Abstract

Pupil filters are widely used to improve the resolution of confocal microscopes. We analyze the possibilities of applying them to N-photon microscopy. We find that taking a linear combination of images obtained with several pupil filters can improve the resolution by a factor of N (compared to a conventional microscope). When applied to saturable fluorescence, this technique allows one to observe fluorescent objects with, in principle, unlimited spatial resolution.

© 2009 Optical Society of America

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2008

M. Yamanaka, S. Kawano, K. Fujita, N. I. Smith, and S. Kawata, J. Biomed. Opt. 13, 050507 (2008).
[CrossRef] [PubMed]

N. R. Ben-Haim and D. Oron, Opt. Lett. 33, 2089 (2008).
[CrossRef] [PubMed]

2007

K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, Phys. Rev. Lett. 99, 228105 (2007).
[CrossRef]

S. W. Hell, Science 316, 1153 (2007).
[CrossRef] [PubMed]

2006

M. J. Rust, M. Bates, and X. Zhuang, Nat. Methods 3, 793 (2006).
[CrossRef] [PubMed]

R. Heintzmann and G. Ficz, Briefings Funct. Genomics Proteomics 5, 289 (2006).
[CrossRef]

2005

2004

S. W. Hell, M. Dyba, and S. Jakobs, Curr. Opin. Neurobiol. 14, 599 (2004).
[CrossRef] [PubMed]

2003

2002

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, Nat. Methods 3, 793 (2006).
[CrossRef] [PubMed]

Ben-Haim, N. R.

Blanca, C.

Caballero, M.

Cheng, J.-X.

J.-X. Cheng, Y. K. Jia, G. Zheng, and X. S. Xie, Biophys. J. 83, 502 (2002).
[CrossRef] [PubMed]

Cremer, C.

Dyba, M.

S. W. Hell, M. Dyba, and S. Jakobs, Curr. Opin. Neurobiol. 14, 599 (2004).
[CrossRef] [PubMed]

Ficz, G.

R. Heintzmann and G. Ficz, Briefings Funct. Genomics Proteomics 5, 289 (2006).
[CrossRef]

Fujita, K.

M. Yamanaka, S. Kawano, K. Fujita, N. I. Smith, and S. Kawata, J. Biomed. Opt. 13, 050507 (2008).
[CrossRef] [PubMed]

K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, Phys. Rev. Lett. 99, 228105 (2007).
[CrossRef]

Gundu, P.

Gustafsson, M. G. L.

M. G. L. Gustafsson, Proc. Natl. Acad. Sci. USA 102, 13081 (2005).
[CrossRef] [PubMed]

Hack, E.

Heintzmann, R.

R. Heintzmann and G. Ficz, Briefings Funct. Genomics Proteomics 5, 289 (2006).
[CrossRef]

R. Heintzmann, T. M. Jovin, and C. Cremer, J. Opt. Soc. Am. A 19, 1599 (2002).
[CrossRef]

Hell, S. W.

S. W. Hell, Science 316, 1153 (2007).
[CrossRef] [PubMed]

S. W. Hell, M. Dyba, and S. Jakobs, Curr. Opin. Neurobiol. 14, 599 (2004).
[CrossRef] [PubMed]

C. Blanca and S. W. Hell, Opt. Express 10, 893 (2002).
[PubMed]

Ibáñez López, C.

Jakobs, S.

S. W. Hell, M. Dyba, and S. Jakobs, Curr. Opin. Neurobiol. 14, 599 (2004).
[CrossRef] [PubMed]

Jia, Y. K.

J.-X. Cheng, Y. K. Jia, G. Zheng, and X. S. Xie, Biophys. J. 83, 502 (2002).
[CrossRef] [PubMed]

Jovin, T. M.

Kawano, S.

M. Yamanaka, S. Kawano, K. Fujita, N. I. Smith, and S. Kawata, J. Biomed. Opt. 13, 050507 (2008).
[CrossRef] [PubMed]

K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, Phys. Rev. Lett. 99, 228105 (2007).
[CrossRef]

Kawata, S.

M. Yamanaka, S. Kawano, K. Fujita, N. I. Smith, and S. Kawata, J. Biomed. Opt. 13, 050507 (2008).
[CrossRef] [PubMed]

K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, Phys. Rev. Lett. 99, 228105 (2007).
[CrossRef]

Kobayashi, M.

K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, Phys. Rev. Lett. 99, 228105 (2007).
[CrossRef]

Martinez-Corral, M.

Oron, D.

Rastogi, P.

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, Nat. Methods 3, 793 (2006).
[CrossRef] [PubMed]

Saavedra, G.

Smith, N. I.

M. Yamanaka, S. Kawano, K. Fujita, N. I. Smith, and S. Kawata, J. Biomed. Opt. 13, 050507 (2008).
[CrossRef] [PubMed]

Webb, W. W.

R. M. Williams, W. R. Zipfel, and W. W. Webb, Nat. Biotechnol. 21, 1369 (2003).
[CrossRef] [PubMed]

Williams, R. M.

R. M. Williams, W. R. Zipfel, and W. W. Webb, Nat. Biotechnol. 21, 1369 (2003).
[CrossRef] [PubMed]

Xie, X. S.

J.-X. Cheng, Y. K. Jia, G. Zheng, and X. S. Xie, Biophys. J. 83, 502 (2002).
[CrossRef] [PubMed]

Yamanaka, M.

M. Yamanaka, S. Kawano, K. Fujita, N. I. Smith, and S. Kawata, J. Biomed. Opt. 13, 050507 (2008).
[CrossRef] [PubMed]

K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, Phys. Rev. Lett. 99, 228105 (2007).
[CrossRef]

Zheng, G.

J.-X. Cheng, Y. K. Jia, G. Zheng, and X. S. Xie, Biophys. J. 83, 502 (2002).
[CrossRef] [PubMed]

Zhuang, X.

M. J. Rust, M. Bates, and X. Zhuang, Nat. Methods 3, 793 (2006).
[CrossRef] [PubMed]

Zipfel, W. R.

R. M. Williams, W. R. Zipfel, and W. W. Webb, Nat. Biotechnol. 21, 1369 (2003).
[CrossRef] [PubMed]

Biophys. J.

J.-X. Cheng, Y. K. Jia, G. Zheng, and X. S. Xie, Biophys. J. 83, 502 (2002).
[CrossRef] [PubMed]

Briefings Funct. Genomics Proteomics

R. Heintzmann and G. Ficz, Briefings Funct. Genomics Proteomics 5, 289 (2006).
[CrossRef]

Curr. Opin. Neurobiol.

S. W. Hell, M. Dyba, and S. Jakobs, Curr. Opin. Neurobiol. 14, 599 (2004).
[CrossRef] [PubMed]

J. Biomed. Opt.

M. Yamanaka, S. Kawano, K. Fujita, N. I. Smith, and S. Kawata, J. Biomed. Opt. 13, 050507 (2008).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Nat. Biotechnol.

R. M. Williams, W. R. Zipfel, and W. W. Webb, Nat. Biotechnol. 21, 1369 (2003).
[CrossRef] [PubMed]

Nat. Methods

M. J. Rust, M. Bates, and X. Zhuang, Nat. Methods 3, 793 (2006).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, Phys. Rev. Lett. 99, 228105 (2007).
[CrossRef]

Proc. Natl. Acad. Sci. USA

M. G. L. Gustafsson, Proc. Natl. Acad. Sci. USA 102, 13081 (2005).
[CrossRef] [PubMed]

Science

S. W. Hell, Science 316, 1153 (2007).
[CrossRef] [PubMed]

Other

T.Wilson, ed., Confocal Microscopy (Academic, 1990).

R.W.Boyd, ed., Nonlinear Optics (Academic, 2003).

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Figures (2)

Fig. 1
Fig. 1

(a) Right to left, PSF of nonconfocal microscope P 1 , of confocal microscope P 2 , and of confocal microscope with adjusted illumination pattern P 3 . (b) Example of 2D PSF of two-photon nonconfocal microscope. The PSF with double resolution jinc 2 ( 2 r ) (dashed curve) is approximated with the difference I 1 2 ( r ) I 2 2 ( r ) (solid curve). I 1 and I 2 are given by Eq. (4) with a 0 = 1.58 , a 1 = 0.45 , a 2 = 0.17 ; b 0 = 1.51 , b 1 = 0.5 , b 2 = 0.16 .

Fig. 2
Fig. 2

Two terms of the expression (5) (thin curves) and the resulting PSF (thick curve) plotted for I 0 = 10 .

Equations (6)

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

sinc 2 ( 3 x ) = 1 9 sinc 2 ( x ) ( 2 cos ( 2 x ) 1 ) 2 .
P eff = 1 9 sinc 2 ( x ) ( 12 I 1 2 + 4 I 2 2 3 I 3 2 ) = sinc 2 ( 3 x ) .
Q = sinc 2 ( x ) ( 12 I 1 2 + 4 I 2 2 3 I 3 2 ) d x sinc 2 ( x ) ( 12 I 1 2 + 4 I 2 2 + 3 I 3 2 ) d x = 1 3 .
I 1 = ( n = 0 2 a n jinc ( r 2 n ) ) 2 ; I 2 = ( n = 0 2 b n jinc ( r 2 n ) ) 2 ,
P eff ( x ) = [ S ( I 2 ( x ) ) S ( I 1 ( x ) ) ] sinc 2 ( x ) ,
Q = [ S ( I 2 ( x ) ) S ( I 1 ( x ) ) ] sinc 2 ( x ) d x [ S ( I 2 ( x ) ) + S ( I 1 ( x ) ) ] sinc 2 ( x ) d x 0.13 .

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