OPTIMAL INTERPOLATION OF RADIATED FIELDS OVER A SPHERE

An optimal sampling interpolation algorithm is developed, which 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 patterns interpolation. The interpolation error, as a function of the retained samples number, has been also evaluated and compared with the theoretical upper bounds. Finally, the algorithm stability versus randomly distributed errors added to the exact samples is demonstrated.