 
Summary: Nonideal Measurement Locations in Planar
NearField Antenna Metrology
R. C. Wittmann, B. K. Alpert, and M. H. Francis
National Institute of Standards and Technology
325 Broadway, Boulder, CO 803033328
1 Introduction
We introduce a neareld to fareld transformation method that relaxes the usual restriction
that data points be located on a planerectangular grid [1]. It is not always practical
or desirable to make uniformly spaced measurements; for example, the maintenance of
positioning tolerances becomes more di˘cult as frequency is increased. Our method can
(1) extend the frequency ranges of existing scanners, (2) make practical the use of portable
scanners for onsite measurements, and (3) support schemes, such as planepolar 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» = b (see section 2). The conjugate gradient method is used
to nd the unknown » in terms of the data b (section 3). The operator A must be
applied once per conjugate gradient iteration, and this is done e˘ciently using the recently
developed unequally spaced fast Fourier transform [2], [3] and local interpolation (section
4). As implemented, each iteration requires O(N log N) operations, where N is the number
