Abstract

A theoretical framework for widefield structured illumination microscopy (SIM) reconstruction from fewer than the commonly used nine raw frame acquisitions is introduced and applied in silico and in vitro. The proposed scheme avoids the recording of redundant spatial frequency components, which was necessary in previous SIM algorithms. This allows for gentler superresolution imaging at faster speeds. A doubling of frame rates is possible solely via changes in the computational reconstruction procedure. Furthermore, we explore numerically the effect of the sample movement on the reconstruction quality and the number of raw frames recordable. Our results show that there exists a limit above which deconvolution microscopy becomes superior to SIM.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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2016 (3)

2015 (2)

F. Ströhl and C. F. Kaminski, Methods Appl. Fluoresc. 3, 014002 (2015).

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, Science 349, aab3500 (2015).

2014 (3)

B. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, W. Michael, C. Janetopoulos, X. S. Wu, J. A. H. Iii, Z. Liu, B. P. English, Y. Mimori-kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-schwartz, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. Serdar, D. P. Kiehart, and E. Betzig, Science 346, 439 (2014).

M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, ChemPhysChem 15, 794 (2014).
[Crossref]

K. Chu, P. J. McMillan, Z. J. Smith, J. Yin, J. Atkins, P. Goodwin, S. Wachsmann-Hogiu, and S. Lane, Opt. Express 22, 8687 (2014).
[Crossref]

2013 (4)

2012 (1)

F. Orieux, E. Sepulveda, V. Loriette, B. Dubertret, and J. C. Olivo-Marin, IEEE Trans. Image Process. 21, 601 (2012).
[Crossref]

2010 (1)

C. B. Müller and J. Enderlein, Phys. Rev. Lett. 104, 198101 (2010).
[Crossref]

2003 (2)

R. Heintzmann, Micron 34, 283 (2003).
[Crossref]

E. Oztas, Neuroanatomy 2, 2 (2003).

2000 (2)

M. Gustafsson, J. Microsc. 198, 82 (2000).
[Crossref]

J. T. Frohn, H. F. Knapp, and A. Stemmer, Proc. Natl. Acad. Sci. USA 97, 7232 (2000).
[Crossref]

Atkins, J.

Ayuk, R.

Azar, L. N.

Baird, M. A.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, Science 349, aab3500 (2015).

Beach, J. R.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, Science 349, aab3500 (2015).

Belkebir, K.

Bembenek, J. N.

B. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, W. Michael, C. Janetopoulos, X. S. Wu, J. A. H. Iii, Z. Liu, B. P. English, Y. Mimori-kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-schwartz, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. Serdar, D. P. Kiehart, and E. Betzig, Science 346, 439 (2014).

Betzig, E.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, Science 349, aab3500 (2015).

B. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, W. Michael, C. Janetopoulos, X. S. Wu, J. A. H. Iii, Z. Liu, B. P. English, Y. Mimori-kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-schwartz, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. Serdar, D. P. Kiehart, and E. Betzig, Science 346, 439 (2014).

Böhme, R.

B. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, W. Michael, C. Janetopoulos, X. S. Wu, J. A. H. Iii, Z. Liu, B. P. English, Y. Mimori-kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-schwartz, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. Serdar, D. P. Kiehart, and E. Betzig, Science 346, 439 (2014).

Boulanger, J.

J. Boulanger, N. Pustelnik, and L. Condat, Proceedings of International Symposium on Biomedical Imaging (2014).

Brandt, R. A. J.

Breedijk, R. M. P.

Chandris, P.

A. G. York, P. Chandris, D. D. Nogare, J. Head, P. Wawrzusin, R. S. Fischer, A. Chitnis, and H. Shroff, Nat. Methods 10, 1122 (2013).
[Crossref]

Chen, B.

B. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, W. Michael, C. Janetopoulos, X. S. Wu, J. A. H. Iii, Z. Liu, B. P. English, Y. Mimori-kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-schwartz, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. Serdar, D. P. Kiehart, and E. Betzig, Science 346, 439 (2014).

Chen, B.-C.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, Science 349, aab3500 (2015).

Chitnis, A.

A. G. York, P. Chandris, D. D. Nogare, J. Head, P. Wawrzusin, R. S. Fischer, A. Chitnis, and H. Shroff, Nat. Methods 10, 1122 (2013).
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Chu, K.

Condat, L.

J. Boulanger, N. Pustelnik, and L. Condat, Proceedings of International Symposium on Biomedical Imaging (2014).

Davidson, M. W.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, Science 349, aab3500 (2015).

de Jong, B. E.

De Luca, G. M. R.

Dubertret, B.

F. Orieux, E. Sepulveda, V. Loriette, B. Dubertret, and J. C. Olivo-Marin, IEEE Trans. Image Process. 21, 601 (2012).
[Crossref]

Enderlein, J.

C. B. Müller and J. Enderlein, Phys. Rev. Lett. 104, 198101 (2010).
[Crossref]

English, B. P.

B. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, W. Michael, C. Janetopoulos, X. S. Wu, J. A. H. Iii, Z. Liu, B. P. English, Y. Mimori-kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-schwartz, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. Serdar, D. P. Kiehart, and E. Betzig, Science 346, 439 (2014).

Fischer, R. S.

A. G. York, P. Chandris, D. D. Nogare, J. Head, P. Wawrzusin, R. S. Fischer, A. Chitnis, and H. Shroff, Nat. Methods 10, 1122 (2013).
[Crossref]

Frohn, J. T.

J. T. Frohn, H. F. Knapp, and A. Stemmer, Proc. Natl. Acad. Sci. USA 97, 7232 (2000).
[Crossref]

Giovannini, H.

Girard, J.

Goodwin, P.

Grill, S. W.

B. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, W. Michael, C. Janetopoulos, X. S. Wu, J. A. H. Iii, Z. Liu, B. P. English, Y. Mimori-kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-schwartz, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. Serdar, D. P. Kiehart, and E. Betzig, Science 346, 439 (2014).

Gustafsson, M.

M. Gustafsson, J. Microsc. 198, 82 (2000).
[Crossref]

Hammer, J. A.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, Science 349, aab3500 (2015).

Head, J.

A. G. York, P. Chandris, D. D. Nogare, J. Head, P. Wawrzusin, R. S. Fischer, A. Chitnis, and H. Shroff, Nat. Methods 10, 1122 (2013).
[Crossref]

Heintzmann, R.

Hoebe, R. A.

Hoogendoorn, E.

M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, ChemPhysChem 15, 794 (2014).
[Crossref]

Iii, J. A. H.

B. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, W. Michael, C. Janetopoulos, X. S. Wu, J. A. H. Iii, Z. Liu, B. P. English, Y. Mimori-kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-schwartz, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. Serdar, D. P. Kiehart, and E. Betzig, Science 346, 439 (2014).

Ingaramo, M.

M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, ChemPhysChem 15, 794 (2014).
[Crossref]

Janetopoulos, C.

B. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, W. Michael, C. Janetopoulos, X. S. Wu, J. A. H. Iii, Z. Liu, B. P. English, Y. Mimori-kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-schwartz, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. Serdar, D. P. Kiehart, and E. Betzig, Science 346, 439 (2014).

Jost, A.

Kaminski, C. F.

F. Ströhl and C. F. Kaminski, Optica 3, 667 (2016).
[Crossref]

L. J. Young, F. Ströhl, and C. F. Kaminski, J. Vis. Exp. 111, e53988 (2016).

F. Ströhl and C. F. Kaminski, Methods Appl. Fluoresc. 3, 014002 (2015).

Kiehart, D. P.

B. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, W. Michael, C. Janetopoulos, X. S. Wu, J. A. H. Iii, Z. Liu, B. P. English, Y. Mimori-kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-schwartz, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. Serdar, D. P. Kiehart, and E. Betzig, Science 346, 439 (2014).

Kirchhausen, T.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, Science 349, aab3500 (2015).

Knapp, H. F.

J. T. Frohn, H. F. Knapp, and A. Stemmer, Proc. Natl. Acad. Sci. USA 97, 7232 (2000).
[Crossref]

Lane, S.

Legant, W. R.

B. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, W. Michael, C. Janetopoulos, X. S. Wu, J. A. H. Iii, Z. Liu, B. P. English, Y. Mimori-kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-schwartz, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. Serdar, D. P. Kiehart, and E. Betzig, Science 346, 439 (2014).

Li, D.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, Science 349, aab3500 (2015).

Lippincott-schwartz, J.

B. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, W. Michael, C. Janetopoulos, X. S. Wu, J. A. H. Iii, Z. Liu, B. P. English, Y. Mimori-kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-schwartz, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. Serdar, D. P. Kiehart, and E. Betzig, Science 346, 439 (2014).

Liu, Z.

B. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, W. Michael, C. Janetopoulos, X. S. Wu, J. A. H. Iii, Z. Liu, B. P. English, Y. Mimori-kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-schwartz, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. Serdar, D. P. Kiehart, and E. Betzig, Science 346, 439 (2014).

Loriette, V.

F. Orieux, E. Sepulveda, V. Loriette, B. Dubertret, and J. C. Olivo-Marin, IEEE Trans. Image Process. 21, 601 (2012).
[Crossref]

Manders, E. M. M.

Mangeat, T.

Manton, J. D.

McMillan, P. J.

Michael, W.

B. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, W. Michael, C. Janetopoulos, X. S. Wu, J. A. H. Iii, Z. Liu, B. P. English, Y. Mimori-kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-schwartz, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. Serdar, D. P. Kiehart, and E. Betzig, Science 346, 439 (2014).

Milkie, D. E.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, Science 349, aab3500 (2015).

B. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, W. Michael, C. Janetopoulos, X. S. Wu, J. A. H. Iii, Z. Liu, B. P. English, Y. Mimori-kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-schwartz, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. Serdar, D. P. Kiehart, and E. Betzig, Science 346, 439 (2014).

Mimori-kiyosue, Y.

B. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, W. Michael, C. Janetopoulos, X. S. Wu, J. A. H. Iii, Z. Liu, B. P. English, Y. Mimori-kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-schwartz, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. Serdar, D. P. Kiehart, and E. Betzig, Science 346, 439 (2014).

Mitchell, D. M.

B. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, W. Michael, C. Janetopoulos, X. S. Wu, J. A. H. Iii, Z. Liu, B. P. English, Y. Mimori-kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-schwartz, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. Serdar, D. P. Kiehart, and E. Betzig, Science 346, 439 (2014).

Moses, B.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, Science 349, aab3500 (2015).

Mudry, E.

Müller, C. B.

C. B. Müller and J. Enderlein, Phys. Rev. Lett. 104, 198101 (2010).
[Crossref]

Mullins, R. D.

B. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, W. Michael, C. Janetopoulos, X. S. Wu, J. A. H. Iii, Z. Liu, B. P. English, Y. Mimori-kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-schwartz, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. Serdar, D. P. Kiehart, and E. Betzig, Science 346, 439 (2014).

Nogare, D. D.

A. G. York, P. Chandris, D. D. Nogare, J. Head, P. Wawrzusin, R. S. Fischer, A. Chitnis, and H. Shroff, Nat. Methods 10, 1122 (2013).
[Crossref]

Olivo-Marin, J. C.

F. Orieux, E. Sepulveda, V. Loriette, B. Dubertret, and J. C. Olivo-Marin, IEEE Trans. Image Process. 21, 601 (2012).
[Crossref]

Orieux, F.

F. Orieux, E. Sepulveda, V. Loriette, B. Dubertret, and J. C. Olivo-Marin, IEEE Trans. Image Process. 21, 601 (2012).
[Crossref]

Oztas, E.

E. Oztas, Neuroanatomy 2, 2 (2003).

Pasham, M.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, Science 349, aab3500 (2015).

Patterson, G. H.

M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, ChemPhysChem 15, 794 (2014).
[Crossref]

Postma, M.

M. Ingaramo, A. G. York, E. Hoogendoorn, M. Postma, H. Shroff, and G. H. Patterson, ChemPhysChem 15, 794 (2014).
[Crossref]

Pustelnik, N.

J. Boulanger, N. Pustelnik, and L. Condat, Proceedings of International Symposium on Biomedical Imaging (2014).

Rees, E. J.

Ritter, A. T.

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Supplementary Material (1)

NameDescription
» Visualization 1: MP4 (10890 KB)      Origin of raw spectra segmentation.

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Figures (5)

Fig. 1.
Fig. 1.

Principle of SIM reconstruction from (a) 9 or (b) 7 images. In the top right-hand corner, the widefield support is shown. Colors are used to indicate different orientations of illumination patterns. Using all orientations concurrently avoids redundancies in the reconstruction process (see the text). (c) 4SIM: here each SI frequency component is decomposed into “superresolution” information and widefield information. Segmenting each SI spectrum into multiple components yields additional equations. Adding a widefield image permits unambiguous SIM reconstruction (see the text).

Fig. 2.
Fig. 2.

SIM spectrum can be divided into 66 segments (left). SIM imaging yields spectra that contain spectral information overlaps. For example, SI 3 shows a superposition of segments [6,52,65], which are highlighted as an example. Hence, each SI spectrum gives rise to 18 equations totaling to 3 × 18 = 56 equations. This equation system is underdetermined as there are 66 distinct spectral elements in the problem, but a maximum likelihood estimation can nevertheless yield resolution improvements comparable to 9SIM. If a widefield spectrum (WF) is recorded and added to the three SI spectra, a unique reconstruction is possible (illustrated by the dotted line). The segmentation is illustrated in further detail in Visualization 1.

Fig. 3.
Fig. 3.

(a) Simulations of widefield imaging and SIM with 25 beads of 80 nm diameter. The widefield image was deconvolved using jRL to allow comparison with 3SIM and 9SIM data. The simulation parameters are listed in the supplementary information. The line profiles show that both 3SIM and 9SIM achieve similar resolution and are beyond the Sparrow limit, while the widefield and deconvolved versions are not. (b) Radially averaged spectra of (a) demonstrate that only 3SIM and 9SIM offer true superresolution and restore frequencies of the ground truth spectrum up to twice the Abbe limit. The scale bars are 0.5 μm.

Fig. 4.
Fig. 4.

Experimental comparison if different imaging modes. For all methods, nine raw SI images were used as the basis for processing. (a) Widefield image was generated by summing all raw images. (b) Widefield image deconvolved with the jRL algorithm. (c) 3SIM image was reconstructed from three of the nine SI raw images. (a)–(d) Inlay panels show two neighboring beads. Both 3SIM and 9SIM distinguish the beads and, thus, achieve resolution beyond the Sparrow limit. The scale bars are 1 μm and 100 nm in the enlarged panels.

Fig. 5.
Fig. 5.

Double-line target with 180 nm spacing generated in silico, as shown in the upper left-hand corner, was modeled to move in a direction perpendicular to the line pattern at different velocities v . The image recording was simulated at 100 Hz. The line profiles through the target are plotted for different v . At velocities up to 1 nm/ms, all SIM modalities were able to resolve the lines clearly. The images of faster moving targets deteriorated as the underlying structure varied significantly during the acquisition sequence. The modalities for which fewer raw images are required permit imaging of faster moving samples. Above 3 nm/ms, the optimal modality is deconvolution microscopy for the target shown.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

i ( x ) = [ s ( x ) × ( 1 + cos ( k o x + ϕ n ) ) ] h ( x ) ,
[ I 1 I 2 I 3 ] ( k ) = [ 1 1 2 e i ϕ 1 1 2 e i ϕ 1 1 1 2 e i ϕ 2 1 2 e i ϕ 2 1 1 2 e i ϕ 3 1 2 e i ϕ 3 ] [ H 0 0 0 H 0 0 0 H ] [ S ( k ) S ( k + k o ) S ( k k o ) ] .
i s = min i s ˜ [ o = 1 3 ( i o ( e o × i s ˜ ) h ) 2 ] .

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