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

JOSA A, Vol. 22, Issue 4, pp. 636-646 (2005)

http://dx.doi.org/10.1364/JOSAA.22.000636

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### Abstract

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

**OCIS Codes**

(050.0050) Diffraction and gratings : Diffraction and gratings

(260.0260) Physical optics : Physical optics

**Citation**

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)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-4-636

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### References

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