Generalized lens: calculation of distribution on the optical axis
A.V. Ustinov, S.N. Khonina

PDF, 695 kB

Full text of article: Russian language.

DOI: 10.18287/0134-2452-2013-37-3-307-315

Pages: 307-315.

Abstract:
We analytically and numerically consider action of the generalized lens – a diffractive optical element with arbitrary degree of dependence of a phase function. Special cases of the generalized lens are axicon and a parabolic lens. On the basis of the modified stationary phase method analytical expressions for the axial distribution formed by the generalized lens in paraxial approach are received. Two types of analytical expressions provide high accuracy of calculation in various ranges of a degree of the generalized lens.

Key words:
axicon, parabolic lens, fracxicon, generalized lens, modified stationary phase method.

References:

  1. McLeod, J.H. The axicon: a new type of optical element / J.H. McLeod // J. Opt. Soc. Am. – 1954. – Vol. 44. – P. 592-597.
  2. Mikula, G. Diffractive elements for imaging with extended depth of focus / G. Mikula, A. Kolodziejczyk, M. Ma­kowski, C. Prokopowicz, M. Sypek // Optical Engineering. – 2005. – Vol. 44(5). – P. 058001–058008.
  3. Khonina, S.N. Axicons application in imaging systems for increasing depth of focus / S.N. Khonina, D.A. Savelyev // Izv. SNC RAS. – 2011. – V. 13, N 6. – P. 7-15. – (In Russian).
  4. Durnin, J. Diffraction-free beams / J. Durnin, J.J. Miceli and J.H. Eberly // Phys. Rev. Lett. – 1987. – V. 58, N 15. – P. 1499-1501.
  5. Khonina, S.N. Fracxicon – diffractive optical element with conical focal domain / S.N. Khonina, S.G. Volotovsky // Computer optics. – 2009. – V. 33, N 4. – P. 401-411. – (In Russian).
  6. Koronkevich, V.P. Lensacon / V.P. Koronkevich, I.A. Mik­haltsova, E.G. Churin and Yu.I. Yurlov // Аppl. Opt. – 1995. – Vol. 34, N 25. – P. 5761-5772.
  7. Sochacki, J. Annular-aperture logarithmic axicon / J. So­chacki, Z. Jaroszewicz, L.R. Staronski and A. Kolodziejc­zyk // J. Opt. Soc. Am. A. – 1993. – V. 10. – P. 1765-1768.
  8. Golub, M.A. Diffraction calculation for an optical element which focuses into a ring / M.A. Golub, N.L. Kazanskiy, I.N. Sisakyan, V.A. Soifer, S.I. Kharitonov // Optoelectronics, Instrumentation and Data Processing. – 1987. – № 6. – P. 7-14.
  9. Kazanskiy, N.L. Numerical investigation of the diffraction characteristics of a focusator in the ring // Computer Optics. – 1992. – No. 10-11. – P. 128-144. – (In Russian).
  10. Ustinov, A.V. Geometrooptic analysis of generalized refractive lenses / A.V. Ustinov, S.N. Khonina // Izv. SNC RAS. – 2012. – V. 14, N 4. – P. 29-37. – (In Russian).
  11. Fedoruk, M.V. Asymptotics Integral and Series / M.V. Fe­doruk. – Moscow: “Nauka” Publisher, 1987. – 544 p. – (In Russian).
  12. Golub, M.A. Diffraction calculation of the intensity of the light field near the focal line / M.A. Golub, L.L. Doskolovich, N.L. Kazanskiy, I.N. Sisakyan, V.A. Soifer, S.I. Kharitonov // Computer Optics. – 1992. – No. 10-11. – P. 122-127. – (In Russian).
  13. Ustinov, A.V. Comparative analysis of parabolic lens and axicon in geometric and scalar paraxial optical models / A.V. Ustinov, A.V. Karsakov, S.N. Khonina // Vestnik SSAU. – 2012. – N 4(35). – P. 230-239. – (In Russian).
  14. Ustinov, A.V. Analysis of the axial distribution formed by a fracxicon in the paraxial and nonparaxial cases / A.V. Ustinov, S.N. Khonina, A.V. Karsakov // Izv. SNC RAS. – 2013. – V. 15, N 4. – P. 18-25. – (In Russian).
  15. Khonina, S.N. Design lenses forming paraxial longitudinal distribution according to their spatial spectra / S.N. Khoni­na, A.V. Ustinov // Computer optics. – 2013. – V. 37, N 2. – P. 193-202. – (In Russian).
© 2009, IPSI RAS
Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; e-mail: ko@smr.ru; Phones: +7 (846 2) 332-56-22, Fax: +7 (846 2) 332-56-20