Effective 3-D sampling interpolation

In the last decade, sampling techniques have been successfully applied to the EM field reconstruction on regular surfaces. Such techniques rely on the fact that the fields radiated or scattered by finite sources enclosed in a ball of radius a and observed on an analytical curve C can be closely approximated by spatially bandlimited functions. The bandwidth is practically /spl beta/a (/spl beta/ being the wavenumber), provided that the phase propagation factor is extracted from the field and the normalized arclength is used to describe C. The extension to the case of a regular surface M is straightforward since this latter can be described by two families of coordinate curves. Recently, efficient sampling techniques have been developed by properly using the theoretical results concerning non-redundant representations of EM fields for source modellings and observation surfaces with the same rotational symmetry. Such techniques allow an accurate field interpolation from a minimum number of data, which remains finite also for unbounded observation geometries. They are based on the most suitable choices for the phase factor and for the parameterizations used to describe M and employ the optimal sampling interpolation (OSI) expansions to minimize the truncation errors. In this paper, the aforementioned 2-D non-redundant field representations are properly extended to obtain an effective 3-D sampling interpolation formula, whose accuracy and effectiveness are assessed by means of numerical tests.