Comparative analysis of the Fresnel lens and the kinoform lens
Greisukh G.I., Stepanov S.A., Antonov A.I.

 

Penza State University of Architecture and Construction, Penza, Russia

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Abstract:
Based on a unified approach in the ray approximation, the focusing properties of Fresnel lenses and kinoform lenses are considered and compared. Particular attention is paid to the energy efficiency, chromatic focal shift and resolving power of these elements. It is shown that the Fresnel lens with same-depth segments is an analogue of the harmonic kinoform lens operating in high diffraction orders. A mechanism of the formation of the diffraction pattern in the focal plane of a Fresnel lens with equidistant annular segments is analyzed. It is shown to differ from the corresponding diffraction pattern formed by a conventional refractive lens by a smaller amount of energy coming to the main maximum and a significant proportion of energy transferred to the side maxima. The target audience of this article is students and graduate students, as well as specialists in the fields of science and technology where optical methods and instruments play an ever increasing role.

Keywords:
Fresnel lens, equally broad and equally deep annular sections, kinoform lens, Fresnel zone, tautochronism, diffraction efficiency, chromatic shift, resolution power.

Citation:
Greisukh GI, Stepanov SA, Antonov AI. Comparative analysis of the Fresnel lens and the kinoform lens. Computer Optics 2018; 42(3): 369-376. DOI: 10.18287/2412-6179-2018-42-3-369-376.

References:

  1. Slyusarev GG. Optical systems with phase layers [In Russian]. Dokl Akad Nauk SSSR 1957; 113(4): 780-782.
  2. Slyusarev GG. Design of optical systems [In Russian]. Leningrad: Mashinostroenie; 1975.
  3. Concentrated solar power experiment with a fresnel lens. Source: <https://rimstar.org/renewnrg/concentrated_solar_power_diy_with_fresnel_lens.htm>.
  4. Solar panels of the lenses. Flat and spherical [In Russian]. Source: <https://rodovid.me/solar_power/linzovye-solnechnye-paneli.html>.
  5. Fresnel lens and illuminators based on it [In Russian]. Source: <http://litedisc.ru/articles/linza-frenelya-i-osvetiteli-na-ee-osnove/>.
  6. Fresnel lens [In Russian]. Source: <https://www.4glaza.ru/katalog/lupy/linza-frenelya/>.
  7. HTC Vive Teardown. Source: <https://www.ifixit.com/Teardown/HTC+Vive+Teardown/62213>.
  8. Oculus Rift CV1 Teardown. Source: <https://www.ifixit.com/Teardown/Oculus +Rift+CV1+Teardown/60612>.
  9. Greisukh GI, Ezhov EG, Kazin SV, Stepanov SA. Single-layer kinoforms for cameras and video cameras of mobile communication devices. Computer Optics 2016; 40(5): 217-226. DOI: 10.18287/0134-2452-2017-41-2-218-226.
  10. Geary JM. Introduction to lens design: With practical ZEMAX examples. Richmond: Willmann-Bell, Inc.; 2002. ISBN: 978-0-943396-75-0.
  11. Khonina SN, Ustinov AV, Skidanov RV, Morozov AA. Comparative study of the spectral characteristics of aspheric lense. Computer Optics 2015; 39(3): 363-369. DOI: 10.18287/0134-2452-2015-39-3-363-369.
  12. Buralli DA, Morris GM, Rogers JR. Optical performance of holographic kinoforms. Appl Opt 1989; 28(5): 976-983. DOI: 10.1364/AO.28.000976.
  13. Greisukh GI, Ezhov EG, Kalashnikov AV, Levin IA, Stepanov SA. The efficiency of the relief-phase diffractive elements at a small number of Fresnel zones. Optics and Spectroscopy 2012; 113(4): 425-430. DOI: 10.1134/S0030400X12100037.
  14. Sweeney DW. Harmonic diffractive lenses. Appl Opt 1995; 34(14): 2469-2475. DOI: 10.1364/AO.34.002469.
  15. Kharitonov SI, Volotovsky SG, Khonina SN. Geometric-optical calculation of the focal spot of a harmonic diffractive lens [In Russian]. Computer Optics 2016; 40(3): 331-337. DOI: 10.18287/2412-6179-2016-40-3-331-337.
  16. Honina SN, Volotovsky SG, Ustinov AV, Kharitonov SI. Analysis of focusing light by a harmonic diffractive lens taking into account the refractive index dispersion [In Russian]. Computer Optics 2017; 41(3): 338-347. DOI: 10.18287/2412-6179-2017-41-3-338-347.
  17. Born M, Wolf E. Principles of optics: Electromagnetic theory of propagation, interference and diffraction of light. 2nd ed. Oxford: Pergamon Press; 1964.
  18. Goodman JW. Introduction to Fourier optics. San Francisco: McGraw-Hill Companies, Inc; 1968.
  19. Yu FTS. Introduction to diffraction, information processing, and holography. Cambridge: The MIT Press, 1973. ISBN: 978-0-26224015-4.
  20. Greysukh GI, Ezhov EG, Stepanov SA. Comparative analysis of chromatism of diffraction and refractive lenses [In Russian]. Computer Optics 2005: 28: 60-65.
  21. Egger JR. Use of Fresnel lenses in optical systems: some advantages and limitations. Proc SPIE 1979; 0193: 63-68. DOI: 10.1117/12.957873.
  22. Moharam, MG, Gaylord TK. Diffraction analysis of dielectric surface-relief. J Opt Soc Am 1982; 72(10): 1385-1392. DOI: 10.1364/JOSA.72.001385.
  23. Greisukh GI, Danilov VA, Ezhov EG, Stepanov SA, Usievich BA. Comparison of electromagnetic and scalar methods for evaluation of efficiency of diffractive lenses for wide spectral bandwidth. Opt Commun 2015; 338: 54-57. DOI: 10.1016/j.optcom.2014.10.037.
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