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.
© 2008 Optical Society of America
Fourier Optics and Signal Processing
Original Manuscript: June 4, 2008
Revised Manuscript: July 14, 2008
Manuscript Accepted: July 18, 2008
Published: August 22, 2008
Julián Espinosa, David Mas, Jorge Pérez, and Carlos Illueca, "Adaptive sampling in convergent beams," Opt. Lett. 33, 1960-1962 (2008)