Theoretical Comparison of Modal Expansion and Integral Equation Methods for Near-Field to Far-Field Transformation

Abstract

-STRICT A theoretical comparison for the application and derivation of modal expansion and integral equation methods is presented. It is shown that one formulation can be transformed into the other one using Fourier transform. From this point of view it can be stated that both method solves the same integral equation but for the modal expansion approach the integral equation is solved in the spectral domain while for the integral equation method the same equation is solved in the space domain. It is shown that for most of the practical antenna types the integral equation method gives more accurate far-field estimation than the modal expansion method, particularly in the planar scanning case. -ION Near-field antenna measurements have become widely used in antenna testing since they allow for accurate measurements of antenna patterns in a controlled environment. The earliest works based on the modal expansion method in which the fields radiated by the test antenna are expanded in terms of planar, cylindrical or spherical wave functions and the measured nearfields are used to determine the coefficients of the wave functions [l-31. The primary drawback of the modal expansion technique is that when Fourier transfonn is used, the fields outside the measurement region are assumed to be zero. Consequently the far-fields are accurately determined only over a particular angular sector which is dependent on the measurement configuration 143. The equivalent current approach which represents an alternate method of computing far-fields from measured near-fields has been recently explored t5-81. Thio method utilizes near-f ield data to determine equivalent electric, magnetic or both electric and magnetic current sources I over a fictitious planar surface which encompasses the aperture of the antenna. These currents are used to ascertain the far-fields. Under certain approximations the currents produce the correct f ar-f ields in all regions in front of the antenna regardless of the geometry over which the near-field measurements are made. In this paper it is shown that the formulation derived from the modal expansion method can be transformed into the formulation derived from the integral equation approach using twodimensional Fourier transform. The basic relationship between the plane wave representation and the integral representation, as an integral over the current distribution, of the fields is known [91. However a detailed comparison for the derivation and application of both method did not appear until now. The purpose of this paper is to clarify the limitation and validation for both method when they are applied for near-field to far-field transformation.