Non-uniform sampling schemes for fast multilevel source imaging of reflector antenna surfaces

Summary form only given. Reconstruction of the radiating fields or equivalent currents on a closed surface enclosing a radiating body, also termed source imaging, is a widely used method in antenna diagnosis for estimating inaccuracy of antenna fabrication or localizing antenna malfunction. The Rayleigh-Sommerfeld (RS) formulation with incoming wave Green function (A. J. Devaney, Mathematical foundations of imaging, tomography and wavefield inversion. Cambridge University Press, 2012) is used in this work to enable the back-propagation from the scalar field measurement on a planar surface. This method provides a good approximation for the field backpropagated from the measurement plane towards the source, though, due to truncation errors, it is suitable mostly for the metrology of directional arrays or large reflector antennas. Direct evaluation of the discretized back-propagation integral is characterized by a computational complexity (CC) of O(N4), where N=ka (a and k being the radius of the smallest sphere circumscribing the measurement domain and the wavenumber, respectively). For antennas that are very large compared to the wavelength, this computational bottleneck renders this approach unattractive. Significant reduction of the CC down to O(N 2logN) is achieved using a modified version of the multilevel non-uniform grid (MLNG) (Y. Brick and A. Boag, IEEE Trans. Ultrason., Ferroelectr., Freq. Control, 57/1, 262-273, 2010). In order to choose the most suitable non-uniform sampling scheme, we conduct a comparison between various sampling and interpolation schemes. Among the tested grid topologies are spherical and oblate spheroidal, volumetric and onsurface ones. The algorithms' performance under each of the choices is studied in terms of accuracy, storage requirements, and run-time. As a representative example, a test case parabolic reflector with a localized surface distortion is analyzed. The comparison between the source distribution, reconstructed from the simulated measurements, and the desired one is used for the localization of anomalies. The quality of localization is measured in terms of location and contrast.