  A major challenge of many diffraction calculations, using some form of the
Rayleigh-Sommerfeld formulas, is the integration of a highly oscillatory
integrand. Here we derive a potentially useful alternative form of solution to
the Helmholtz equation, which implies a sampling theorem for the evaluation of
a diffracted scalar field. This alternative solution bears close resemblance to
the Rayleigh-Sommerfeld diffraction formulas, but instead incorporates the
boundary conditions digitally. Hence, the integration is replaced by a simple
summation. This formulation may be more efficient for accurate computer-based
calculation of the diffracted scalar field.
