This paper further develops a recently proposed method for computing the diffraction integrals of optics based on sinc series approximation by presenting a numerical implementation, parameter selection criteria based on rigorous error analysis, and example optical propagation simulations demonstrating those criteria. Unlike fast Fourier transform (FFT)-based methods that are based on Fourier series, such as the well-known angular spectrum method (ASM), the sinc method uses a basis that is naturally suited to problems on an infinite domain. As such, it has been shown that the sinc method avoids the problems of artificial periodicity inherent in the ASM. After a brief review of the method, the detailed error analysis we provide confirms its super-algebraic convergence and verifies the claim that the accuracy of the method is independent of wavelength, propagation distance, and observation plane discretization; it depends only on the accuracy of the source field approximation. Based on this analysis, we derive parameter selection criteria for achieving a prescribed error tolerance, which will be valuable to potential users. Numerical simulations of Gaussian beam and optical phased array propagation verify the high-order accuracy and computational efficiency of the proposed algorithms. To facilitate the reproduction of numerical results, we provide a Matlab code that implements our numerical approach for the Fresnel diffraction integral. For comparison, we also present numerical results obtained with the ASM as well as the band-limited angular spectrum method.