Skip to main content Accessibility help
×
Home

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

  • Tim Dahmen (a1), Holger Kohr (a2), Niels de Jonge (a3) and Philipp Slusallek (a1)

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.

Copyright

Corresponding author

* Corresponding author. Tim.Dahmen@dfki.de

References

Hide All
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/#.
Aoyama, K., Takagi, T., Hirase, A. & Miyazawa, A. (2008). STEM tomography for thick biological specimens. Ultramicroscopy 109(1), 7080.
Batenburg, K. & Sijbers, J. (2007). DART: A fast heuristic algebraic reconstruction algorithm for discrete tomography. Image Process. 2007. ICIP 2007 4(2), IV133.
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.
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.
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.
Bracewell, R. (1956). Strip integration in radio astronomy. Aust J Phys 9(2), 198.
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.
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.
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.
Elfving, T., Hansen, P.C. & Nikazad, T. (2014). Semi-convergence properties of Kaczmarz’s method. Inverse Probl 30(5), 055007.
Fernandez, J.J. (2012). Computational methods for electron tomography. Micron 43(10), 10101030.
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.
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.
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.
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.
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.
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.
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.
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.
Lewitt, R.M. (1990). Multidimensional digital image representations using generalized Kaiser-Bessel window functions. J Opt Soc Am A 7(10), 18341846.
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.
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.
Midgley, P.A. & Dunin-Borkowski, R.E. (2009). Electron tomography and holography in materials science. Nat Mater 8(4), 271280.
Natterer, F. (1986). The Mathematics of Computerized Tomography. Philadelphia: SIAM.
Penczek, P., Marko, M., Buttle, K. & Frank, J. (1995). Double-tilt electron tomography. Ultramicroscopy 60(3), 393410.
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.
Rudin, W. (1987). Real and Complex Analysis. Boston: McGraw-Hill.
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.
Zeng, G.L. & Gullberg, G.T. (2000). Unmatched projector/backprojector pairs in an iterative reconstruction algorithm. IEEE Trans Med Imaging 19(5), 548555.

Keywords

Related content

Powered by UNSILO

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

  • Tim Dahmen (a1), Holger Kohr (a2), Niels de Jonge (a3) and Philipp Slusallek (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.