the resulting asymptotic far-field parameters. In the event that the probe satisfies this symmetry requirement, then near-field data is only required for two angles of probe rotation about its axis of χ = 0 and 90 degrees and numerical integration in χ is not required. This reduces both measurement and computation time as only two orthogonal tangential near electric field components are sampled and processed. Thus, it is highly desirable to use probes that satisfy the μ = ±1 criteria. Circularly symmetric probes can be constructed that reduce the higher order modes to very low levels. Examples of these devices include cylindrical waveguide probes that are excited by the TE₁₁ fundamental mode. However for probes using open ended rectangular waveguides (OEWG) the effect of the higher order modes can also be limited by using a measurement radius that reduces the subtended angle of the AUT at the probe. Some analysis and simulation have been published that estimate the effect of using a probe with higher order modes [4, 5, 6, 7, 8] and the following study is another effort to develop further guidelines for the properties of the probe and the measurement radius that will reduce the effect of higher order azimuthal modes to acceptable levels. Previous simulation studies [9, 10, 11] have focused primarily on the effect of higher order azimuthal probe modes in rectangular OEWG probes. These showed that for radii of twice the maximum radial extent (MRE) of the test antenna the differences in the near-field, and far-field, are on the order of -50 dB below the peak amplitudes. For larger measurement radii, the differences were found to be below -60 dB. In contrast to the previously published work, this paper presents the results of a similar study in which a broadband dual ridged horn antenna was used as a near-field probe for spherical testing. Such probes are often utilized for spherical near-field testing as they have wide frequency bandwidths that cover several, typically three or more, rectangular or circular waveguide bands. Thus, the use of such devices is attractive as they can greatly simplify measurement setup, and minimize test times. Thus, although it does not satisfy the μ = ±1 criteria, these probes are widely used within the antenna measurement community. However, comparatively little information is available within the published open literature regarding specific guidelines for the properties of the probe and the measurement radius needed that will reduce the effect of higher order azimuthal modes to acceptable levels and is the motivation for this work. The results of these additional simulations are presented and guidelines developed to aid in the choice of spherical near-field probes and measurement radii for typical antennas are presented and discussed.