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
Original Manuscript: August 6, 2004
Manuscript Accepted: September 11, 2004
Published: April 1, 2005
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)