Approximation of the encircled energy function for the far-field diffraction of a plane light wave by planar complex-shaped apertures
I.M. Sizova

 

P.N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia

Full text of article: Russian language.

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Abstract:
A method for approximating the encircled energy in a definite solid angle in the Fraunhofer region by the simulation of the optical transfer function derivative is proposed. The selection of free model parameters allow one to obtain a valid expansion of the encircled energy at the origin of the angular coordinate and at infinity, providing a good approximation in the intermediate domain.

Keywords:
apertures, diffraction, diffraction theory.

Citation:
Sizova IM. Approximation of the encircled energy function for the far-field diffraction of a plane light wave by planar complex-shaped apertures. Computer Optics 2015; 39(5): 635-43. DOI: 10.18287/0134-2452-2015-39-5-635-43.

References:

  1. Borovich BL, Zuev VS, Katulin VA, Mikheev LD, Nikolaev FA, Nosach OYu, Rozanov VB. High-current emitting discharges and optically pumped gas lasers [In Russian]. Progress in Science and Technology, Radio Engineering Series 1978; 15: 300.
  2. Sizova IM. Approximate scaling relationships of light diffraction by apertures with complicated shapes. Appl Opt 1992; 31(28): 5930-6.
  3. Sizova IM. Similarity diffracted in the far field by apertures of complicated shape. J of Sov Laser Res 1992; 13(1): 25-45.
  4. Born M, Wolf E. Principles of Optics. New York: Macmillan; 1959.
  5. Piatakhin MV, Suchkov AF. Plane electromagnetic wave diffraction by the circular diaphragm [In Russian]. Moscow: FIAN Preprint; 1985; 254.
  6. Clark PP, Howard JW, Freniere ER. Asymptotic approximation to the encircled energy function for arbitrary aperture shapes.Appl Opt 1984; 23(2): 353-7.
  7. Willis HF. A formula for expanding an integral as a series. Philosophical Magazine 1948; 39: 455-9.
  8. Harvey JE, Ftaclas C. Diffraction effects of telescope secondary mirror spiders on various image-quality criteria. Appl Opt 1995; 34(28): 6337-49.
  9. Orlov EP, Sizova IM. The similarity of statistical properties of narrow-band random processes with arbitrary spectra. Part I. Compact spectra [In Russian]. Moscow: FIAN Preprint; 2010; 14.
  10. Orlov EP, Sizova IM. The similarity of statistical properties of narrow-band random processes with arbitrary spectra. Part II. Noncompact diachromic spectra [In Russian]. Moscow: FIAN Preprint; 2011: 18.
  11. Sizova IM. On the approximation of some integrals in the theory of light diffraction by apertures with complicated shapes [In Russian]. Moscow: FIAN Preprint; 2014: 16.
  12. Sizova IM. On the approximation of some integrals in the theory of light diffraction by apertures with complicated shapes. One more model [In Russian]. Moscow: FIAN Preprint; 2015: 2.
  13. Sizova IM. Approximation of encircled energy function in the far-field Fraunhofer zone under the diffraction of plane light wave on plane apertures of complicated shapes [In Russian]. Moscow: FIAN Preprint; 2015: 5.
  14. MacKinnon RF. The asymptotic expansions of Hankel transforms and related integrals. Mathematics of Computation 1972; 26(118): 515-27.
  15. Abramovitz L, Stegun IA (eds). Handbook of mathematical functions. National Bureau of Standards: Applied Mathematical Serues-55 1964; Chap 9.
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