Nonideal measurement locations in planar near-field antenna metrology

We introduce a near-field to far-field transformation method that relaxes the usual restriction that data points be located on a plane-rectangular grid. It is not always practical or desirable to make uniformly spaced measurements; for example, the maintenance of positioning tolerances becomes more difficult as frequency is increased. Our method can (1) extend the frequency ranges of existing scanners, (2) make practical the use of portable scanners for on-site measurements, and (3) support schemes, such as plane-polar scanning, where data are collected on a nonrectangular grid. Although "ideal" locations are not required, we assume that probe positions are known. (In practice, laser interferometry is often used for this purpose.) Our approach is based on a linear model of the form A/spl xi/=b. The conjugate gradient method is used to find the "unknown" /spl xi/ in terms of the "data" b. The operator A must be applied once per conjugate gradient iteration, and this is done efficiently using the recently developed unequally spaced fast Fourier transform and local interpolation. As implemented, each iteration requires O (N log N) operations, where N is the number of measurements. The required number of iterations depends on desired computational accuracy and on conditioning. We present a simulation that is based on actual near-field antenna data.