Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-13T01:16:23.930Z Has data issue: false hasContentIssue false
  • English
  • Français

Automatic Alignment of an Orbital Angular Momentum Sorter in a Transmission Electron Microscope Using a Convolutional Neural Network

Published online by Cambridge University Press:  09 September 2022

Paolo Rosi Open the ORCID record for Paolo Rosi [Opens in a new window] ,
Alexander Clausen Open the ORCID record for Alexander Clausen [Opens in a new window] ,
Dieter Weber Open the ORCID record for Dieter Weber [Opens in a new window] ,
Amir H. Tavabi ,
Stefano Frabboni ,
Peter Tiemeijer ,
Rafal E. Dunin-Borkowski ,
Enzo Rotunno Open the ORCID record for Enzo Rotunno [Opens in a new window]  and
Vincenzo Grillo
Paolo Rosi
Affiliation:
Istituto Nanoscienze - CNR, via G. Campi 213/A, Modena 41125, Italy FIM Department, University of Modena and Reggio Emilia, via G. Campi 213/A, Modena 41125, Italy
Alexander Clausen
Affiliation:
Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich, Jülich 52425, Germany
Dieter Weber
Affiliation:
Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich, Jülich 52425, Germany
Amir H. Tavabi
Affiliation:
Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich, Jülich 52425, Germany
Stefano Frabboni
Affiliation:
Istituto Nanoscienze - CNR, via G. Campi 213/A, Modena 41125, Italy FIM Department, University of Modena and Reggio Emilia, via G. Campi 213/A, Modena 41125, Italy
Peter Tiemeijer
Affiliation:
Thermo Fisher Scientific, PO Box 80066, 5600 KA Eindhoven, The Netherlands
Rafal E. Dunin-Borkowski
Affiliation:
Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich, Jülich 52425, Germany
Enzo Rotunno*
Affiliation:
Istituto Nanoscienze - CNR, via G. Campi 213/A, Modena 41125, Italy
Vincenzo Grillo
Affiliation:
Istituto Nanoscienze - CNR, via G. Campi 213/A, Modena 41125, Italy
*
*Corresponding author: Enzo Rotunno, E-mail: enzo.rotunno@nano.cnr.it
Get access

Abstract

We report on the automatic alignment of a transmission electron microscope equipped with an orbital angular momentum sorter using a convolutional neural network. The neural network is able to control all relevant parameters of both the electron-optical setup of the microscope and the external voltage source of the sorter without input from the user. It can compensate for mechanical and optical misalignments of the sorter, in order to optimize its spectral resolution. The alignment is completed over a few frames and can be kept stable by making use of the fast fitting time of the neural network.

Keywords

artificial intelligenceelectron beam shapingelectron vortex beamorbital angular momentum sortertransmission electron microscope
Type
Original Article
Information
Microscopy and Microanalysis , First View , pp. 1 - 9
Check for updates
Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of the Microscopy Society of America

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abadi, M, Agarwal, A, Barham, P, Brevdo, E, Chen, Z, Citro, C, Corrado, GS, Davis, A, Dean, J, Devin, M, Ghemawat, S, Goodfellow, I, Harp, A, Irving, G, Isard, M, Jia, Y, Jozefowicz, R, Kaiser, L, Kudlur, M, Levenberg, J, Mane, D, Monga, R, Moore, S, Murray, D, Olah, C, Schuster, M, Shlens, J, Steiner, B, Sutskever, I, Talwar, K, Tucker, P, Vanhoucke, V, Vasudevan, V, Viegas, F, Vinyals, O, Warden, P, Wattenberg, M, Wicke, M, Yu, Y & Zheng, X (2016). TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems. Available at http://arxiv.org/abs/1603.04467Google Scholar
Béché, A, Juchtmans, R & Verbeeck, J (2017). Efficient creation of electron vortex beams for high resolution STEM imaging. Ultramicroscopy 178, 12–19.CrossRefGoogle ScholarPubMed
Béché, A, Van Boxem, R, Van Tendeloo, G & Verbeeck, J (2014). Magnetic monopole field exposed by electrons. Nat Phys 10, 26–29.CrossRefGoogle Scholar
Berkhout, GCG, Lavery, MPJ, Courtial, J, Beijersbergen, MW & Padgett, MJ (2010). Efficient sorting of orbital angular momentum states of light. Phys Rev Lett 105, 153601.CrossRefGoogle Scholar
Bhusal, N, Lohani, S, You, C, Hong, M, Fabre, J, Zhao, P, Knutson, EM, Glasser, RT & Magaña-Loaiza, OS (2021). Spatial mode correction of single photons using machine learning. Adv Quantum Technol 4, 2000103.CrossRefGoogle Scholar
Bliokh, KYY, Ivanov, IPP, Guzzinati, G, Clark, L, Van Boxem, R, Béché, A, Juchtmans, R, Alonso, MAA, Schattschneider, P, Nori, F & Verbeeck, J (2017). Theory and applications of free-electron vortex states. Phys Rep 690, 1–70.CrossRefGoogle Scholar
Boothroyd, C, Kovács, A & Tillmann, K (2016). FEI titan G2 60-300 HOLO. J Large-Scale Res Facil JLSRF 2, A44.CrossRefGoogle Scholar
Chaize, J, Goetz, A, Klotz, W, Meyer, J, Perez, M, Taurel, E & Verdier, P (2001). The ESRF TANGO control system status. Available at https://www.tango-controls.org/Google Scholar
Clark, L, Béché, A, Guzzinati, G & Verbeeck, J (2014). Quantitative measurement of orbital angular momentum in electron microscopy. Phys Rev A 89, 053818.CrossRefGoogle Scholar
Clark, L, Guzzinati, G, Béché, A, Lubk, A & Verbeeck, J (2016). Symmetry-constrained electron vortex propagation. Phys Rev A 93, 063840.CrossRefGoogle Scholar
Clausen, A, Weber, D, Strauch, A, Müller-Caspary, K & Dunin-Borkowski, RE (2021). LiberTEM/LiberTEM-live: 0.1.0. Available at https://zenodo.org/record/4916316Google Scholar
Coles, MM, Williams, MD, Saadi, K, Bradshaw, DS & Andrews, DL (2013). Chiral nanoemitter array: A launchpad for optical vortices. Laser Photonics Rev 7, 1088–1092.CrossRefGoogle Scholar
Decker, AJ (1993). Neural-Network-Directed Alignment of Optical Systems Using the Laser-Beam Spatial Filter as an Example. NASA.Google Scholar
Dellby, N, Krivanek, OL, Nellist, PD, Batson, PE & Lupini, AR (2001). Progress in aberration-corrected scanning transmission electron microscopy. Microscopy 50, 177–185.CrossRefGoogle ScholarPubMed
Dwyer, C, Erni, R & Etheridge, J (2010). Measurement of effective source distribution and its importance for quantitative interpretation of STEM images. Ultramicroscopy 110, 952–957.CrossRefGoogle Scholar
Grillo, V & Carlino, E (2006). A novel method for focus assessment in atomic resolution STEM HAADF experiments. Ultramicroscopy 106, 603–613.CrossRefGoogle Scholar
Grillo, V, Karimi, E, Balboni, R, Gazzadi, GC, Venturi, F, Frabboni, S, Pierce, JS, McMorran, BJ & Boyd, RW (2015). Electron holograms encoding amplitude and phase for the generation of arbitrary wavefunctions. Microsc Microanal 21, 503–504.CrossRefGoogle Scholar
Grillo, V, Karimi, E, Gazzadi, GC, Frabboni, S, Dennis, MR & Boyd, RW (2014). Generation of nondiffracting electron bessel beams. Phys Rev X 4, 011013.Google Scholar
Gulli, A & Pal, S (2017). Deep Learning with Keras. Packt Publishing Ltd.Google Scholar
Guzzinati, G, Clark, L, Béché, A & Verbeeck, J (2014). Measuring the orbital angular momentum of electron beams. Phys Rev A 89, 025803.CrossRefGoogle Scholar
Haider, M, Müller, H, Uhlemann, S, Zach, J, Loebau, U & Hoeschen, R (2008). Prerequisites for a Cc/Cs-corrected ultrahigh-resolution TEM. Ultramicroscopy 108, 167–178.CrossRefGoogle ScholarPubMed
Haider, M, Rose, H, Uhlemann, S, Kabius, B & Urban, K (1998 a). Towards 0.1 nm resolution with the first spherically corrected transmission electron microscope. J Electron Microsc 47, 395–405.CrossRefGoogle Scholar
Haider, M, Uhlemann, S, Schwan, E, Rose, H, Kabius, B & Urban, K (1998 b). Electron microscopy image enhanced. Nature 392, 768–769.CrossRefGoogle Scholar
Harris, J, Grillo, V, Mafakheri, E, Gazzadi, GC, Frabboni, S, Boyd, RW & Karimi, E (2015). Structured quantum waves. Nat Phys 11, 629–634.CrossRefGoogle Scholar
Harvey, TR, Grillo, V & McMorran, BJ (2017). Stern-Gerlach-like approach to electron orbital angular momentum measurement. Phys Rev A 95, 021801.CrossRefGoogle Scholar
Herbert, T & de Bruijn, W (n.d.). Network scaling. Available at https://www.kernel.org/doc/Documentation/networking/scaling.txtGoogle Scholar
Jin, Y, Zhang, Y, Hu, L, Huang, H, Xu, Q, Zhu, X, Huang, L, Zheng, Y, Shen, H-L, Gong, W & Si, K (2018). Machine learning guided rapid focusing with sensor-less aberration corrections. Opt Express 26, 30162.CrossRefGoogle ScholarPubMed
Kabius, B, Hartel, P, Haider, M, Muller, H, Uhlemann, S, Loebau, U, Zach, J & Rose, H (2009). First application of Cc-corrected imaging for high-resolution and energy-filtered TEM. J Electron Microsc 58, 147–155.CrossRefGoogle ScholarPubMed
Karimi, E, Schulz, SA, De Leon, I, Qassim, H, Upham, J & Boyd, RW (2014). Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface. Light Sci Appl 3, e167–e167.CrossRefGoogle Scholar
Kingma, DP & Ba, J (2014). Adam: A Method for Stochastic Optimization. Available at http://arxiv.org/abs/1412.6980Google Scholar
Knoll, M & Ruska, E (1932). Das elektronenmikroskop. Z Phys 78, 318–339.CrossRefGoogle Scholar
Kramberger, C, Löffler, S, Schachinger, T, Hartel, P, Zach, J & Schattschneider, P (2019). Π/2 mode converters and vortex generators for electrons. Ultramicroscopy 204, 27–33.CrossRefGoogle ScholarPubMed
Krivanek, OL, Dellby, N & Lupini, AR (1999). Towards sub-Å electron beams. Ultramicroscopy 78, 1–11.CrossRefGoogle Scholar
Krivanek, OL, Lovejoy, TC, Dellby, N, Aoki, T, Carpenter, RW, Rez, P, Soignard, E, Zhu, J, Batson, PE, Lagos, MJ, Egerton, RF & Crozier, PA (2014). Vibrational spectroscopy in the electron microscope. Nature 514, 209–212.CrossRefGoogle ScholarPubMed
Larocque, H, Bouchard, F, Grillo, V, Sit, A, Frabboni, S, Dunin-Borkowski, RE, Padgett, MJ, Boyd, RW & Karimi, E (2016). Nondestructive measurement of orbital angular momentum for an electron beam. Phys Rev Lett 117, 154801.CrossRefGoogle ScholarPubMed
Larocque, H, Kaminer, I, Grillo, V, Leuchs, G, Padgett, MJ, Boyd, RW, Segev, M & Karimi, E (2018). ‘Twisted’ electrons. Contemp Phys 59, 126–144.CrossRefGoogle Scholar
Lopatin, S, Cheng, B, Liu, W-T, Tsai, M-L, He, J-H & Chuvilin, A (2018). Optimization of monochromated TEM for ultimate resolution imaging and ultrahigh resolution electron energy loss spectroscopy. Ultramicroscopy 184, 109–115.CrossRefGoogle ScholarPubMed
Lupini, AR, Wang, P, Nellist, PD, Kirkland, AI & Pennycook, SJ (2010). Aberration measurement using the Ronchigram contrast transfer function. Ultramicroscopy 110, 891–898.CrossRefGoogle ScholarPubMed
Mafakheri, E, Tavabi, AH, Lu, P-H, Balboni, R, Venturi, F, Menozzi, C, Gazzadi, GC, Frabboni, S, Sit, A, Dunin-Borkowski, RE, Karimi, E & Grillo, V (2017). Realization of electron vortices with large orbital angular momentum using miniature holograms fabricated by electron beam lithography. Appl Phys Lett 110, 093113.CrossRefGoogle Scholar
McMorran, BJ, Agrawal, A, Ercius, PA, Grillo, V, Herzing, AA, Harvey, TR, Linck, M & Pierce, JS (2017 a). Origins and demonstrations of electrons with orbital angular momentum. Philos Trans R Soc A 375, 20150434.CrossRefGoogle ScholarPubMed
McMorran, BJ, Harvey, TR & Lavery, MPJJ (2017 b). Efficient sorting of free electron orbital angular momentum. New J Phys 19, 023053.CrossRefGoogle Scholar
Mirhosseini, M, Malik, M, Shi, Z & Boyd, RW (2013). Efficient separation of the orbital angular momentum eigenstates of light. Nat Commun 4, 2781.CrossRefGoogle Scholar
Morishita, S, Mukai, M, Suenaga, K & Sawada, H (2016). Resolution enhancement in transmission electron microscopy with 60-kV monochromated electron source. Appl Phys Lett 108, 013107.CrossRefGoogle Scholar
Pozzi, G, Grillo, V, Lu, P-H, Tavabi, AH, Karimi, E & Dunin-Borkowski, RE (2020). Design of electrostatic phase elements for sorting the orbital angular momentum of electrons. Ultramicroscopy 208, 112861.CrossRefGoogle ScholarPubMed
Pu, M, Li, X, Ma, X, Wang, Y, Zhao, Z, Wang, C, Hu, C, Gao, P, Huang, C, Ren, H, Li, X, Qin, F, Yang, J, Gu, M, Hong, M & Luo, X (2015). Catenary optics for achromatic generation of perfect optical angular momentum. Sci Adv 1, e1500396.CrossRefGoogle ScholarPubMed
Rashidi, M & Wolkow, RA (2018). Autonomous scanning probe microscopy in situ tip conditioning through machine learning. ACS Nano 12, 5185–5189.CrossRefGoogle ScholarPubMed
Rosi, P, Venturi, F, Medici, G, Menozzi, C, Gazzadi, GC, Rotunno, E, Frabboni, S, Balboni, R, Rezaee, M, Tavabi, AH, Dunin-Borkowski, RE, Karimi, E & Grillo, V (2022). Theoretical and practical aspects of the design and production of synthetic holograms for transmission electron microscopy. J Appl Phys 131, 031101.CrossRefGoogle Scholar
Rotunno, E, Tavabi, AH, Rosi, P, Frabboni, S, Tiemeijer, P, Dunin-Borkowski, RE & Grillo, V (2021). Alignment of electron optical beam shaping elements using a convolutional neural network. Ultramicroscopy 228, 113338.CrossRefGoogle ScholarPubMed
Ruffato, G, Rotunno, E, Giberti, LMC & Grillo, V (2021). Arbitrary conformal transformations of wave functions. Phys Rev Appl 10, 1–11. doi:10.1103/PhysRevApplied.15.054028Google Scholar
Ruska, E (1987). The development of the electron microscope and of electron microscopy. Biosci Rep 7, 607–629.CrossRefGoogle ScholarPubMed
Saitoh, K, Hasegawa, Y, Hirakawa, K, Tanaka, N & Uchida, M (2013). Measuring the orbital angular momentum of electron vortex beams using a forked grating. Phys Rev Lett 111, 074801.CrossRefGoogle ScholarPubMed
Sawada, H, Sannomiya, T, Hosokawa, F, Nakamichi, T, Kaneyama, T, Tomita, T, Kondo, Y, Tanaka, T, Oshima, Y, Tanishiro, Y & Takayanagi, K (2008). Measurement method of aberration from Ronchigram by autocorrelation function. Ultramicroscopy 108, 1467–1475.CrossRefGoogle ScholarPubMed
Schattschneider, P, Stöger-Pollach, M & Verbeeck, J (2012). Novel vortex generator and mode converter for electron beams. Phys Rev Lett 109, 084801.CrossRefGoogle ScholarPubMed
Shiloh, R, Lu, P-H, Remez, R, Tavabi, AH, Pozzi, G, Dunin-Borkowski, RE & Arie, A (2019). Nanostructuring of electron beams. Phys Scr 94, 034004.CrossRefGoogle Scholar
Sorokin, D, Ulanov, A, Sazhina, E & Lvovsky, A (2020). Interferobot: Aligning an optical interferometer by a reinforcement learning agent. Adv Neural Inf Process Syst 33, 13238–13248.Google Scholar
Tavabi, AH, Larocque, H, Lu, P-H, Duchamp, M, Grillo, V, Karimi, E, Dunin-Borkowski, RE & Pozzi, G (2020). Generation of electron vortices using nonexact electric fields. Phys Rev Res 2, 013185.CrossRefGoogle Scholar
Tavabi, AH, Rosi, P, Rotunno, E, Roncaglia, A, Belsito, L, Frabboni, S, Pozzi, G, Gazzadi, GC, Lu, P-H, Nijland, R, Ghosh, M, Tiemeijer, P, Karimi, E, Dunin-Borkowski, RE & Grillo, V (2021). Experimental demonstration of an electrostatic orbital angular momentum sorter for electron beams. Phys Rev Lett 126, 094802. doi:10.1103/PhysRevLett.126.094802.CrossRefGoogle ScholarPubMed
Thakkar, P, Guzenko, VA, Lu, P-H, Dunin-Borkowski, RE, Abrahams, JP & Tsujino, S (2020). Fabrication of low aspect ratio three-element Boersch phase shifters for voltage-controlled three electron beam interference. J Appl Phys 128, 134502.CrossRefGoogle Scholar
Tiemeijer, PC (1999). Analytical electron microscopy-operation modes of a TEM monochromator. In Institute of Physics Conference Series, Vol. 161, Boston: Adam Hilger, Ltd., pp. 191–194. c1985.Google Scholar
Verbeeck, J, Béché, A, Müller-Caspary, K, Guzzinati, G, Luong, MA & Den Hertog, M (2018). Demonstration of a 2 × 2 programmable phase plate for electrons. Ultramicroscopy 190, 58–65.CrossRefGoogle Scholar
Verbeeck, J, Guzzinati, G, Clark, L, Juchtmans, R, Van Boxem, R, Tian, H, Béché, A, Lubk, A & Van Tendeloo, G (2014). Shaping electron beams for the generation of innovative measurements in the (S)TEM. C R Phys 15, 190–199.CrossRefGoogle Scholar
Xu, M, Kumar, A & LeBeau, J (2021). Automating electron microscopy through machine learning and USETEM. Microsc Microanal 27, 2988–2989.CrossRefGoogle Scholar
Zemlin, F, Weiss, K, Schiske, P, Kunath, W & Herrmann, K-H (1978). Coma-free alignment of high resolution electron microscopes with the aid of optical diffractograms. Ultramicroscopy 3, 49–60.CrossRefGoogle Scholar