  In several areas of optics and photonics like wave propagation, digital
holography, holographic microscopy, diffraction imaging, biomedical imaging and
diffractive optics, the behavior of the electromagnetic waves has to be
calculated with the scalar theory of diffraction by computational methods. Many
of these high speed diffraction algorithms based on a fast Fourier
transformation are in principle approximations of the Rayleigh-Sommerfeld
Diffraction (RSD) theory. However, to investigate their numerical accuracy,
they should be compared with and verified by RSD. All numerical simulations are
in principle based on a sampling of the analogue continuous field. In this
article we demonstrate a novel validity condition for the well-sampling in RSD,
which makes a systematic treatment of sampling in RSD possible. We show the
fundamental restrictions due to this condition and the anomalies caused by its
violation. We also demonstrate that the restrictions are completely removed by
a sampling below the Abbe resolution limit. Furthermore, we present a very
general unified approach for applying the RSD outside its validity domain by
the combination of a forward and reverse calculation.
