Reconstruction of optical fields with the Quasi-discrete Hankel transform.

Unlike the FFT, the Quasi Discrete Hankel Transform (QDHT) is not sampled on a uniform grid; in particular the field may no longer be sampled on axis. We demonstrate how the generalised sampling theorem may be applied to optical problems, evaluated with the QDHT, to efficiently and accurately reconstruct the optical field at any point. Without sacrificing numerical accuracy this is demonstrated to be typically 50x faster than using an equivalent 2D FFT.