Abstract

It is experimentally demonstrated that even though the numerical aperture in the object space is fixed, the resolution of an imaging system still can be improved by adjusting the parameters in the image space. This strategy cannot be realized until the discovery of the violation of the Lagrange invariant in a kind of self-interference holography. With the violation, parameters in the image space can escape the constraint of the object space for resolution improvement. Experiments that directly confirm this new ability are implemented and results agree well with the theoretical prediction. Additionally, better performance on frequency recording and finer details beyond the diffraction limit have been recorded with this method.

© 2015 Optical Society of America

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References

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2014 (1)

2013 (2)

2012 (2)

2011 (2)

2007 (1)

2006 (3)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

2002 (1)

2000 (1)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[Crossref] [PubMed]

1994 (1)

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Bouchal, P.

Bouchal, Z.

Brooker, G.

Campos, J.

Chmelík, R.

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Fu, L.

Girirajan, T. P. K.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref] [PubMed]

Gustafsson, M. G. L.

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[Crossref] [PubMed]

Hell, S. W.

Hess, H. F.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Hess, S. T.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref] [PubMed]

Hussain, A.

Kapitán, J.

Kato, J.

Katz, B.

Kelner, R.

Lai, X.

Lindwasser, O. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Lippincott-Schwartz, J.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Lizana, A.

Lv, X.

Martínez, J. L.

Mason, M. D.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref] [PubMed]

Matsumura, T.

Olenych, S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Rosen, J.

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

Siegel, N.

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Wichmann, J.

Yamaguchi, I.

Yuan, J.

Zeng, S.

Zhao, Y.

Zhou, Z.

Zhuang, X.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

Biophys. J. (1)

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref] [PubMed]

J. Microsc. (1)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[Crossref] [PubMed]

Nat. Methods (1)

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

Opt. Express (5)

Opt. Lett. (5)

Science (1)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Other (2)

M. Gu, Principles Of Three-Dimensional Imaging In Confocal Microscopes (World Scientific Publishing Co Pte Ltd, 1996).

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2005).

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Figures (6)

Fig. 1
Fig. 1 Schematic of an SH system. (a), Hologram recording; (b), (c), (d), image reconstruction. The actual SLM is reflective but is illustrated as transmissive for clarity.
Fig. 2
Fig. 2 Relationship between NAi and MT when NAo is fixed. The blue line is for a classical imaging system in which the Lagrange invariant holds.
Fig. 3
Fig. 3 Changes in the resolving power by altering NAi or MT in a wide-field system where the Lagrange invariant holds. (a), (c), Case w#1, NAi = Ls/1000, MT = 22.2; (b), (d), case w#2, NAi = Ls/592, MT = 13.2. Scale bar, 50 μm.
Fig. 4
Fig. 4 Influence of NAi on the resolving power when MT remains unchanged. (a), (c), Case #1, NAi = Ls/550, MT = 22.2; (b), (d), case #2, NAi = Ls/2200, MT = 22.2. Cases #1 and #2 have the same lateral MT as case w#1, but case #1 has higher NAi while case #2 has lower NAi. Scale bar, 50 μm.
Fig. 5
Fig. 5 Influence of MT on the resolving power when NAi keeps unchanged. (a), (c), Case #3, NAi = Ls/1000, MT = 39.5; (b), (d), case #4, NAi = Ls/1000, MT = 13.2. For each object, cases #3 and #4 have the same NAi as case w#1, but case #3 has larger MT while case #4 has smaller MT. Because of differences in magnification, the size and contrast of images have been adjusted and some margin areas have been cut for display. Scale bar, 50 μm.
Fig. 6
Fig. 6 Comparison of the spectrum. (a), Spectral distribution of the wide-field image given in Fig. 3(c). (b), Spectral distribution of the holographic image given in Fig. 4(c).

Tables (1)

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Table 1 Parameters for each experiment (zs = 0).

Equations (6)

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U 1 * ( x,y ) U 2 ( x,y )=P( r )exp[ ik r 2 2 d r ]exp{ ikx x 10 f o ( f 2 T t1 f 1 T t2 ) T t1 T t2 }
d r = 1 1/ ( l i2 d ) 1/ ( l i1 d )
U( x i , y i )=[ 2 J 1 ( 2π r i L H λ d r ) 2π r i L H λ d r ]δ( x i λ d r + x 10 f o ( f 2 T t1 f 1 T t2 ) λ T t1 T t2 , y i λ d r )
N A i = L H | f 1 f 2 | | ( d f 1 )( d f 2 ) |
M T =d/ f o
δ o =0.61λ/( M T N A i )

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