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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 18 — Aug. 30, 2010
  • pp: 19141–19155

A technique for calculating the amplitude distribution of propagated fields by Gaussian sampling

Moisés Cywiak, Arquímedes Morales, Manuel Servín, and Rafael Gómez-Medina  »View Author Affiliations

Optics Express, Vol. 18, Issue 18, pp. 19141-19155 (2010)

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We present a technique to solve numerically the Fresnel diffraction integral by representing a given complex function as a finite superposition of complex Gaussians. Once an accurate representation of these functions is attained, it is possible to find analytically its diffraction pattern. There are two useful consequences of this representation: first, the analytical results may be used for further theoretical studies and second, it may be used as a versatile and accurate numerical diffraction technique. The use of the technique is illustrated by calculating the intensity distribution in a vicinity of the focal region of an aberrated converging spherical wave emerging from a circular aperture.

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OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(080.1010) Geometric optics : Aberrations (global)
(080.1510) Geometric optics : Propagation methods
(080.1753) Geometric optics : Computation methods
(070.7345) Fourier optics and signal processing : Wave propagation

ToC Category:
Physical Optics

Original Manuscript: June 7, 2010
Revised Manuscript: July 21, 2010
Manuscript Accepted: August 4, 2010
Published: August 25, 2010

Moisés Cywiak, Arquímedes Morales, Manuel Servín, and Rafael Gómez-Medina, "A technique for calculating the amplitude distribution of propagated fields by Gaussian sampling," Opt. Express 18, 19141-19155 (2010)

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  1. M. Born, and E. Wolf, Principles of Optics 7th ed. (Pergamon, New York, 1980), Chap. 8.
  2. E. H. Linfoot, Recent Advances in Optics (Clarendon Press, Oxford, 1955), Chap. 3.
  3. J. E. A. Landgrave and L. R. Berriel-Valdos, “Sampling expansions for three-dimensional light amplitude distribution in the vicinity of an axial image point,” J. Opt. Soc. Am. A 14(11), 2962–2976 (1997). [CrossRef]
  4. J. J. Stamnes and H. Heier, “Scalar and electromagnetic diffraction point-spread functions,” Appl. Opt. 37(17), 3612–3622 (1998). [CrossRef]
  5. Y. Li, “Expansions for irradiance distribution near the focus in systems of different Fresnel numbers,” J. Opt. Soc. Am. A 23(3), 730–740 (2006). [CrossRef]
  6. J. J. Stamnes, “Waves in focal regions,” The Adam Hilger series on Optics and Optoelectronics, (1986).
  7. M. Sypek, “Ligth propagation in the Fresnel region. New numerical approach,” Opt. Commun. 116(1-3), 43–48 (1995). [CrossRef]
  8. A. W. Greynolds, “Propagation of generally astigmatic Gaussian beams along skew ray paths,” Proc. SPIE 560, 33–50 (1985).
  9. M. M. Popov, “A new method of computation of wave fields using Gaussian beams,” Wave Motion 4(1), 85–97 (1982). [CrossRef]
  10. M. Cywiak, M. Servín, and F. Mendoza-Santoyo, “Wave-front propagation by Gaussian superposition,” Opt. Commun. 195(5-6), 351–359 (2001). [CrossRef]
  11. H. P. Hsu, Fourier Analysis (Simon & Schuster, Inc. New York, 1970), Chap. 9.
  12. R. W. Southworth, and S. L. Deleeuw, Digital and computation and numerical methods (McGraw-Hill, N.Y., 1965) Chap. 9.
  13. M. Abramovitz, and I. Stegun, Handbook of mathematical functions in Applied Mathematics series-55, 299 (1972).

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