Adaptive sampling in convergent beams

Numerical calculation of convergent Fresnel patterns through fast Fourier transform usually requires a large number of samples to fulfill the Nyquist sampling condition around the focus. From polynomial decomposition of the wavefront it is possible to determine which polynomial orders are the main contributors to the number of samples. This information can be used to properly modify the initial wavefront and relax the Nyquist condition thus giving a more efficient numerical algorithm.