Multifocal spectral diffractive lens
Doskolovich L.L., Bezus E.A., Kazanskiy N.L.

Image Processing Systems Institute оf RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Samara, Russia,
Samara National Research University, Samara, Russia


We present a method for calculating a spectral multifocal diffractive lens that forms a given set of fixed-position foci at multiple operating wavelengths. It is based on minimizing a function represented as a squared absolute value of difference between the complex amplitudes of beams formed by the relief of a spectral lens at the given wavelengths and the complex transmission functions of multifocal lenses calculated for these wavelengths. As an example, we calculated zone plates that form three fixed foci at three and four operating wavelengths. The results obtained may find application in the development and creation of new multifocal contact and intraocular lenses with reduced chromatic aberrations.

multifocal lens, diffractive lens, zone plate, diffractive optics.

Doskolovich LL, Bezus EA, Kazanskiy NL. Multifocal spectral diffractive lens. Computer Optics 2018; 42(2): 219-226. DOI: 10.18287/2412-6179-2018-42-2-219-226.


  1. Soifer VA, Kotlyar VV, Doskolovich LL. Iterative methods for diffractive optical elements computation. London, Bristol: Taylor & Francis; 1997. ISBN: 0-7484-0634-4.
  2. Golub MA, Doskolovich LL, Kazanskiy NL, Kharitonov SI, Soifer VA. Computer generated diffractive multi-focal lens. J Mod Opt 1992; 39(6): 1245-1251. DOI: 10.1080/713823549.
  3. Golub MA. Laser beam splitting by diffractive optics. Opt Photon News 2004; 15(2): 36-41. DOI: 10.1364/OPN.15.2.000036.
  4. Ravikumar S, Bradley A, Thibos LN. Chromatic aberration and polychromatic image quality with diffractive multifocal intraocular lenses. J Cataract Refract Surg 2014; 40(7): 1192-1204. DOI: 10.1016/j.jcrs.2013.11.035.
  5. Gatinel D, Pagnoulle C, Houbrechts Y, Gobin L. Design and qualification of a diffractive trifocal optical profile for intraocular lenses. J Cataract Refract Surg 2011; 37(11): 2060-2067. DOI: 10.1016/j.jcrs.2011.05.047.
  6. Akondi V, Dorronsoro C, Gambra E, Marcos S. Temporal multiplexing to simulate multifocal intraocular lenses: theoretical considerations. Biomed Opt Express 2017; 8(7): 3410-3425. DOI: 10.1364/BOE.8.003410.
  7. Lane SS, Morris M, Nordan L, Packer M, Tarantino N, Wallace 3rd RB. Multifocal intraocular lenses. Ophthalmol Clin N Am 2006; 19(1): 89-105. DOI: 10.1016/j.ohc.2005.09.002.
  8. Valle PJ, Oti JE, Canales VF, Cagigal MP. Visual axial PSF of diffractive trifocal lenses. Opt Express 2005; 13(7): 2782-2792. DOI: 10.1364/OPEX.13.002782.
  9. Osipov V, Doskolovich LL, Bezus EA, Drew T, Zhou K, Sawalha K, Swadener G, Wolffsohn JSW. Application of nanoimprinting technique for fabrication of trifocal diffractive lens with sine-like radial profile. J Biomed Opt 2015; 20(2): 025008. DOI: 10.1117/1.JBO.20.2.025008.
  10. Hinze U, El-Tamer A, Doskolovich LL, Bezus EA, Reiß S, Stolz H, Guthoff RF, Stachs O, Chichkov B. Additive manufacturing of a trifocal diffractive-refractive lens. Opt Commun 2016; 372: 235-240. DOI: 10.1016/j.optcom.2016.04.029.
  11. Kohnen T. First implantation of a diffractive quadrafocal (trifocal) intraocular lens. J Cataract Refract Surg 2015; 41(10): 2330-2332. DOI: 10.1016/j.jcrs.2015.11.012.
  12. Dammann H. Color separation gratings. Appl Opt 1978; 17(15): 2273-2279. DOI: 10.1364/AO.17.002273.
  13. Dong B-Z, Yang G-Z, Gu B-Y, Zhang G-Q. Diffractive phase elements that implement wavelength demultiplexing and spatial annular focusing simultaneously. JOSA A 1997; 14(1): 44-48. DOI: 10.1364/JOSAA.14.000044.
  14. Dong B-Z, Zhang G-Q, Yang G-Z, Gu B-Y, Zheng S-H, Li D-H, Chen Y-S, Cui X-M, Chen M-L, Liu H-D. Design and fabrication of a diffractive phase element for wavelength demultiplexing and spatial focusing simultaneously. Appl Opt 1996; 35(35): 6859-6864. DOI: 10.1364/AO.35.006859.
  15. Bengtsson J. Kinoforms designed to produce different fan-out patterns for two wavelengths. Appl Opt 1998; 37(11): 2011-2020. DOI: 10.1364/AO.37.002011.
  16. Doskolovich LL, Repetto PM. Design of DOEs for wavelength demultiplexing and spatial focusing. J Opt A: Pure Appl Opt 2000; 2: 488-493. DOI: 10.1088/1464-4258/2/5/323.
  17. Soifer VA, ed. Methods for computer design of diffractive optical elements. New York: Wiley; 2002. ISBN: 978-0-471-09533-0.
  18. Doskolovich LL, Kazanskiy NL, Khonina SN, Skidanov RV, Heikkilä N, Siitonen S, Turunen J. Design and investigation of color separation diffraction gratings. Appl Opt 2007; 46(15): 2825-2830. DOI: 10.1364/AO.46.002825.
  19. Sweeney DW, Sommargren GE. Harmonic diffractive lenses. Appl Opt 1995; 34(14): 2469-2475. DOI: 10.1364/AO.34.002469.
  20. Khonina SN, Volotovsky SG, Ustinov AV, Kharitonov SI. Analysis of focusing light by a harmonic diffractive lens taking into account the refractive index dispersion. Computer Optics 2017; 41(3): 338-347. DOI: 10.18287/2412-6179-2017-41-3-338-347.
  21. Greisukh GI, Ezhov EG, Stepanov SA, Bezus EA, Bykov DA. Suppression of the spectral selectivity of two-layer phase-relief diffraction structures. Opt Spectrosc 2009; 106(4): 621-626. DOI: 10.1134/S0030400X09040249.
  22. Gurenko VM, Kastorsky LB, Kiryanov VP, Kiryanov AV, Kokarev SA, Vedernikov VM, Verkhogliad AG. Laser writing system CLWS-300/C-M for microstructure synthesis on axisymmetric 3D surfaces. Proc SPIE 2002; 4900: 320-325. DOI: 10.1117/12.484573.

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