Skip to main content Accessibility help
×
Home
Hostname: page-component-888d5979f-g2njx Total loading time: 0.187 Render date: 2021-10-26T13:23:24.404Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

Matched Backprojection Operator for Combined Scanning Transmission Electron Microscopy Tilt- and Focal Series

Published online by Cambridge University Press:  05 June 2015

Tim Dahmen*
Affiliation:
German Research Center for Artificial Intelligence GmbH (DFKI), 66123 Saarbrücken, Germany
Holger Kohr
Affiliation:
Department of Mathematics, KTH Royal Institute of Technology, Lindstedtsvägen 25, Stockholm, SE 100 44, Sweden
Niels de Jonge
Affiliation:
INM Leibniz Institute for New Materials, 66123 Saarbrücken, Germany
Philipp Slusallek
Affiliation:
German Research Center for Artificial Intelligence GmbH (DFKI), 66123 Saarbrücken, Germany
*
* Corresponding author. Tim.Dahmen@dfki.de

Abstract

Combined tilt- and focal series scanning transmission electron microscopy is a recently developed method to obtain nanoscale three-dimensional (3D) information of thin specimens. In this study, we formulate the forward projection in this acquisition scheme as a linear operator and prove that it is a generalization of the Ray transform for parallel illumination. We analytically derive the corresponding backprojection operator as the adjoint of the forward projection. We further demonstrate that the matched backprojection operator drastically improves the convergence rate of iterative 3D reconstruction compared to the case where a backprojection based on heuristic weighting is used. In addition, we show that the 3D reconstruction is of better quality.

Type
Techniques and Equipment Development
Copyright
© Microscopy Society of America 2015 

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

AMD (2013). AMD Math Libraries OpenCL Fast Fourier Transforms (FFTs) clAmdFft. http://developer.amd.com/tools-and-sdks/opencl-zone/amd-accelerated-parallel-processing-math-libraries/#.Google Scholar
Aoyama, K., Takagi, T., Hirase, A. & Miyazawa, A. (2008). STEM tomography for thick biological specimens. Ultramicroscopy 109(1), 7080.CrossRefGoogle ScholarPubMed
Batenburg, K. & Sijbers, J. (2007). DART: A fast heuristic algebraic reconstruction algorithm for discrete tomography. Image Process. 2007. ICIP 2007 4(2), IV133.Google Scholar
Baudoin, J.P., Jerome, W.G., Kübel, C. & de Jonge, N. (2013). Whole-cell analysis of low-density lipoprotein uptake by macrophages using STEM tomography. PLoS One 8(1), e55022.CrossRefGoogle ScholarPubMed
Behan, G., Cosgriff, E.C., Kirkland, A.I. & Nellist, P.D. (2009). Three-dimensional imaging by optical sectioning in the aberration-corrected scanning transmission electron microscope. Phil Trans A Math Phys Eng Sci 367(1903), 38253844.CrossRefGoogle ScholarPubMed
Borisevich, A.Y., Lupini, A.R. & Pennycook, S.J. (2006). Depth sectioning with the aberration-corrected scanning transmission electron microscope. Proc Natl Acad Sci USA. 103(9), 30443048.CrossRefGoogle ScholarPubMed
Bracewell, R. (1956). Strip integration in radio astronomy. Aust J Phys 9(2), 198.CrossRefGoogle Scholar
Dahmen, T., Baudoin, J.P., Lupini, A.R., Kübel, C., Slusallek, P. & de Jonge, N. (2014). Combined scanning transmission electron microscopy tilt- and focal series. Microsc Microanal 20(2), 548560.CrossRefGoogle ScholarPubMed
de Jonge, N., Sougrat, R., Northan, B.M. & Pennycook, S.J. (2010). Three-dimensional scanning transmission electron microscopy of biological specimens. Micros Microanal 16(1), 5463.CrossRefGoogle ScholarPubMed
Dukes, M.J., Ramachandra, R., Baudoin, J.P., Gray Jerome, W. & de Jonge, N. (2011). Three-dimensional locations of gold-labeled proteins in a whole mount eukaryotic cell obtained with 3nm precision using aberration-corrected scanning transmission electron microscopy. J Struct Biol 174(3), 552562.CrossRefGoogle Scholar
Elfving, T., Hansen, P.C. & Nikazad, T. (2014). Semi-convergence properties of Kaczmarz’s method. Inverse Probl 30(5), 055007.CrossRefGoogle Scholar
Fernandez, J.J. (2012). Computational methods for electron tomography. Micron 43(10), 10101030.CrossRefGoogle ScholarPubMed
Frigo, S.P., Levine, Z.H. & Zaluzec, N.J. (2002). Submicron imaging of buried integrated circuit structures using scanning confocal electron microscopy. Appl Phys Lett 81(11), 2112.CrossRefGoogle Scholar
Goris, B., Van den Broek, W., Batenburg, K.J., Heidari Mezerji, H. & Bals, S. (2012). Electron tomography based on a total variation minimization reconstruction technique. Ultramicroscopy 113, 120130.CrossRefGoogle Scholar
Hohmann-Marriott, M.F., Sousa, A.A., Azari, A.A., Glushakova, S., Zhang, G., Zimmerberg, J. & Leapman, R.D. (2009). Nanoscale 3D cellular imaging by axial scanning transmission electron tomography. Nat Meth 6(10), 729731.CrossRefGoogle ScholarPubMed
Hovden, R., Ercius, P., Jiang, Y., Wang, D., Yu, Y., Abruña, H.D., Elser, V. & Muller, D.A. (2014). Breaking the Crowther limit: Combining depth-sectioning and tilt tomography for high-resolution, wide-field 3D reconstructions. Ultramicroscopy 140, 2631.CrossRefGoogle ScholarPubMed
Intaraprasonk, V., Xin, H.L. & Muller, D.A. (2008). Analytic derivation of optimal imaging conditions for incoherent imaging in aberration-corrected electron microscopes. Ultramicroscopy 108(11), 14541466.CrossRefGoogle ScholarPubMed
Koster, A.J., Grimm, R., Typke, D., Hegerl, R., Stoschek, A., Walz, J. & Baumeister, W. (1997). Perspectives of molecular and cellular electron tomography. J Struct Biol 120(3), 276308.CrossRefGoogle ScholarPubMed
Kübel, C., Voigt, A., Schoenmakers, R., Otten, M., Su, D., Lee, T.C., Carlsson, A. & Bradley, J. (2005). Recent advances in electron tomography: TEM and HAADF-STEM tomography for materials science and semiconductor applications. Microsc Microanal 11(5), 378400.CrossRefGoogle ScholarPubMed
Lanzavecchia, S., Cantele, F., Bellon, P.L., Zampighi, L., Kreman, M., Wright, E. & Zampighi, G.A. (2005). Conical tomography of freeze-fracture replicas: A method for thestudy of integral membrane proteins inserted in phospholipid bilayers. J Struct Biol 149(1), 8798.CrossRefGoogle Scholar
Lewitt, R.M. (1990). Multidimensional digital image representations using generalized Kaiser-Bessel window functions. J Opt Soc Am A 7(10), 18341846.CrossRefGoogle ScholarPubMed
Lupini, A.R. & de Jonge, N. (2011). The three-dimensional point spread function of aberration-corrected scanning transmission electron microscopy. Micros Microanal 17(5), 817826.CrossRefGoogle ScholarPubMed
Marabini, R., Herman, G.T. & Carazo, J.M. (1998). 3D reconstruction in electron microscopy using ART with smooth spherically symmetric volume elements (blobs). Ultramicroscopy 72(1–2), 5365.CrossRefGoogle Scholar
Midgley, P.A. & Dunin-Borkowski, R.E. (2009). Electron tomography and holography in materials science. Nat Mater 8(4), 271280.CrossRefGoogle ScholarPubMed
Natterer, F. (1986). The Mathematics of Computerized Tomography. Philadelphia: SIAM.Google Scholar
Penczek, P., Marko, M., Buttle, K. & Frank, J. (1995). Double-tilt electron tomography. Ultramicroscopy 60(3), 393410.CrossRefGoogle ScholarPubMed
Ramachandra, R. & de Jonge, N. (2012). Optimized deconvolution for maximum axial resolution in three-dimensional aberration-corrected scanning transmission electron microscopy. Microsc Microanal 18(1), 218228.CrossRefGoogle ScholarPubMed
Rudin, W. (1987). Real and Complex Analysis. Boston: McGraw-Hill.Google Scholar
Van Aert, S., Batenburg, K.J., Rossell, M.D., Erni, R. & Van Tendeloo, G. (2011). Three-dimensional atomic imaging of crystalline nanoparticles. Nature 470, 374377.CrossRefGoogle ScholarPubMed
Zeng, G.L. & Gullberg, G.T. (2000). Unmatched projector/backprojector pairs in an iterative reconstruction algorithm. IEEE Trans Med Imaging 19(5), 548555.CrossRefGoogle Scholar
6
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Matched Backprojection Operator for Combined Scanning Transmission Electron Microscopy Tilt- and Focal Series
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Matched Backprojection Operator for Combined Scanning Transmission Electron Microscopy Tilt- and Focal Series
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Matched Backprojection Operator for Combined Scanning Transmission Electron Microscopy Tilt- and Focal Series
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *