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Effect of diffraction on images matched with prolate spheroidal wave functions

S.N. Khonina, V.V. Kotlyar

Image Processing Systems Institute of RAS, Samara

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Pages: 58-63.

Full text of article: Russian language.

Abstract:
The paper considers the properties of prolongate zero-order spheroidal wave functions, important for the diffractive optics: invariance to the Fourier transform, resistance to diaphragming in optical systems, and self-reproduction at a certain distance in free space. The paper investigates the influence of the diaphragm size on the accuracy of transmission of a signal matched by lens systems with prolongate spheroidal wave functions. A comparison with the Gauss-Hermite functions is performed.

Citation:
Khonina SN, Kotlyar VV. Effect of diffraction on images matched with prolate spheroidal wave functions. Computer Optics 2001; 21: 58-63.

References:
  1. Khurgin YI, Yakovlev VP. Methods of the theory of entire functions in radio physics, communications theory, and optics. Moscow: Fizmatgiz; 1962.
  2. Komarov IV, Ponomarev LI, Slavyanov SY. Spheroidal and coulombian spheroidal functions. Moscow: Nauka Publisher;1976.
  3. M. Bertero, E. R. Pike Resolution in diffractionlimited imaging, a singular value analysis // I. The case of coherent illumination, Optica Acta, 29(6), P. 727-746. (1982).
  4. M. Piche, P. Lavigne, F. Martin, P.A. Belanger Modes of resonator with internal apertures // Appl.Opt., 22(13), Р. 1999-2006 (1983).
  5. D. Slepian, H.O. Pollak, Prolate spheroidal wave functions. Fourier Analysis and Uncertainty – I, The Bell System Technical Journal, 40, P. 43-46 (1961).
  6. H.J. Landau, H.O. Pollak Prolate spheroidal wave functions // Fourier Analysis and Uncertainty – II, The Bell System Technical Journal, 40, Р. 65-84 (1961).
  7. D. Slepian, H.O. Pollak Prolate spheroidal wave functions // Fourier analysis and uncertainty – III: The dimension of essentially time-and band-limited signals, Bell Syst. Tech. J., 41, Р. 1295-1336. (1962).
  8. W.D. Montgomery Algebraic formulation of diffraction applied to self-imaging // J. Opt. Soc. Am., 58(8), Р. 1112-1124. (1968).
  9. D. Slepian Prolate spheroidal wave functions. Fourier Analysis and Uncertainty – IV: Extensions to many dimensions; generalized prolate spheroidal functions, The Bell System Technical Journal, 43, Р. 3009-3057 (1964).
  10. D. Slepian Some asymptotic expansions for prolate spheroidal wave functions // J. Math. & Phys., 44, Р. 99-140. (1965).
  11. Flammer K. Tables of spheroidal wave functions, Vych. Tsentr Akad. Nauk SSSR; Moscow; 1962.
  12. Lowan A. Spheroidal wave functionsin Reference book on special functions edited by Abramovits M, Stigan I. Moscow: Nauka Publisher; 1979: 830.
  13. P. De Santis, C. Palma Degrees of freedom of aberrated images // Optica Acta, 23(9), 743-752 (1976).
  14. A.W. Lohmann, D. Mendlovic Self-Fourier objects and other self- transform objects // J. Opt. Soc. Am. A, 9(11), 2009-2012, (1992).
  15. Khonina SN, Kotlyar VV. Prolate spheroidal functions in diffractive optics. Proceedings of the International Youth School on Optics, Laser Physics and Biophysics. Saratov: Saratov University Publishing House; 2000; 50-51.
  16. Khonina SN. А finite series approximation of spheroidal wave functions. Computer Optics; 1999; 19: 65-70.
  17. Volotovsky SG, Kazanskiy NL, Khonina SN. Analysis and development of the methods for calculating eigenvalues of prolongate spheroidal functions of zero order. Proceedings of the 5th International Conference PRIA-5-2000; Samara; 2000; 4: 697-700.

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