Mathematical Tool for Calculating the Microstructure of a Harmonic Kinoform Lens

  • A. I. Antonov
  • G. I. GreisukhEmail author
  • E. G. Ezhov
  • E. A. Ryzhova
Optical Information Technologies


The paper presents a mathematical tool based on the requirement of tautochronism in each of the diffraction orders of a harmonic kinoform lens, which was used as the basis to develop a method for calculating the lens microstructure. The method provides a limitation of the relative longitudinal chromatism of the lens to a given level. In addition, it allows obtaining the initial parameters necessary for the ray calculation and optimization of an optical system with a harmonic kinoform lens using well-known commercial optical design computer programs.


harmonic kinoform lens harmonic Fresnel zone sawtooth relief-phase microstructure tautochronism longitudinal chromatism 


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  1. 1.
    D. W. Sweeney, “Harmonic Diffractive Lenses,” Appl. Opt. 34 (14), 2469–2475 (1995).ADSCrossRefGoogle Scholar
  2. 2.
    S. I. Kharitonov, “Geometric-Optical Calculation of the Focal Spot of a Harmonic Diffraction Lens,” Komp. Opt. 40 (3), 331–337 (2016).CrossRefGoogle Scholar
  3. 3.
    S. N. Khonina, “Analysis of the Focusing by a Harmonic Diffraction Lens Taking into Account the Dispersion of the Refractive Index,” Komp. Opt. 41 (3), 338–347 (2017).CrossRefGoogle Scholar
  4. 4.
    G. G. Slusarev, “Optical Systems with Phase Layers,” DAN SSSR 113 (4), 780–782 (1957).Google Scholar
  5. 5.
    A. I. Antonov, “Diffractive Elements for Imaging Optical Systems,” Autometrya 53 (5), 4–16 (2017) [Optoelecton., Instrum. Data Process. 53 (5), 421–430 (2017)].Google Scholar
  6. 6.
    G. I. Greysukh, “Harmonic Kinoform Lens: Diffraction Efficiency and Chromatism,” Opt. Spektr. 125 (2), 223–228 (2018).ADSGoogle Scholar
  7. 7.
    M. G. Moharam, “Diffraction Analysis of Dielectric Surface-Relief Gratings,” JOSA 72 (10), 1385–1392 (1982).ADSCrossRefGoogle Scholar
  8. 8.
    N. M. Lyndin, “Modal and C Methods Grating Design and Analysis Software,” Scholar
  9. 9.
    M. Kovatchev, “Aberration Characteristics of Optical Elements,” Proc. SPIE. 1183, 643–652 (1989).ADSCrossRefGoogle Scholar
  10. 10.
    J. M. Geary, Introduction to Lens Design: With Practical ZEMAX Examples (Willmann-Bell, Inc., Richmond, 2002).Google Scholar

Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  • A. I. Antonov
    • 1
  • G. I. Greisukh
    • 1
    Email author
  • E. G. Ezhov
    • 1
  • E. A. Ryzhova
    • 1
  1. 1.Penza State University of Architecture and ConstructionPenzaRussia

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