An Iterative Technique to Correct Probe Position Errors in Planar Near-Field to Far-Field Transformations

Publication Title: An Iterative Technique to Correct Probe Position Errors in Planar Near-Field to Far-Field Transformations

Government Author: Commerce Department, National Institute of Standards and Technology (NIST) .

Abstract: The authors have developed a general theoretical procedure to take into account probe position errors when planar near-field data are transformed to the far field. If the probe position errors are known, measured data can be represented as a Taylor series, whose terms contain the error function and the ideal spectrum of the antenna. Then the ideal spectrum can be solved in terms of the measured data and the measured position errors by inverting the Taylor series. This is complicated by the fact that the derivatives of the ideal data are unknown; that is, they can only be approximated by the derivatives of the measured data. This introduces additional computational errors, which must be properly taken into account. The authors have shown that the first few terms of the inversion can be easily obtained by simple approximation techniques, where the order of the approximation is easily specified. A more general solution can also be written by formulating the problem as an integral equation and using the method of successive approximations to obtain a general solution. An important criterion that emerges from the condition of convergence of the solution to the integral equation is that the total averaged position error must be less than some fraction of the sampling criterion for the antenna under test.