(50-3) 04 * << * >> * Russian * English * Content * All Issues

Harmonic DOE design for generating required intensity distributions
L.L. Doskolovich1,2, E.V. Byzov1,2, N.V. Golovastikov1,2, E.A. Bezus1,2, D.A. Bykov1,2, R.V. Skidanov1,2

1 Image Processing Systems Institute, NRC "Kurchatov Institute", Molodogvardeyskaya Str. 151, Samara, 443001, Russia;
2 Samara National Research University, Moskovskoye Shosse 34, Samara, 443086, Russia

  Full text (PDF)

DOI: 10.18287/COJ1757

Article ID: 1757

Language: Russian

Abstract:
A method for designing diffractive optical elements with a smooth phase function is proposed. The method generalizes harmonic diffractive lenses and is intended for generating a specified intensity distribution at multiple harmonic wavelengths. Within this method, the phase function is defined as an expansion in a system of smooth and differentiable functions. The expansion coefficients are treated as optimization parameters and are computed using a gradient-based method to minimize an error function representing the discrepancy between the generated and target intensity distributions. Examples of element designs with a phase function represented as a sum of B-splines are presented. It is shown that for the effective performance of said elements, the error function must explicitly account for the generated intensity distributions not only at the central wavelength but also at other harmonic wavelengths.

Keywords:
diffractive optical element, scalar diffraction theory, phase function, inverse problem, target intensity distribution, gradient method.

Acknowledgements:
This work was funded by the Russian Science Foundation under project No. 24-19-00080 (Development of the gradient-based method for designing harmonic DOEs, design of DOEs, and performance characterization); the NRC "Kurchatov Institute" government project (Development of software for simulating DOE operation using the scalar diffraction theory); and the Ministry of Science and Higher Education of the Russian Federation under Samara University's government project FSSS-2024-0016 (Analysis of the DOE performance under deviations of the incident radiation wavelength from the design value.

Citation:
Doskolovich LL, Byzov EV, Golovastikov NV, Bezus EA, Bykov DA, Skidanov RV. Harmonic DOE design for generating required intensity distributions. Computer Optics 2026; 50(3): 1757. doi: 10.18287/COJ1757.

References:

  1. Zhang J, Pégard N, Zhong J, Adesnik H, Waller L. 3D computer-generated holography by non-convex optimization. Optica 2017; 4(10): 1306-1313. doi:10.1364/OPTICA.4.001306.
  2. Wang H, Piestun R. Dynamic 2D implementation of 3D diffractive optics. Optica 2018; 5(10): 1220-1228. doi:10.1364/OPTICA.5.001220.
  3. Schmidt S, Thiele S, Toulouse A, Bösel C, Tiess T, Herkommer A, Gross H, Giessen H. Tailored micro-optical freeform holograms for integrated complex beam shaping. Optica 2020; 7(10): 1279-1286. doi:10.1364/OPTICA.395177.
  4. Zhang Q, He Z, Xie Z, Tan Q, Sheng Y, Jin G, Cao L, Yuan X. Diffractive optical elements 75 years on: from micro-optics to metasurfaces. Photonics Insights 2023; 2(4): R09. doi:10.3788/PI.2023.R09.
  5. Gerchberg RW, Saxton WO. A practical algorithm for the determination of phase from image and diffraction plane pictures. Optik 1972; 35: 237-246.
  6. Fienup JR. Phase retrieval algorithms: a comparison. Appl Opt 1982; 21(15): 2758-2769. doi:10.1364/AO.21.002758.
  7. Kotlyar VV, Khonina SN, Soifer VA. Iterative calculation of diffractive optical elements focusing into a three dimensional domain and the surface of the body of rotation. J Mod Opt 1996; 43(7): 1509-1524.
  8. Soifer VA, Kotlyar VV, Doskolovich LL. Iterative methods for diffractive optical elements computation. Taylor & Francis; 1997. ISBN: 978-0-7484-0634-4.
  9. Latychevskaia T. Iterative phase retrieval in coherent diffractive imaging: practical issues. Appl Opt 2018; 57(22): 7187-7197. doi:10.1364/AO.57.007187.
  10. Ripoll O, Kettunen V, Herzig HP. Review of iterative Fourier transform algorithms for beam shaping applications. Opt Eng 2004; 43(11): 2549-2556. doi:10.1117/1.1804543.
  11. Doskolovich LL, Mingazov AA, Byzov EV, Skidanov RV, Ganchevskaya SV, Bykov DA, Bezus EA, Podlipnov VV, Porfirev AP, Kazanskiy NL. Hybrid design of diffractive optical elements for optical beam shaping. Opt Express 2021; 29(20): 31875-31890. doi:10.1364/OE.439641.
  12. Motz GA, Soshnikov DV, Doskolovich LL, Byzov EV, Bezus EA, Bykov DA. Design of cascaded diffractive optical elements generating different intensity distributions at several operating wavelengths. Optik 2025; 320: 172140. doi:10.1016/j.ijleo.2024.172140.
  13. Sweeney DW, Sommargren GE. Harmonic diffractive lenses. Appl Opt 1995; 34(14): 2469-2475. doi:10.1364/AO.34.002469.
  14. Rossi M, Kunz RE, Herzig HP. Refractive and diffractive properties of planar micro-optical elements. Appl Opt 1995; 34(26): 5996-6007. doi:10.1364/AO.34.005996.
  15. Sales TRM, Morris GM. Diffractive-refractive behavior of kinoform lenses. Appl Opt 1997; 36(1): 253-257. doi:10.1364/AO.36.000253.
  16. Faklis D, Morris GM. Spectral properties of multiorder diffractive lenses. Appl Opt 1995; 34(14): 2462-2468. doi:10.1364/AO.34.002462.
  17. Doskolovich LL, Skidanov RV, Bezus EA, Ganchevskaya SV, Bykov DA, Kazanskiy NL. Design of diffractive lenses operating at several wavelengths. Opt Express 2020; 28(8): 11705-11720. doi:10.1364/OE.389458.
  18. Kharitonov SI, Volotovsky SG, Khonina SN. Geometric-optical calculation of the focal spot of a harmonic diffractive lens. Computer Optics 2016; 40(3): 331-337. doi:10.18287/2412-6179-2016-40-3-331-337.
  19. Khonina SN, Volotovsky SG, Ustinov AV, Kharitonov SI. Analysis of focusing light by a harmonic diffractive lens with regard for the refractive index dispersion. Computer Optics 2017; 41(3): 338-347. doi:10.18287/2412-6179-2017-41-3-338-347.
  20. Skinner GK. Design of achromatic diffractive lenses. Opt Express 2024; 32(1): 230-247. doi:10.1364/OE.509946.
  21. Kingma DP, Ba J. Adam: A method for stochastic optimization. arXiv preprint 2014; arXiv:1412.6980.
  22. 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.
  23. Piegl L, Tiller W. The NURBS book. Berlin: Springer; 1996. ISBN: 3-540-61545-8.
  24. Cubillos M, Jimenez E. Numerical simulation of optical propagation using sinc approximation. J Opt Soc Am A 2022; 39(8): 1403-1413. doi:10.1364/JOSAA.461355.

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