Numerical stability and near-field reconstruction

A Fourier decomposition technique is used to reconstruct the near-field from far-field pattern data. Upper and lower bounds are derived on the number of Fourier componentsNrequired for accurate field convergence. It is shown thatNdepends on both the distance from the origin of the near-field reconstruction point and the error levelε⁻²which arises from errors in the data and numerical quadratures. The theoretical results are shown to be in agreement with observations on near-field reconstruction for centered cylinders. It is then found that field reconstructions for less regular objects made in accordance with the convergence bounds enable certain estimates to be made of the character of the scattering object. With this, analytic continuation techniques may be applied and a second reconstruction performed nearer to the object's expected location. The nonregular scatterers treated in this paper are off-axis cylinders.