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.
© 2005 Optical Society of America
Jan A. C. Veerman, Jurgen J. Rusch, and H. Paul Urbach, "Calculation of the Rayleigh-Sommerfeld diffraction integral by exact integration of the fast oscillating factor," J. Opt. Soc. Am. A 22, 636-646 (2005)