Error model for Contour-FFT evaluation of the free-space on-plane Green's function

Closed-form analytical expressions are derived for the numerical integration of the spectral Green's function with Contour-FFT. Results indicates that a proper uniform grid of spatial points enhances the convergence rate of the truncation error, that the Nyquist-Shannon theorem can be generalized to inverse Laplace transforms on linear path and that the relative error specific to Contour-FFT is a regularized gamma function. Two examples illustrate the modularity of the approach.