Abstract
Diffractive optical elements (DOEs) provide significant advantages over refractive optical elements due to their flexible design capabilities, leading to increasing usage in electro-optical systems. When the transmission function of diffractive lenses can be known analytically, determining the point spread function (PSF) becomes straightforward. However, in cases where analytical transmission equations cannot be derived, a general approach is necessary. In this study, we propose a new method that can be applied to any type of DOE to determine the numerical PSF. The simulation results are then compared to analytical and numerical methods. The findings of this research make significant contributions to the advancement of diffractive lenses by addressing the challenge of designing and analyzing these diffractive lenses. By offering a general approach for determining the PSF, the modulation transfer function (MTF) of the elements can also be determined by the proposed approach, even when the specific transmission function is difficult to ascertain. This study provides important contributions to the development of DOEs.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
Not applicable.
References
Aristizabal, S.L., Cirino, G.A., Montagnoli, A.N., Sobrinho, A.N., Rubert, J.B., Hospital, M., Mansano, R.D.: Microlens array fabricated by a low-cost grayscale lithography maskless system. Opt. Eng. 52(12), 125101–125101 (2013). https://doi.org/10.1117/1.OE.52.12.125101
Atwood, D.: Soft X-rays and Extreme Ultraviolet. Cambridge University Press, Cambridge, pp. 338–363 (2000)
Baek, S-.H., Ikoma, H, Jeon, D.S., Yuqi Li, Heidrich, W., Wetzstein, G, Kim, M.H.: Single-shot hyperspectral-depth imaging with learned diffractive optics, In Proceedings of the IEEE/CVF international conference on computer vision, pp. 2651-2660, (2021). https://doi.org/10.1109/ICCV48922.2021.00265
Banerji, S., Meem, M., Majumder, A., Guevara, F.V., Sensale-Rodriguez, B., Menon, R.: Ultra-thin Near Infrared camera enabled by a flat multi-level diffractive lens. Opt. Soc. Am. 5450–5452 (2019). https://doi.org/10.1364/OL.99.099999
Banerji, S., Meem, M., Majumder, A., Sensale-Rodriguez, B., Menon, R.: Imaging over an unlimited bandwidth with a single diffractive surface, arXiv.org > physics > arXiv:1907.06251, Submitted 2019.
Blahut, R.E.: Theory of Remote Image Formation. Cambridge University Press, Cambridge, pp. 115–121 (2004)
Britton, W.A., Chen, Y., Sgrignuoli, F., Negro, L.D.: Compact dual-band multi-focal diffractive lenses. Laser Photonics Rev. 15, 2000207–2000214 (2021). https://doi.org/10.1002/lpor.202000207
Buralli, D.A., Morris, G.M., Rogers, J.R.: Optical performance of holographic kinoforms. Appl. Opt. 28(5), 976–983 (1989). https://doi.org/10.1364/Ao.28.000976
Cao, A., Pang, H., Zhang, M., Shi, L., Deng, Q., Song, Hu.: Design and fabrication of an artificial compound eye for multi-spectral imaging. MDPI Micromachines 10, 208–217 (2019). https://doi.org/10.3390/mi10030208
Cheng, Y., Zhu, J., Song, Hu., Zhao, L., Wei Yan, Yu., He, W.J., Liu, J.: Focusing properties of single-focus photon sieve. IEEE Photonics Technol. Lett. 29, 275–278 (2017). https://doi.org/10.1109/LPT.2016.2636334
Cheng, Y., Cao, J., Zhang, Y., Hao, Q.: Review of state-of-the-art artificial compound eye imaging systems. Bioinspir. Biomim. 14(3), 031002–031044 (2019). https://doi.org/10.1088/1748-3190/aaffb5
Cheng X, Xie W, Bai Y, Jia X, Xing T.: Athermal design for infrared refractive, diffractive, reflective hybrid optical system, Proc. SPIE 9280, In: 7th International symposium on advanced optical manufacturing and testing technologies: large mirrors and telescopes, vol. 928018, pp. 292–298, (2014); https://doi.org/10.1117/12.2068585
Chung, H.-H., Bradman, N.M., Davidson, M.R.: Dual wavelength photon sieves. Opt. Eng. 47(11), 118001–118001 (2008). https://doi.org/10.1117/1.3029672
Dun, X., Wang, Z., Peng, Y.: Joint-designed achromatic diffractive optics for full-spectrum computational imaging. Optoelectron. Imag.multimed. Technol. VI 111870I, 112–119 (2019). https://doi.org/10.1117/12.2536617
Dun, X., Ikoma, H., Wetzstein, G., Wang, Z., Cheng, X., Peng, Y.: Learned rotationally symmetric diffractive achromat for full-spectrum computational imaging. Optica 7, 913–922 (2020). https://doi.org/10.1364/OPTICA.394413
Faklis, D., Michael Morris, G.: Spectral properties of multiorder diffractive lenses. Appl. Opt. 34, 2462–2468 (1995). https://doi.org/10.1364/AO.34.002462
Fan, Y., Ooi, B.-L., Hristov, H.D., Leong, M.-S.: Compound diffractive lens consisting of fresnel zone plate and frequency selective screen. IEEE Trans. Antennas Propag. 58(6), 1842–1847 (2010). https://doi.org/10.1109/TAP.2010.2046849
Ghebjagh, S.G., Fischer, D., Sinzinger, S.: Multifocal multi-value phase zone plate for 3D focusing. Appl. Opt. 58(32), 8943 (2019). https://doi.org/10.1364/AO.58.008943
Goodman, J.W.: Introduction to Fourier Optics, 2nd edn. New York, McGraw-Hill Series, pp. 66–73 (2005)
Greĭsukh, G.I., Ezhov, E.G., Stepanov, S.A.: Taking diffractive efficiency into account in the design of refractive/diffractive optical systems. J. Opt. Technol. 83, 163–167 (2016)
Grulois, T., Druart, G., Guérineau, N., Crastes, A., Sauer, H., Chavel, P.: Extra-thin infrared camera for low-cost surveillance applications. Opt. Lett. 39, 3169–3172 (2014). https://doi.org/10.1364/OL.39.003169
Hallada, F.D., Franz, A.L., Hawks, M.R.: Fresnel zone plate light field spectral imaging simulation. Algorithms Technol. Multispectral, Hyperspectral, and Ultraspectral Imag. 1019804, 29–43 (2017). https://doi.org/10.1117/12.2261846
Hazra, L., Delisle, C.A.: Higher order kinoform lenses: diffraction efficiency and aberrational properties. Opt. Eng. 36(5), 1500–1507 (1997). https://doi.org/10.1117/1.601375
He, K., Xiaolei Wang, Z.W., Wang, H.Y., Scherer, N.F., Katsaggelos, A.K., Cossaırt, O.: Snapshot multifocal light field microscopy. Opt. Express 28, 12108–12120 (2020). https://doi.org/10.1364/OE.390719
He, C., Huang, P., Dong, X., Fan, B.: Optical design of compact unobscured ground-based diffractive telescope. Optik 205, 163696–163705 (2020). https://doi.org/10.1016/j.ijleo.2019.163696
Hinnrichs, M., Hinnrichs, B., McCutchen, E.: Infrared hyperspectral imaging miniaturized for UAV applications. Infrared Technol. Appli. XLIII 10177, 107–117 (2017). https://doi.org/10.1117/122262125
Howells, M., Jacobsen, C., Warwick, T., Van den Bos, A.: Principles and applications of zone plate x-ray microscopes. In: Hawkes, P.W., Spence, J.C.H. (eds.) Science of Microscopy. Springer, New York, NY (2007). https://doi.org/10.1007/978-0-387-49762-4_13
Jason, D.: Schmidt, Numerical Simulation of Optical Wave Propagation With Examples in MATLAB. SPIE Press, Washington, pp. 87–113 (2010)
Jeon, D.S., Baek, S.-H., Yi, S., Fu, Q., Dun, X., Heidrich, W., Kim, M.H.: Compact snapshot hyperspectral imaging with diffracted rotation. ACM Transactions on Graphics 38(4), 1–13 (2019). https://doi.org/10.1145/3306346.3322946
Jiang, W., SongHu, YuHec, YunBu: An Artificial Compound Eye of Photon Sieves. Elsevier, Netherlands (2015)
Julıan, M.N., Macdonnell, D.G., Gupta, M.C.: High-efficiency flexible multilevel photon sieves by single-step laser-based fabrication and optical analysis. Appl. Opt. 58(1), 109–114 (2019)
Ke, J., Zhang, J.: Focusing properties of phase-only generalized fibonacci photon sieves. Opt. Commun. 368, 34–38 (2016). https://doi.org/10.1016/j.optcom.2016.01.075
Khatri, N., Sonam Berwal, K., Manjunath, B.S., Mishra, V., Goel, S.: Research on development of aspheric diffractive optical element for mid-infrared imaging. Infrared Phys. Technol. 129, 104582–104594 (2023). https://doi.org/10.1016/j.infrared.2023.104582
Kim, J., Kim, H., Lee, G.-Y., Kim, J., Lee, B., Jeong, Y.I.D.: Numerical and experimental study on multi-focal metallic fresnel zone plates designed by the phase selection rule via virtual point sources. Appl. Sci. 8, 449–459 (2018). https://doi.org/10.3390/app8030449
Li, Y., Wang, C., Zhao, X., Feng, Xu., Wang, C.: Multispectral and large bandwidth achromatic imaging with a single diffractive photon sieve. Opt. Express 26(16), 21141–21152 (2018). https://doi.org/10.1364/OE.26.021141
Li, L., Kuang, F.-L., Wang, J.-H., Zhou, Y., Wang, Q.-H.: Zoom liquid lens employing a multifocal fresnel zone plate. Opt. Express 415483, 2135–2141 (2021). https://doi.org/10.1364/OE.415483
Meem, M., Majumder, A., Rajesh, M.: Free-form broadband flat lenses for visible imaging. OSA Continuum 4(2), 491–497 (2021). https://doi.org/10.1364/OSAC.418378
Monjurul Meem, Sourangsu Banerji, Apratim Majumder, Juan C. Garcia, Philip W. C. Hon, Berardi Sensale-Rodriguez and Rajesh Menon.: Imaging from the visible to the longwave infrared wavelengths via an inverse-designed flat lens”, arXiv.org > physics > arXiv:2001.03684, 2020.
Meema, M., Banerjia, S., Majumdera, A., Guevara Vasquezb, F., Sensale-Rodrigueza, B., Menona, R.: Broadband lightweight flat lenses for long-wave infrared imaging. 21376 PNAS 116(43), 21375–21378 (2019). https://doi.org/10.1073/pnas.1908447116
Mills, J.P.: Conformal optics: theory and practice. In: Novel Optical Systems Design and Optimization IV, vol.4442, pp. 101–107, (2001); https://doi.org/10.1117/12.449962
Moghimi, M., Fernandes, J., Kanhere, A., et al.: Micro-fresnel-zone-plate array on flexible substrate for large field-of-view and focus scanning. Sci. Rep. 5, 15861–15871 (2015). https://doi.org/10.1038/srep15861
Mohammad, N., Meem, M., Shen, B., Wang, P., Rajesh, M.: Broadband imaging with one planar diffractive lens. Sci. Rep. 8, 2799–2804 (2018). https://doi.org/10.1038/s41598-018-21169-4
Monsoriu, J.A., Calatayud, A., Remon, L., Furlan, W.D., Saavedra, G., Andres, P.: Bifocal fibonacci diffractive lenses. IEEE 5(3), 3400106–3400106 (2013). https://doi.org/10.1109/JPHOT.2013.2248707
Moreno, V., Román, J.F., Salgueiro, J.R.: High efficiency diffractive lenses: Deduction of kinoform profile. Am. J. Phys. 65(6), 556–562 (1997). https://doi.org/10.1119/1.18587
Muzychenko, Y.B., Zinchik,A.A., Stafeev,S.C., Tomilin,M. G.: Fractal diffraction elements with variable transmittance and phase shift, In: 22nd Congress of the international commission for optics: light for the development of the world, 80112F (2011). https://doi.org/10.1117/12.903551
Nemes-Czopf, A., Bercsényi, D., Erdei, G.: Simulation of relief type diffractive lenses in ZEMAX using parametric modelling and scalar diffraction. Appl. Opt. 58(32), 8931–8942 (2019)
Niu, H.-J., Zhang, J., Yan, A.-q, Leng, H.-B., Fei, J.-q, Deng-shan, Wu., Cao, J.-Z.: Optical system design for wide-angle airborne mapping camera with diffractive optical element, (icPOE 2014), 94492N. Int. Conf. Photonics Opt. Eng. 9449, 703–708 (2015). https://doi.org/10.1117/12.2085042
O’Shea, D.C., Suleski, T.J., Kathman, A.D., Prather, D.W.: Diffractive Optics Design, Fabrication, and Test. The Society of Photo-Optical Instrumentation Engineers, Bellingham (2004). https://doi.org/10.1117/3.527861
Peng, Y., Qiang, Fu., Amata, H., Shuochen, Su., Heide, F., Heidrich, W.: Computational imaging using lightweight diffractive-refractive optics. Opt. Express 23(24), 31393–31407 (2015). https://doi.org/10.1364/Oe.23.031393|
Peng, Y., Fu, Q., Heide, F., Heidrich, W.: The diffractive achromat: full spectrum computational imaging with diffractive optics. ACM Trans. Graph. 35(4), 1–31 (2016). https://doi.org/10.1145/2897824.2925941
Sabatyan, A., Ebrahimi, H.: Modified photon sieve as a high-performance bifocal and trifocal diffractive optical element. J. Opt. Soc. Am. 35(10), 1692–1700 (2018)
Shannon, R.R.: Overview of conformal optics, Proc. SPIE 3705, Window and Dome Technologies and Materials VI, vol. 3705, pp. 180–188, (1999); https://doi.org/10.1117/12.354622
Sun, W., Yongxiang, Hu., Macdonnell, D.G., Kim, H.J., Weimer, C., Baize, R.R.: Fully transparent photon sieve. Opt. Express 25, 17356–17363 (2017). https://doi.org/10.1364/OE.25.017356
Swanson, G.J.: binary optics technology: theoretical limts on the diffraction efficiency of multilevel diffractive optical elements. Lincoln Lab. Mass. Inst. Techlnol. Tech. Rep. 914, 1–27 (1991)
Tehrani, M.K., Fard, S.S.M.: Design of diffraction limited head mounted display optical system based on high efficiency diffractive elements. Curr. Opt. Photon. 1, 150–156 (2017)
Torcal-Milla, F.J., Sanchez-Brea, L.M.: Single-focus binary Fresnel zone plate. Opt. Laser Technol. 97, 316–320 (2017). https://doi.org/10.1016/j.optlastec.2017.07.008. (ISSN 0030-3992)
Ünal, A.: Semi-active laser seeker design with combined diffractive optical element (CDOE). J. Opt. 52, 956–968 (2022). https://doi.org/10.1007/s12596-022-00954-5
Ünal, A.: Laser seeker design with multi-focal diffractive lens. Eng. Res. Express 5, 045014–045028 (2023a). https://doi.org/10.1088/2631-8695/ad0024
Ünal, A.: Frequency selective diffractive optical element (FSDOE), In: Window and Dome Technologies and Materials, vol. 125180C, pp 84–97 (2023)
Ünal, A.: Dual mode, imaging infrared and semi-active laser, seeker design with squinted combined diffractive optical element. J Opt , pp. 1–22, (2024). https://doi.org/10.1007/s12596-024-01657-9
Wang, Qi., Zhang, D.-W., Chen, J.-B., Zhuang, S.-L.: Liquid crystal variable focus lens based on Fresnel zone plate. Photonics Optoelectron. Meet. (POEM) 2008: Optoelectron Devices and Integr. 72791, 502–508 (2009). https://doi.org/10.1117/12.823827
Wang, P., Mohammad, N., Menon, R.: Chromatic-aberration-corrected diffractive lenses for ultra-broadband focusing. Sci. Rep. 6, 21545–21551 (2016). https://doi.org/10.1038/srep21545
Wood, A., Babington, J.: Diffractive Lens Design, Theory, Design, Methodologies And Applications. IOP Publishing Ltd, Bristol (2023)
Xia, T., Cheng, S., Tao, S.: Four equal-intensity foci generated by a Cantor–Thue–Morse zone plate. Laser Phys. 29, 085003–085011 (2019). https://doi.org/10.1088/1555-6611/ab27b7
Yang, Hu., Cui, Q., Zhao, L., Piao, M.: PSF model for diffractive optical elements with improved imaging performance in dual-waveband infrared systems. Opt. Express 26(21), 26845–26857 (2018). https://doi.org/10.1364/OE.26.026845
Yao-JuZhang, C.-W., Xiao, H.-C.: Improving the resolution of a solid immersion lens optical system using a multiphase fresnel zone plate. Opt. Laser Technol. 37, 444–448 (2005). https://doi.org/10.1016/j.optlastec.2004.07.011
Zhang, Y., Chen, J., Yea, X.: Multilevel phase Fresnel zone plate lens as a near-field optical element. Opt. Commun. 269, 271–273 (2007). https://doi.org/10.1016/j.optcom.2006.08.006
Zhang, W., Zuo, B., Chen, S., Xiao, H., Fan, Z.: Design of fixed correctors used in conformal optical system based on diffractive optical elements. Appl. Opt. 52, 461–466 (2013). https://doi.org/10.1364/AO.52.000461
Zhang, Z., Guo, C., Wang, R., Haixiang, Hu., Zhou, X., Liu, T., Xue, D., Zhang, X., Zhang, F., Zhang, X.: Hybrid-level fresnel zone plate for diffraction efficiency enhancement. Opt. Express 25, 33676–33687 (2017). https://doi.org/10.1364/OE.25.033676
Zhang, S., Zhou, L., Xue, C., Wang, L.: Design and simulation of a superposition compound eye system based on hybrid diffractive-refractive lenses. Appl. Opt. 56, 7442–7449 (2017). https://doi.org/10.1364/AO.56.007442
Zhao, X.N., Xu, F., Hu, J.P., Wang, C.H.: Broadband photon sieves imaging with wavefront coding. Opt. Exp. 23(13), 16812–16822 (2015). https://doi.org/10.1364/OE.23.016812
Zhao, X., Jingpei, Hu., Lin, Yu., Feng, Xu., Zhu, X., Donglin, Pu., Chen, L., Wang, C.: Ultra-broadband achromatic imaging with diffractive photon sieves. Sci. Rep. 6, 28319–28428 (2016). https://doi.org/10.1038/srep28319
Zhao, X., Jingpei, Hu., Feng, Xu., Zhu, A., Wang, C.: Wide field-of-view imaging with wavefront coded diffractive photon sieves. IEEE Photonics J. 8, 1–8 (2016). https://doi.org/10.1109/JPHOT.2016.2620808
Zhao, H., Liu, Y., Xiaojie, Yu., Jing, Xu., Wang, Y., Zhang, L., Zhong, X., Xue, F., Sun, Q.: Diffractive optical imaging spectrometer with reference channel. Opt. Spectrosc. Imag. Biomed. Opt. 11566, 170–175 (2020). https://doi.org/10.1117/12.2580407
Zhou, C., Dong, X., Shi, L., Wang, C., Chunlei, Du.: Experimental study of a multiwavelength photon sieve designed by random-area-divided approach. Appl. Opt. 48(8), 1649–1623 (2009). https://doi.org/10.1364/AO.48.001619
Funding
No funding was received to assist with the preparation of this manuscript.
Author information
Authors and Affiliations
Contributions
Not applicable.
Corresponding author
Ethics declarations
Conflict of interest
The author has no competing interests to declare that are relevant to the content of this article.
Ethical approval
Not applicable.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Ünal, A. Analytical and numerical fresnel models of phase diffractive optical elements for imaging applications. Opt Quant Electron 56, 960 (2024). https://doi.org/10.1007/s11082-024-06906-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-024-06906-6