This chapter aims to address the need to perform near-field antenna measurements with improved flexibility as compared to the traditional approaches of canonical measurement surfaces using regular sampling. Inverse equivalent source solvers (IESSs) are derived for the transformation of measured near field data into a set of equivalent sources, which can in turn be used to calculate near- and far-fields anywhere in the solution domain. This enables near-field antenna measurements to be made on non-canonical surfaces and/or with irregular grids. A by-product of these IESSs is that they allow a very flexible modelling of the antenna under test (AUT), which can, with the inclusion of a priori knowledge about the geometric extent of the AUT, provide 'measured' currents on the antenna structure.

Chapter Contents:

• 9.1 Introduction
• 9.2 Measurement configuration with non-canonical surfaces
• 9.3 The reciprocity theorem
• 9.4 Mathematical formulation of the Huygens principle and equivalence principles
• 9.5 Forward transmission equation with probe correction
• 9.5.1 Voltage-equivalent current formulation
• 9.5.2 Spectral representation with propagating plane waves
• 9.5.3 Gain normalised transmission equation
• 9.5.4 Spatial and spectral probe representation
• 9.6 Types and discretisation of equivalent sources for representing the AUT
• 9.6.1 Surface current densities
• 9.6.2 Surface current densities with Love condition
• 9.6.3 Surface current densities with combined-source condition
• 9.6.4 Sources in complex space
• 9.6.5 Distributed spherical-wave or plane-wave expansion
• 9.7 Equivalent source representations of the measurement probe
• 9.8 Discretisation of the forward problem
• 9.8.1 Discretisation of the transmission equations
• 9.8.2 Discretisation of supplementary constraint equations
• 9.9 Inversion of the discretised forward problem
• 9.10 Rapid computation of the forward operator
• 9.10.1 Single-level algorithm
• 9.10.2 Multi-level algorithm
• 9.10.3 Far-field translations
• 9.10.4 Gaussian-beam translations
• 9.11 Evaluation of constraint equations and adjoint operators
• 9.12 Applications and evaluations
• 9.12.1 Pyramidal horn antenna – synthetic measurement data
• 9.12.2 Planar aperture antennas – synthetic measurement data
• 9.12.3 Double-ridged waveguide antenna – spherical and multi-planar near-field measurements
• 9.12.4 Parabolic reflector with defect – synthetic measurement data
• 9.12.5 Satellite mock-up with Ku-band reflectors – synthetic measurement data
• 9.12.6 Reflector antenna – irregular near-field measurements
• 9.13 Antenna field transformations above ground
• 9.13.1 Introduction
• 9.13.2 Inverse equivalent source formulation above ground
• 9.13.3 Post-processing of equivalent sources above different ground materials
• 9.13.4 Field transformation results above ground – synthetic measurement data
• 9.14 Summary
• References

Inspec keywords: antenna radiation patterns; antenna testing; inverse problems; computational electromagnetics

Other keywords: antenna under test; noncanonical surfaces; near-field antenna measurements; irregular grids; inverse equivalent source solvers; near-field calculation; IESS; flexible AUT modelling; near-field data transformation; far-field calculation; antenna field transformation

Subjects: Antenna theory; Electric and magnetic fields; Mathematical analysis; Single antennas