  We propose a method based on sinc series approximations for computing the
Rayleigh-Sommerfeld and Fresnel diffraction integrals of optics. The
diffraction integrals are given in terms of a convolution, and our proposed
numerical approach is not only super-algebraically convergent, but it also
satisfies an important property of the convolution -- namely, the preservation
of bandwidth. Furthermore, the accuracy of the proposed method depends only on
how well the source field is approximated; it is independent of wavelength,
propagation distance, and observation plane discretization. In contrast,
methods based on the fast Fourier transform (FFT), such as the angular spectrum
method (ASM) and its variants, approximate the optical fields in the source and
observation planes using Fourier series. We will show that the ASM introduces
artificial periodic boundary conditions and violates the preservation of
bandwidth property, resulting in limited accuracy which decreases for longer
propagation distances. The sinc-based approach avoids both of these problems.
Numerical results are presented for Gaussian beam propagation and circular
aperture diffraction to demonstrate the high-order accuracy of the sinc method
for both short-range and long-range propagation. For comparison, we also
present numerical results obtained with the angular spectrum method.
