(45-3) 06 * << * >> * Russian * English * Content * All Issues

Design of a stigmatic lens with minimal Fresnel losses
L.L. Doskolovich 1,2, D.A. Bykov 1,2, G.I. Greisukh 3, Y.S. Strelkov 1,2

IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,
443001, Samara, Russia, Molodogvardeyskaya st. 151,
Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34,
Penza State University of Architecture and Constructing,
440028, Penza, Russia, Titova st. 28

 PDF, 865 kB

DOI: 10.18287/2412-6179-CO-813

Pages: 350-355.

Full text of article: Russian language.

A method for designing double aspheric lenses enabling minimal Fresnel losses in the class of stigmatic lenses is considered. Minimization of the Fresnel losses is provided by ensuring equal ray-deviation angles on both aspheric surfaces of the lens. The design of the lens is reduced to the integration of an explicit ordinary differential equation. Simple analytical approximations for the lens profiles are also presented.

lens, aspheric surface, Fresnel losses, Abbe sine condition.

Doskolovich LL, Bykov DA, Greysukh GI, Strelkov YS. Design of a stigmatic lens with minimal Fresnel losses. Computer Optics 2021; 45(3): 350-355. DOI: 10.18287/2412-6179-CO-813.

The development of the design method was funded by the Russian Science Foundation under project 18-19-00326, the investigation of the designed double aspheric lens was funded by the Russian Science Foundation under project 20-19-00081, and the implementation of the lens design software was funded by the Russian Federation Ministry of Science and Higher Education (State contract with the "Crystallography and Photonics" Research Center of the RAS).


  1. González-Acuña RG, Chaparro-Romo HA. General formula for bi-aspheric singlet lens design free of spherical aberration. Appl Opt 2018; 57(31): 9341-9345.
  2. González-Acuña RG, Avendaño-Alejo M, Gutiérrez-Vega JC. Singlet lens for generating aberration-free patterns on deformed surfaces. J Opt Soc Am A 2019; 36(5): 925-929.
  3. Mashaal H, Feuermann D, Gordon MJ. Aplanatic Fresnel optics. Opt Express 2017; 25(8): A274-A282.
  4. Mashaal H, Feuermann D, Gordon JM. Aplanatic lenses revisited: the full landscape. Appl Opt 2016; 55(10): 2537-2542.
  5. Silva-Lora A, Torres R. Superconical aplanatic ovoid singlet lenses. J Opt Soc Am A 2020; 37(7): 1155-1165.
  6. Mashaal H, Feuermann D, Gordon JM. New types of refractive-reflective aplanats for maximal flux concentration and collimation. Opt Express 2015; 23(24): A1541-A1548.
  7. Chassagne B, Canioni L. Analytical solution of a personalized intraocular lens design for the correction of spherical aberration and coma of a pseudophakic eye. Biomed Opt Express 2020; 11(2): 850-866.
  8. González-Acuña RG, Chaparro-Romo HA, Gutierrez-Vega JC. Exact equations for stigmatic singlet design meeting the Abbe sine condition. Opt Commun 2021; 479: 126415.
  9. Zeng L, Fang F. Advances and challenges of intraocular lens design [Invited]. Appl Opt 2018; 57(25): 7363-7376.
  10. Tabernero J, Qureshi MA, Robbie SJ, Artal P. An aspheric intraocular telescope for age-related macular degeneration patients. Biomed Opt Express 2015; 6(3): 1010-1020.
  11. Atchison DA. Spectacle lens design: a review. Appl Opt 1992; 31(19): 3579-3585.
  12. Gross H. Handbook of optical systems: Volume 1: Fundamentals of technical optics. Wiley Online Library; 2005: 207.
  13. Born M, Wolf E. Principles of optics. Electromagnetic theory of propagation, interference and diffraction of light. 7th ed. Cambridge: Cambridge University Press; 1999.
  14. Moiseev MA, Byzov EV, Kravchenko SV, Doskolovich LL. Design of LED refractive optics with predetermined balance of ray deflection angles between inner and outer surfaces. Opt Express 2015; 23(19): A1140-A1148. DOI: 10.1364/OE.23.0A1140.
  15. Kravchenko SV, Moiseev MA, Byzov EV, Doskolovich LL. Design of axisymmetric double-surface refractive optical elements generating required illuminance distributions. Opt Commun 2020; 459: 124976. DOI: 10.1016/j.optcom.2019.124976.
  16. Doskolovich LL, Bykov DA, Andreeva KV, Kazanskiy NL. Design of an axisymmetrical refractive optical element generating required illuminance distribution and wavefront. J Opt Soc Am A 2018; 35(11): 1949-1953. DOI: 10.1364/JOSAA.35.001949.
  17. Moiseev MA, Doskolovich LL. Design of TIR optics generating the prescribed irradiance distribution in the circle region. J Opt Soc Am A 2012; 29(9): 1758-1763. DOI: 10.1364/JOSAA.29.001758.
  18. Optical systems design software Zemax. Source: <https://www.zemax.com/>.
  19. Bobrov ST, Greisukh GI, Tyrkevich YG. Optics of diffractive elements and systems [In Russian]. Leningrad: “Mashinostroenie” Publisher; 1986.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: ko@smr.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20