Calculation of the Rayleigh–Sommerfeld diffraction integral by exact integration of the fast oscillating factor

We describe a numerical method that can be used to calculate the propagation of light in a medium of constant (possibly complex) index of refraction n. The method integrates the Rayleigh-Sommerfeld diffraction integral numerically. After an appropriate change of integration variables, the integrand of the diffraction integral is split into a slowly varying and an (often fast) oscillating quadratic factor. The slowly varying factor is approximated by a spline fit, and the resulting Fresnel integrals are subsequently integrated exactly. Although the method is not as fast as methods involving a fast Fourier transform, such as plane-wave propagation or Fresnel approximation, it is accurate over a greater range than these methods.