Abstract

As the resolution of X-ray tomography improves, the limited long-term stability and accuracy of nanoimaging tools does not allow computing artifact-free three-dimensional (3D) reconstructions without an additional step of numerical alignment of the measured projections. However, the common iterative alignment methods are significantly more computationally demanding than a simple tomographic reconstruction of the acquired volume. Here, we address this issue and present an alignment toolkit, which exploits methods with deep-subpixel accuracy combined with a multi-resolution scheme. This leads to robust and accurate alignment with significantly reduced computational and memory requirements. The performance of the presented methods is demonstrated on simulated and measured datasets for tomography and also laminography acquisition geometries. A GPU accelerated implementation of our alignment framework is publicly available.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (4)

Z. Gao, M. Guizar-Sicairos, V. Lutz-Bueno, A. Schröter, M. Liebi, M. Rudin, and M. Georgiadis, “High-speed tensor tomography: iterative reconstruction tensor tomography (IRTT) algorithm,” Acta Crystallogr., Sect. A: Found. Adv. 75(2), 223–238 (2019).
[Crossref]

M. Odstrcil, M. Holler, J. Raabe, A. Sepe, X. Sheng, S. Vignolini, C. G. Schroer, and M. Guizar-Sicairos, “Ab initio nonrigid X-ray nanotomography,” Nat. Commun. 10(1), 2600 (2019).
[Crossref]

M. Holler, M. Odstrčil, M. Guizar-Sicairos, M. Lebugle, E. Müller, S. Finizio, G. Tinti, C. David, J. Zusman, W. Unglaub, O. Bunk, J. Raabe, A. F. J. Levi, and G. Aeppli, “Three-dimensional imaging of integrated circuits with macro-to nanoscale zoom,” Nat. Electron. 2(10), 464–470 (2019).
[Crossref]

M. Odstrčil, M. Lebugle, M. Guizar-Sicairos, C. David, and M. Holler, “Towards optimized illumination for high-resolution ptychography,” Opt. Express 27(10), 14981–14997 (2019).
[Crossref]

2018 (5)

H. Öztürk, H. Yan, Y. He, M. Ge, Z. Dong, M. Lin, E. Nazaretski, I. K. Robinson, Y. S. Chu, and X. Huang, “Multi-slice ptychography with large numerical aperture multilayer laue lenses,” Optica 5(5), 601–607 (2018).
[Crossref]

J. C. Da Silva, M. Guizar-Sicairos, M. Holler, A. Diaz, J. A. van Bokhoven, O. Bunk, and A. Menzel, “Quantitative region-of-interest tomography using variable field of view,” Opt. Express 26(13), 16752–16768 (2018).
[Crossref]

J. Deng, Y. H. Lo, M. Gallagher-Jones, S. Chen, A. Pryor, Q. Jin, Y. P. Hong, Y. S. Nashed, S. Vogt, J. Miao, and C. Jacobsen, “Correlative 3D x-ray fluorescence and ptychographic tomography of frozen-hydrated green algae,” Sci. Adv. 4(11), eaau4548 (2018).
[Crossref]

F. Pfeiffer, “X-ray ptychography,” Nat. Photonics 12(1), 9–17 (2018).
[Crossref]

H. Yu, S. Xia, C. Wei, Y. Mao, D. Larsson, X. Xiao, P. Pianetta, Y.-S. Yu, and Y. Liu, “Automatic projection image registration for nanoscale X-ray tomographic reconstruction,” J. Synchrotron Radiat. 25(6), 1819–1826 (2018).
[Crossref]

2017 (7)

D. Gürsoy, Y. P. Hong, K. He, K. Hujsak, S. Yoo, S. Chen, Y. Li, M. Ge, L. M. Miller, Y. S. Chu, V. De Andrade, K. He, O. Cossairt, A. K. Katsaggelos, and C. Jacobsen, “Rapid alignment of nanotomography data using joint iterative reconstruction and reprojection,” Sci. Rep. 7(1), 11818 (2017).
[Crossref]

D. N. Mastronarde and S. R. Held, “Automated tilt series alignment and tomographic reconstruction in IMOD,” J. Struct. Biol. 197(2), 102–113 (2017).
[Crossref]

J. Deng, D. J. Vine, S. Chen, Q. Jin, Y. S. Nashed, T. Peterka, S. Vogt, and C. Jacobsen, “X-ray ptychographic and fluorescence microscopy of frozen-hydrated cells using continuous scanning,” Sci. Rep. 7(1), 445 (2017).
[Crossref]

T. Ramos, J. S. Jørgensen, and J. W. Andreasen, “Automated angular and translational tomographic alignment and application to phase-contrast imaging,” J. Opt. Soc. Am. A 34(10), 1830–1843 (2017).
[Crossref]

C.-C. Wang, C.-C. Chiang, B. Liang, G.-C. Yin, Y.-T. Weng, and L.-C. Wang, “Fast projection matching for x-ray tomography,” Sci. Rep. 7(1), 3691 (2017).
[Crossref]

A. Pryor, Y. Yang, A. Rana, M. Gallagher-Jones, J. Zhou, Y. H. Lo, G. Melinte, W. Chiu, J. A. Rodriguez, and J. Miao, “GENFIRE: A generalized Fourier iterative reconstruction algorithm for high-resolution 3D imaging,” Sci. Rep. 7(1), 10409 (2017).
[Crossref]

C. Donnelly, M. Guizar-Sicairos, V. Scagnoli, S. Gliga, M. Holler, J. Raabe, and L. J. Heyderman, “Three-dimensional magnetization structures revealed with x-ray vector nanotomography,” Nature 547(7663), 328–331 (2017).
[Crossref]

2016 (1)

2015 (9)

M. Guizar-Sicairos, J. J. Boon, K. Mader, A. Diaz, A. Menzel, and O. Bunk, “Quantitative interior x-ray nanotomography by a hybrid imaging technique,” Optica 2(3), 259–266 (2015).
[Crossref]

W. van Aarle, W. J. Palenstijn, J. De Beenhouwer, T. Altantzis, S. Bals, K. J. Batenburg, and J. Sijbers, “The ASTRA Toolbox: A platform for advanced algorithm development in electron tomography,” Ultramicroscopy 157, 35–47 (2015).
[Crossref]

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution,” Sci. Rep. 4(1), 3857 (2015).
[Crossref]

J. Deng, D. J. Vine, S. Chen, Y. S. Nashed, Q. Jin, N. W. Phillips, T. Peterka, R. Ross, S. Vogt, and C. J. Jacobsen, “Simultaneous cryo x-ray ptychographic and fluorescence microscopy of green algae,” Proc. Natl. Acad. Sci. 112(8), 2314–2319 (2015).
[Crossref]

R. Han, L. Wang, Z. Liu, F. Sun, and F. Zhang, “A novel fully automatic scheme for fiducial marker-based alignment in electron tomography,” J. Struct. Biol. 192(3), 403–417 (2015).
[Crossref]

M. Liebi, M. Georgiadis, A. Menzel, P. Schneider, J. Kohlbrecher, O. Bunk, and M. Guizar-Sicairos, “Nanostructure surveys of macroscopic specimens by small-angle scattering tensor tomography,” Nature 527(7578), 349–352 (2015).
[Crossref]

F. Schaff, M. Bech, P. Zaslansky, C. Jud, M. Liebi, M. Guizar-Sicairos, and F. Pfeiffer, “Six-dimensional real and reciprocal space small-angle x-ray scattering tomography,” Nature 527(7578), 353–356 (2015).
[Crossref]

S. Jeught, J. Sijbers, and J. Dirckx, “Fast Fourier-based phase unwrapping on the graphics processing unit in real-time imaging applications,” J. Imaging 1(1), 31–44 (2015).
[Crossref]

A. Yousef, J. Li, and M. Karim, “High-speed image registration algorithm with subpixel accuracy,” IEEE Signal Process. Lett. 22(10), 1796–1800 (2015).
[Crossref]

2014 (3)

C.-C. Cheng, C.-C. Chien, H.-H. Chen, Y. Hwu, and Y.-T. Ching, “Image alignment for tomography reconstruction from synchrotron x-ray microscopic images,” PLoS One 9(1), e84675 (2014).
[Crossref]

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft X-ray microscopy,” Nat. Photonics 8(10), 765–769 (2014).
[Crossref]

M. Guizar-Sicairos, I. Johnson, A. Diaz, M. Holler, P. Karvinen, H.-C. Stadler, R. Dinapoli, O. Bunk, and A. Menzel, “High-throughput ptychography using Eiger: scanning X-ray nano-imaging of extended regions,” Opt. Express 22(12), 14859–14870 (2014).
[Crossref]

2013 (1)

A. Myagotin, A. Voropaev, L. Helfen, D. Hänschke, and T. Baumbach, “Efficient volume reconstruction for parallel-beam computed laminography by filtered backprojection on multi-core clusters,” IEEE Trans. Image Process. 22(12), 5348–5361 (2013).
[Crossref]

2012 (3)

F. Marone and M. Stampanoni, “Regridding reconstruction algorithm for real-time tomographic imaging,” J. Synchrotron Radiat. 19(6), 1029–1037 (2012).
[Crossref]

M. Scott, C.-C. Chen, M. Mecklenburg, C. Zhu, R. Xu, P. Ercius, U. Dahmen, B. Regan, and J. Miao, “Electron tomography at 2.4-ångström resolution,” Nature 483(7390), 444–447 (2012).
[Crossref]

D. Y. Parkinson, C. Knoechel, C. Yang, C. A. Larabell, and M. A. Le Gros, “Automatic alignment and reconstruction of images for soft x-ray tomography,” J. Struct. Biol. 177(2), 259–266 (2012).
[Crossref]

2011 (2)

M. Guizar-Sicairos, A. Diaz, M. Holler, M. S. Lucas, A. Menzel, R. A. Wepf, and O. Bunk, “Phase tomography from X-ray coherent diffractive imaging projections,” Opt. Express 19(22), 21345–21357 (2011).
[Crossref]

L. Helfen, A. Myagotin, P. Mikulík, P. Pernot, A. Voropaev, M. Elyyan, M. Di Michiel, J. Baruchel, and T. Baumbach, “On the implementation of computed laminography using synchrotron radiation,” Rev. Sci. Instrum. 82(6), 063702 (2011).
[Crossref]

2010 (1)

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[Crossref]

2009 (2)

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2005 (2)

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2004 (1)

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1999 (1)

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1996 (1)

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1994 (1)

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1993 (1)

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1989 (1)

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1988 (1)

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1984 (1)

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J. Dengler, “A multi-resolution approach to the 3D reconstruction from an electron microscope tilt series solving the alignment problem without gold particles,” Ultramicroscopy 30(3), 337–348 (1989).
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Figures (8)

Fig. 1.
Fig. 1. Flow diagram describing our alignment strategy.
Fig. 2.
Fig. 2. Filling of the Fourier space by the tomographic projections (gray stripes). Darker regions in the diagram denote regions with higher information redundancy.
Fig. 3.
Fig. 3. (a) An axial slice through our phantom, (b) Horizontal displacement error before (red) and after (blue) initial cross-correlation-based prealignment for Dataset 1.
Fig. 4.
Fig. 4. Root mean square (RMS) error of the positions recovered using the MR-PMA method for different downsampling levels in tomography geometry. The RMS error for each downsampling level was calculated in the original pixel size. (b) Number of iterations and time per iteration needed to reach converge threshold in Eq. (13) for Dataset 1. In (a) and (b), the result at previous downsampling level is provided as the initial guess for the next higher resolution level. At downsampling of 4×, 2× and 1× only one iteration is needed due to the deep subpixel accuracy at higher downsampling levels.
Fig. 5.
Fig. 5. FBP reconstruction quality after alignment by our MR-PMA method. Columns show reconstruction at different downsampling levels from 32 up to 1, and rows correspond to different synthetic datasets. Insets in the last column show detail of the reconstruction quality for the full resolution dataset.
Fig. 6.
Fig. 6. (a) RMS error of the positions recovered using the MR-PMA method for different downsampling levels in laminography geometry. (b) Number of iterations and time per iteration.
Fig. 7.
Fig. 7. (a) RMS of displacement update between subsequent downsampling levels for the experimental nano-laminography dataset. Convergence criterion of 0.2 pixel RMS was reached at 8$\times$ downsampled resolution. (b) Number of iterations and time per iteration required by the MR-PMA method. (c) Total displacement of each projection versus rotation angle.
Fig. 8.
Fig. 8. Laminography slices of the two finest transistor metal layers M0 and M1 are shown in (a) and (b), respectively. The red squares inside of the full circular fields of view denote the regions magnified in the detailed views. (c) Fourier shell correlation of the laminography reconstruction.

Tables (1)

Tables Icon

Table 1. Root mean square (RMS) displacement error for all three-alignment methods in pixel units. Displacement error for MR-PMA were estimated after the final full-resolution refinement.

Equations (18)

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T ( x , y ) = exp ( 2 π i λ 0 L Z [ n ( x , y , z ) 1 ] d z ) ,
P A ( x , y ) = log ( | T ( x , y ) | ) = 2 π λ 0 L Z β ( x , y , z ) d z ,
ϕ ( x , y ) = arg ( T ( x , y ) ) = 2 π λ 0 L Z δ ( x , y , z ) d z .
V Θ ( x , y ) = | x T Θ | 2 + | y T Θ | 2 ,
m Θ ( y ) = x p Θ ( x , y ) d x   .
y ϕ = Im { T ¯ Θ | T Θ | 2 F 1 [ 2 π u y F ( T Θ ) ] } ,
p ^ Θ = A Θ A 1 p   ,
p = [ p Θ 0 , p Θ 1 , , p Θ n ]   .
min Δ x Θ , Δ y Θ W Θ   F hp { p Θ ( x , y ) p ^ Θ ( x + Δ x Θ , y + Δ y Θ ) }   ,
Δ x Θ ( i ) = W Θ 2   F hp { x p ^ Θ ( i ) } F hp { p Θ ( i ) p ^ Θ ( i ) } W Θ 2 [ F hp { p Θ ( i ) p ^ Θ ( i ) } ] 2
Δ y Θ ( i ) = W Θ 2   F hp { y p ^ Θ ( i ) } F hp { p Θ ( i ) p ^ Θ ( i ) } W Θ 2 [ F hp { p Θ ( i ) p ^ Θ ( i ) } ] 2 ,
x p ^ Θ = F 1 [ 2 π i u x F ( p ^ Θ ) ]  
y p ^ Θ = F 1 [ 2 π i u y F ( p ^ Θ ) ] ,
p Θ ( i + 1 ) = F 1 { exp [ 2 π i ( Δ x Θ ( i ) u x + Δ y Θ ( i ) u y ) ] F ( p Θ ( i ) ) } .
max Θ ( Δ x Θ ( i ) , Δ y Θ ( i ) ) < γ / D ,
x ^ ( n ) = 1 M m = 0 M 1 X ( m ) exp [ 2 π i ( n 1 / 2 ) m M ]
X ( m ) = { n = 0 N 1 x ( n ) exp [ 2 π i ( n 1 / 2 ) m N ] if  0 m < M 0 if  m M
min β Θ , x , β Θ , y , β Θ , 0 W Θ ( p Θ + β Θ , x x + β Θ , y y + β Θ , 0 p ^ Θ ) ,