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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 3 — Jan. 31, 2011
  • pp: 1892–1904

Diffractive and geometric optical systems characterization with the Fresnel Gaussian shape invariant

Moisés Cywiak, Manuel Servín, and Arquímedes Morales  »View Author Affiliations

Optics Express, Vol. 19, Issue 3, pp. 1892-1904 (2011)

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Full characterization of optical systems, diffractive and geometric, is possible by using the Fresnel Gaussian Shape Invariant (FGSI) previously reported in the literature. The complex amplitude distribution in the object plane is represented by a linear superposition of complex Gaussians wavelets and then propagated through the optical system by means of the referred Gaussian invariant. This allows ray tracing through the optical system and at the same time allows calculating with high precision the complex wave-amplitude distribution at any plane of observation. This method is similar to conventional ray tracing additionally preserving the undulatory behavior of the field distribution. That is, we are propagating a linear combination of Gaussian shaped wavelets; keeping always track of both, the ray trajectory, and the wave phase of the whole complex optical field. This technique can be applied in a wide spectral range where the Fresnel diffraction integral applies including visible, X-rays, acoustic waves, etc. We describe the technique and we include one-dimensional illustrative examples.

© 2011 OSA

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: November 10, 2010
Revised Manuscript: December 23, 2010
Manuscript Accepted: December 27, 2010
Published: January 18, 2011

Moisés Cywiak, Manuel Servín, and Arquímedes Morales, "Diffractive and geometric optical systems characterization with the Fresnel Gaussian shape invariant," Opt. Express 19, 1892-1904 (2011)

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