Abstract

Temporal focusing allows for optically sectioned wide-field microscopy. The optical sectioning arises because this method takes a pulsed input beam, stretches the pulses by diffracting off a grating, and focuses the stretched pulses such that only at the focal plane are the pulses re-compressed. This approach generates nonlinear optical processes at the focal plane and results in depth discrimination. Prior theoretical models of temporal focusing processes approximate the contributions of the different spectral components by their mean. This is valid for longer pulses that have narrower spectral bandwidth but results in a systematic deviation when broad spectrum, femtosecond pulses are used. Further, prior model takes the paraxial approximation but since these pulses are focused with high numerical aperture (NA) objectives, the effects of the vectorial nature of light should be considered. In this paper we present a paraxial and a vector theory of temporal focusing that takes into account the finite spread of the spectrum. Using paraxial theory we arrive at an analytical solution to the electric field at the focus for temporally focused wide-field two-photon (TF2p) microscopy as well as in the case of a spectrally chirped input beam. We find that using paraxial theory while accounting for the broad spectral spread gives results almost twice vector theory. Experiment results agree with predictions of the vector theory giving an axial full-width half maximum (FWHM) of 2.1μmand1.8μmrespectively as long as spectral spread is taken into account. Using our system parameters, the optical sectioning of the TF2p microscope is found to be 8μm. The optical transfer function (OTF) of a TF2p microscope is also derived and is found to pass a significantly more limited band of axial frequencies than a point scanning two-photon (2p) microscope or a single photon (1p) confocal microscope.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express13(5), 1468–1476 (2005).
    [CrossRef] [PubMed]
  2. G. H. Zhu, J. van Howe, M. Durst, W. Zipfel, and C. Xu, “Simultaneous spatial and temporal focusing of femtosecond pulses,” Opt. Express13(6), 2153–2159 (2005).
    [CrossRef] [PubMed]
  3. A. Vaziri and C. V. Shank, “Ultrafast widefield optical sectioning microscopy by multifocal temporal focusing,” Opt. Express18(19), 19645–19655 (2010).
    [CrossRef] [PubMed]
  4. E. Tal, D. Oron, and Y. Silberberg, “Improved depth resolution in video-rate line-scanning multiphoton microscopy using temporal focusing,” Opt. Lett.30(13), 1686–1688 (2005).
    [CrossRef] [PubMed]
  5. O. D. Therrien, B. Aubé, S. Pagès, P. D. Koninck, and D. Côté, “Wide-field multiphoton imaging of cellular dynamics in thick tissue by temporal focusing and patterned illumination,” Biomed. Opt. Express2(3), 696–704 (2011).
    [CrossRef] [PubMed]
  6. E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods7(10), 848–854 (2010).
    [CrossRef] [PubMed]
  7. D. Kim and P. T. C. So, “High-throughput three-dimensional lithographic microfabrication,” Opt. Lett.35(10), 1602–1604 (2010).
    [CrossRef] [PubMed]
  8. Y.-C. Li, L.-C. Cheng, C.-Y. Chang, C.-H. Lien, P. J. Campagnola, and S.-J. Chen, “Fast multiphoton microfabrication of freeform polymer microstructures by spatiotemporal focusing and patterned excitation,” Opt. Express20(17), 19030–19038 (2012).
    [CrossRef] [PubMed]
  9. D. N. Vitek, D. E. Adams, A. Johnson, P. S. Tsai, S. Backus, C. G. Durfee, D. Kleinfeld, and J. A. Squier, “Temporally focused femtosecond laser pulses for low numerical aperture micromachining through optically transparent materials,” Opt. Express18(17), 18086–18094 (2010).
    [CrossRef] [PubMed]
  10. C. Froehly, B. Colombeau, and M. Vampouille, “II Shaping and Analysis of Picosecond Light Pulses,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1983), pp. 63–153.
  11. O. E. Martinez, J. P. Gordon, and R. L. Fork, “Negative group-velocity dispersion using refraction,” J. Opt. Soc. Am. A1(10), 1003–1006 (1984).
    [CrossRef]
  12. M. E. Durst, G. H. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing for axial scanning,” Opt. Express14(25), 12243–12254 (2006).
    [CrossRef] [PubMed]
  13. H. Suchowski, D. Oron, and Y. Silberberg, “Generation of a dark nonlinear focus by spatio-temporal coherent control,” Opt. Commun.264(2), 482–487 (2006).
    [CrossRef]
  14. M. M. Wefers and K. A. Nelson, “Space-time profiles of shaped utrafast optical waveforms,” IEEE J. Quantum Electron.32(1), 161–172 (1996).
    [CrossRef]
  15. M. B. Danailov and I. P. Christov, “Time-Space Shaping of Light-Pulses by Fourier Optical-Processing,” J. Mod. Opt.36(6), 725–731 (1989).
    [CrossRef]
  16. O. E. Martinez, “Grating and Prism Compressors in the Case of Finite Beam Size,” J. Opt. Soc. Am. B3(7), 929–934 (1986).
    [CrossRef]
  17. D. Oron and Y. Silberberg, “Harmonic generation with temporally focused ultrashort pulses,” J. Opt. Soc. Am. B22(12), 2660–2663 (2005).
    [CrossRef]
  18. B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
    [CrossRef]
  19. C. J. R. Sheppard and K. G. Larkin, “The three-dimensional transfer function and phase space mappings,” Optik (Stuttg.)112(5), 189–192 (2001).
    [CrossRef]
  20. M. R. Arnison and C. J. R. Sheppard, “A 3D vectorial optical transfer function suitable for arbitrary pupil functions,” Opt. Commun.211(1-6), 53–63 (2002).
    [CrossRef]
  21. S. Akturk, X. Gu, M. Kimmel, and R. Trebino, “Extremely simple single-prism ultrashort- pulse compressor,” Opt. Express14(21), 10101–10108 (2006).
    [CrossRef] [PubMed]
  22. C. W. McCutchen, “Generalized Aperture and the Three-Dimensional Diffraction Image,” J. Opt. Soc. Am.54(2), 240–242 (1964).
    [CrossRef]

2012

2011

2010

2006

2005

2002

M. R. Arnison and C. J. R. Sheppard, “A 3D vectorial optical transfer function suitable for arbitrary pupil functions,” Opt. Commun.211(1-6), 53–63 (2002).
[CrossRef]

2001

C. J. R. Sheppard and K. G. Larkin, “The three-dimensional transfer function and phase space mappings,” Optik (Stuttg.)112(5), 189–192 (2001).
[CrossRef]

1996

M. M. Wefers and K. A. Nelson, “Space-time profiles of shaped utrafast optical waveforms,” IEEE J. Quantum Electron.32(1), 161–172 (1996).
[CrossRef]

1989

M. B. Danailov and I. P. Christov, “Time-Space Shaping of Light-Pulses by Fourier Optical-Processing,” J. Mod. Opt.36(6), 725–731 (1989).
[CrossRef]

1986

1984

1964

1959

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
[CrossRef]

Adams, D. E.

Akturk, S.

Anselmi, F.

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods7(10), 848–854 (2010).
[CrossRef] [PubMed]

Arnison, M. R.

M. R. Arnison and C. J. R. Sheppard, “A 3D vectorial optical transfer function suitable for arbitrary pupil functions,” Opt. Commun.211(1-6), 53–63 (2002).
[CrossRef]

Aubé, B.

Backus, S.

Bègue, A.

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods7(10), 848–854 (2010).
[CrossRef] [PubMed]

Campagnola, P. J.

Chang, C.-Y.

Chen, S.-J.

Cheng, L.-C.

Christov, I. P.

M. B. Danailov and I. P. Christov, “Time-Space Shaping of Light-Pulses by Fourier Optical-Processing,” J. Mod. Opt.36(6), 725–731 (1989).
[CrossRef]

Côté, D.

Danailov, M. B.

M. B. Danailov and I. P. Christov, “Time-Space Shaping of Light-Pulses by Fourier Optical-Processing,” J. Mod. Opt.36(6), 725–731 (1989).
[CrossRef]

de Sars, V.

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods7(10), 848–854 (2010).
[CrossRef] [PubMed]

Durfee, C. G.

Durst, M.

Durst, M. E.

Emiliani, V.

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods7(10), 848–854 (2010).
[CrossRef] [PubMed]

Fork, R. L.

Glückstad, J.

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods7(10), 848–854 (2010).
[CrossRef] [PubMed]

Gordon, J. P.

Gu, X.

Isacoff, E. Y.

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods7(10), 848–854 (2010).
[CrossRef] [PubMed]

Johnson, A.

Kim, D.

Kimmel, M.

Kleinfeld, D.

Koninck, P. D.

Larkin, K. G.

C. J. R. Sheppard and K. G. Larkin, “The three-dimensional transfer function and phase space mappings,” Optik (Stuttg.)112(5), 189–192 (2001).
[CrossRef]

Li, Y.-C.

Lien, C.-H.

Martinez, O. E.

McCutchen, C. W.

Nelson, K. A.

M. M. Wefers and K. A. Nelson, “Space-time profiles of shaped utrafast optical waveforms,” IEEE J. Quantum Electron.32(1), 161–172 (1996).
[CrossRef]

Oron, D.

Pagès, S.

Papagiakoumou, E.

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods7(10), 848–854 (2010).
[CrossRef] [PubMed]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
[CrossRef]

Shank, C. V.

Sheppard, C. J. R.

M. R. Arnison and C. J. R. Sheppard, “A 3D vectorial optical transfer function suitable for arbitrary pupil functions,” Opt. Commun.211(1-6), 53–63 (2002).
[CrossRef]

C. J. R. Sheppard and K. G. Larkin, “The three-dimensional transfer function and phase space mappings,” Optik (Stuttg.)112(5), 189–192 (2001).
[CrossRef]

Silberberg, Y.

So, P. T. C.

Squier, J. A.

Suchowski, H.

H. Suchowski, D. Oron, and Y. Silberberg, “Generation of a dark nonlinear focus by spatio-temporal coherent control,” Opt. Commun.264(2), 482–487 (2006).
[CrossRef]

Tal, E.

Therrien, O. D.

Trebino, R.

Tsai, P. S.

van Howe, J.

Vaziri, A.

Vitek, D. N.

Wefers, M. M.

M. M. Wefers and K. A. Nelson, “Space-time profiles of shaped utrafast optical waveforms,” IEEE J. Quantum Electron.32(1), 161–172 (1996).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
[CrossRef]

Xu, C.

Zhu, G. H.

Zipfel, W.

Biomed. Opt. Express

IEEE J. Quantum Electron.

M. M. Wefers and K. A. Nelson, “Space-time profiles of shaped utrafast optical waveforms,” IEEE J. Quantum Electron.32(1), 161–172 (1996).
[CrossRef]

J. Mod. Opt.

M. B. Danailov and I. P. Christov, “Time-Space Shaping of Light-Pulses by Fourier Optical-Processing,” J. Mod. Opt.36(6), 725–731 (1989).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nat. Methods

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods7(10), 848–854 (2010).
[CrossRef] [PubMed]

Opt. Commun.

H. Suchowski, D. Oron, and Y. Silberberg, “Generation of a dark nonlinear focus by spatio-temporal coherent control,” Opt. Commun.264(2), 482–487 (2006).
[CrossRef]

M. R. Arnison and C. J. R. Sheppard, “A 3D vectorial optical transfer function suitable for arbitrary pupil functions,” Opt. Commun.211(1-6), 53–63 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Optik (Stuttg.)

C. J. R. Sheppard and K. G. Larkin, “The three-dimensional transfer function and phase space mappings,” Optik (Stuttg.)112(5), 189–192 (2001).
[CrossRef]

Proc. R. Soc. Lond. A Math. Phys. Sci.

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
[CrossRef]

Other

C. Froehly, B. Colombeau, and M. Vampouille, “II Shaping and Analysis of Picosecond Light Pulses,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1983), pp. 63–153.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

The excitation beam is incident on the grating (G) at some angle θ in such that the central wavelength λ 0 propagates along the optical axis after the grating. The grating disperses the spectrum of the pulse at some angle θ d,λ which is dependent on the wavelength. The focusing tube lens (TL) focuses the spectrum at the back focal plane (BFP) of the objective (Obj). The function of the objective is to form an image of the grating in the object space. It is here that all the colors overlap thereby creating a plane of high photon flux necessary for nonlinear optical phenomenon.

Fig. 2
Fig. 2

(a) The envelope of the temporal focus i.e I TF2p ( z ) for the paraxial approximation (open blue circles) and that calculated from vector theory (red line). The FWHM for the paraxial approach is 15.6 μm whereas for the vector approach is 7.6 μm. (b) and (c) are the contour plots of the neck region of the OTF for paraxial and vector cases respectively.

Fig. 3
Fig. 3

(a) Slice view of the OTF for a 1p fluorescence wide-field microscope. The missing cone indicates that no axial information is transmitted. On the other hand, (b) is the slice of the 1p confocal microscope. The missing cone has been filled in and has optical sectioning. A similar OTF is found for (c) a conventional 2p microscope. (d) is the slice OTF of a TF2p microscope. The approximate extent of the OTF has been outlined in white as a visual aid.

Fig. 4
Fig. 4

Plotting the transfer function along the s-axis indicates that the frequency support for TF2p is close to half that of the conventional 2p transfer function. The 1p confocal has a frequency support twice that of conventional 2p. The cut-off frequency for the 2p microscope is about twice as large as that of a TF2p microscope. In all cases, the excitation wavelength was 790 nm and the emission wavelength of 395 nm.

Fig. 5
Fig. 5

Comparison between the numerically calculated OTF and that obtained experimentally. (a) The cross-section of the numerically calculated OTF and (b) experimentally obtained OTF. In both cases, the excitation wavelength was 790 nm and the emission wavelength was taken as 485 nm for (a).

Fig. 6
Fig. 6

Axial intensity of the image of a bead. Excitation and imaging was done with the same objective, a Zeiss 40x NA 1.3 oil immersion objective. The experiment (blue open circles) yielded a FWHM of 2.1 μm whereas numerical calculations (red solid line) gave a FWHM of 1.8 μm.

Fig. 7
Fig. 7

A thick layer of Rhodamine was scanned through the temporal focus and the recorded signal (blue, solid line) is plotted. The first derivative of the signal was obtained and a curve fitted to it (red, dashed line). Both are measures of the optical sectioning property of the TF2p microscope.

Fig. 8
Fig. 8

A thin layer of fluorescence (red open circles) was scanned through the temporal focus and the captured image was summed over an area corresponding to around 2 Airy Units (AU). This experiment is equivalent to taking the first derivative of the optical response to a sea of fluorescence. The data is compared to vector theory (blue line) and a good fit is obtained between experiment and theory.

Tables (2)

Tables Icon

Table 1 List of variables used

Tables Icon

Table 2 Shift of temporal focus with chirp

Equations (16)

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

E G ( x G ;Δk )= b G exp( iγcΔk x G ψ 2 x G 2 s G 2 ),
A( Δω )= τ 2 1ia exp( i τ 2 Δ ω 2 4( i+a ) ).
E BFP ( x BFP ;Δk )=A( Δω ) ¯ [ E G ( x G ;Δk ) ] = b BFP A( Δω )exp( ( x BFP x 0 ) 2 s BFP 2 ).
E TF,0 ( x TF ;Δk )= b TF A( Δω )exp( ψ 2 x TF 2 M 2 s G 2 icΔkγ x TF M ).
E TF ( dz,Δω )= b TF exp( i γ 2 dz 2 k 0 M 2 + 8d z 2 ψ 2 k 0 M 2 s G 4 Δ ω 2 i τ 2 4( i+a ) Δ ω 2 ) b TF exp( i γ 2 dz 2 k 0 M 2 Δ ω 2 i τ 2 4( i+a ) Δ ω 2 ).
I TF2p ( dz )= | ˜ [ E TF,0 h ] | 4 1 1+ 4a γ 2 M 2 k 0 τ 2 dz+ 4( 1+ a 2 ) γ 4 M 4 k 0 2 τ 4 d z 2 1 1+ ( a+ Γ( 1+ a 2 ) M 2 dz ) 2 .
I TF2p ( dz ) 1 1+ ( a+χ Δ ν 2 M 2 dz ) 2 .
E( x,y,z )= Q( ξ,η ) exp( ikq·r ) dξdη ς ,
P( ξ,η )= Q( ξ,η ) ς .
a( ξ,η,ς )=( ( ξ 2 ς+ η 2 ) / l 2 ξη( 1ς ) / l 2 ξ ),
P( ξ,η )=a( ξ,η )S( ξ,η )Φ( ξ,η ),
E BFP ( x BFP , y BFP , z BFP ;Δk )=A( Δk ) ¯ (2) [ exp( iγΔωx )exp( y BFP 2 + ψ 2 x BFP 2 s G 2 ) ] =A( Δk )exp( ψ 2 y BFP 2 + ( x BFP x 0 ) 2 s BFP 2 ),
x 0 = 2mπ f TL Δk ( Δk+ k 0 )d 1 ( 2mπ d( Δk+ k 0 ) sin θ in ) 2 .
E TF,0 ( x,y,z,Δk;z )= ¯ (2) [ P( ξ,η,ς,Δk )exp( i k z z i τ 2 c 2 Δ k 2 4( i+a ) ) ].
E TF ( x,y,z,t )= Δk Δk E TF,0 ( x,y,Δk;z )exp ( ic k 0 t )d( Δk ) = ˜ [ E TF,0 ( x,y,Δk;z ) ].
I TF2p ( z )= C( 0,0,s )exp( izs )ds .

Metrics