Estimating the Uncertainties Due to Truncation in Planar Near-Field Holograms
Author:Allen C. Newell
A combination of analysis and simulation are used to estimate the amplitude and phase errors in the hologram calculated from planar near-field data. The antenna hologram is modeled as the sum of a continuous function that essentially represents a correctly aligned antenna and one or more step function discontinuities located at elements that are misaligned. The spectrum of the step function can be calculated exactly from the assumed amplitude, phase, pulse width and location of the element. This spectrum is then filtered in k-space to simulate the effect of truncating the measurement plane. It is well known that the primary result of truncation is the filtering of real and evanescent plane waves beyond an angle defined by the antenna and measurement plane geometry.
Using the results of the analysis, a script program was developed for the NSI2000 software that would calculate the spectrum from the input parameters, perform the filtering and calculate the hologram using the Fast Fourier Transform. The change in the amplitude of the reconstructed hologram pulse is then used to determine the error that results in the calculated element amplitude and/or phase. Sample curves are generated to illustrate the technique.