Optimal interpolation of radiated fields over a sphere

An optimal sampling interpolation algorithm is developed that allows the accurate recovery of scattered or radiated fields over a sphere from a minimum number of samples. Using the concept of the field equivalent (spatial) bandwidth, a central interpolation scheme is developed to compute the field in theta , phi coordinates, starting from its samples. The maximum allowable sample spacing and error upper bounds are also rigorously derived. Several simulated examples of pattern reconstruction are presented, for both the cases of field and power pattern interpolation. The interpolation error, as a function of the retained sample number, has been also evaluated and compared with the theoretical upper bounds. The algorithm stability versus randomly distributed errors added to the exact samples is demonstrated. >

[1]  L. Peters,et al.  Evaluation of edge-diffracted fields including equivalent currents for the caustic regions , 1969 .

[2]  G. James,et al.  Reflector antenna radiation pattern analysis by equivalent edge currents , 1973 .

[3]  R. Kouyoumjian,et al.  A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface , 1974 .

[4]  John J. Knab,et al.  Interpolation of band-limited functions using the approximate prolate series (Corresp.) , 1979, IEEE Trans. Inf. Theory.

[5]  Giorgio Franceschetti,et al.  Fast analysis of large antennas--A new computational philosophy , 1980 .

[6]  R. Hingorani,et al.  Direct Fourier reconstruction in computer tomography , 1981 .

[7]  John J. Knab,et al.  The sampling window , 1983, IEEE Trans. Inf. Theory.

[8]  Application of sampling techniques to near-field far-field transformation , 1986 .

[9]  G. Franceschetti,et al.  On the spatial bandwidth of scattered fields , 1987 .

[10]  H. Stark,et al.  Interpolation from Samples on a Linear Spiral Scan , 1987, IEEE Transactions on Medical Imaging.

[11]  Yahya Rahmat-Samii,et al.  Nonuniform sampling techniques for antenna applications , 1987 .

[12]  Henry Stark,et al.  Direct Fourier Reconstruction in Fan-Beam Tomography , 1987, IEEE Transactions on Medical Imaging.

[13]  Ovidio Mario Bucci,et al.  Use of sampling expansions in near-field-far-field transformation: the cylindrical case , 1988 .

[14]  Ovidio Mario Bucci,et al.  The truncation error in the application of sampling series to electromagnetic problems , 1988 .

[15]  G. Franceschetti,et al.  On the degrees of freedom of scattered fields , 1989 .

[16]  Ovidio Mario Bucci,et al.  Fast and accurate near-field-far-field transformation by sampling interpolation of plane-polar measurements , 1991 .