Abstract

Temporal focusing (TF) allows for axially confined wide-field multi-photon excitation at the temporal focal plane. For temporally focused Gaussian beams, it was shown both theoretically and experimentally that the temporal focus plane can be shifted by applying a quadratic spectral phase to the incident beam. However, the case for more complex wave-fronts is quite different. Here we study the temporal focus plane shift (TFS) for a broader class of excitation profiles, with particular emphasis on the case of temporally focused computer generated holography (CGH) which allows for generation of arbitrary, yet speckled, 2D patterns. We present an analytical, numerical and experimental study of this phenomenon. The TFS is found to depend mainly on the autocorrelation of the CGH pattern in the direction of the beam dispersion after the grating in the TF setup. This provides a pathway for 3D control of multi-photon excitation patterns.

© 2014 Optical Society of America

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References

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2013 (4)

E. Papagiakoumou, A. Bègue, B. Leshem, O. Schwartz, B. M. Stell, J. Bradley, D. Oron, V. Emiliani, “Functional patterned multiphoton excitation deep inside scattering tissue,” Nat. Photonics 7, 274–278 (2013).
[CrossRef]

E. Block, M. Greco, D. Vitek, O. Masihzadeh, D. A. Ammar, M. Y. Kahook, N. Mandava, C. Durfee, J. Squier, “Simultaneous spatial and temporal focusing for tissue ablation,” Bio. Opt. Express 4, 831–841 (2013).
[CrossRef]

I. Reutsky-Gefen, L. Golan, N. Farah, A. Schejter, L. Tsur, I. Brosh, S. Shoham, “Holographic optogenetic stimulation of patterned neuronal activity for vision restoration,” Nat. Commun. 4, 1509 (2013).
[CrossRef] [PubMed]

E. Yew, C. J. R. Sheppard, P. T. C. So, “Temporally focused wide-field two-photon microscopy: Paraxial to vectorial,” Opt. Express 21, 12951–12963 (2013).
[CrossRef] [PubMed]

2012 (2)

H. Dana, S. Shoham, “Remotely scanned multiphoton temporal focusing by axial grism scanning,” Opt. Lett. 37, 2913–2915 (2012).
[CrossRef] [PubMed]

D. Oron, E. Papagiakoumou, F. Anselmi, V. Emiliani, “Two-photon optogenetics,” Prog. Brain Res. 196, 119–143 (2012).
[CrossRef] [PubMed]

2011 (2)

S. Yang, E. Papagiakoumou, M. Guillon, V. de Sars, C.-M. Tang, V. Emiliani, “Three-dimensional holographic photostimulation of the dendritic arbor,” J. Neur. Eng. 8, 046002 (2011).
[CrossRef]

F. Anselmi, C. Ventalon, A. Bègue, D. Ogden, V. Emiliani, “Three-dimensional imaging and photostimulation by remote-focusing and holographic light patterning,” Proc. Natl. Acad. Sci. U. S. A. 108, 19504–19509 (2011).
[CrossRef] [PubMed]

2010 (1)

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7, 848–854 (2010).
[CrossRef] [PubMed]

2008 (4)

A. Vaziri, J. Tang, H. Shroff, C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl Acad. Sci. U. S. A. 105, 20221–20226 (2008).
[CrossRef] [PubMed]

M. E. Durst, G. Zhu, C. Xu, “Simultaneous spatial and temporal focusing in nonlinear microscopy,” Opt. Commun. 281, 1796–1805 (2008).
[CrossRef] [PubMed]

C. Lutz, T. S. Otis, V. de Sars, S. Charpak, D. A. DiGregorio, V. Emiliani, “Holographic photolysis of caged neurotransmitters,” Nat. Methods 5, 821–827 (2008).
[CrossRef]

E. Papagiakoumou, V. de Sars, D. Oron, V. Emiliani, “Patterned two-photon illumination by spatiotemporal shaping of ultrashort pulses,” Opt. Express 16, 22039–22047 (2008).
[CrossRef] [PubMed]

2006 (2)

M. E. Durst, G. Zhu, C. Xu, “Simultaneous spatial and temporal focusing for axial scanning,” Opt. Express 14, 12243–12254 (2006).
[CrossRef] [PubMed]

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

2005 (2)

2002 (1)

J. E. Curtis, B. A. Koss, D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

1999 (1)

1987 (1)

O. Martinez, “3000 times grating compressor with positive group velocity dispersion: Application to fiber compensation in 1.3–1.6 μm region,” IEEE J. Quantum Electron. 23, 59–64 (1987).
[CrossRef]

1972 (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Ammar, D. A.

E. Block, M. Greco, D. Vitek, O. Masihzadeh, D. A. Ammar, M. Y. Kahook, N. Mandava, C. Durfee, J. Squier, “Simultaneous spatial and temporal focusing for tissue ablation,” Bio. Opt. Express 4, 831–841 (2013).
[CrossRef]

Anselmi, F.

D. Oron, E. Papagiakoumou, F. Anselmi, V. Emiliani, “Two-photon optogenetics,” Prog. Brain Res. 196, 119–143 (2012).
[CrossRef] [PubMed]

F. Anselmi, C. Ventalon, A. Bègue, D. Ogden, V. Emiliani, “Three-dimensional imaging and photostimulation by remote-focusing and holographic light patterning,” Proc. Natl. Acad. Sci. U. S. A. 108, 19504–19509 (2011).
[CrossRef] [PubMed]

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7, 848–854 (2010).
[CrossRef] [PubMed]

Bègue, A.

E. Papagiakoumou, A. Bègue, B. Leshem, O. Schwartz, B. M. Stell, J. Bradley, D. Oron, V. Emiliani, “Functional patterned multiphoton excitation deep inside scattering tissue,” Nat. Photonics 7, 274–278 (2013).
[CrossRef]

F. Anselmi, C. Ventalon, A. Bègue, D. Ogden, V. Emiliani, “Three-dimensional imaging and photostimulation by remote-focusing and holographic light patterning,” Proc. Natl. Acad. Sci. U. S. A. 108, 19504–19509 (2011).
[CrossRef] [PubMed]

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7, 848–854 (2010).
[CrossRef] [PubMed]

A. Bègue, E. Papagiakoumou, B. Leshem, R. Conti, L. Enke, D. Oron, V. Emiliani, “Multiphoton excitation in scattering media by holographic beams and their application in optogenetic stimulation,” Biomed. Opt. Express (to be published) (2013).
[CrossRef]

Block, E.

E. Block, M. Greco, D. Vitek, O. Masihzadeh, D. A. Ammar, M. Y. Kahook, N. Mandava, C. Durfee, J. Squier, “Simultaneous spatial and temporal focusing for tissue ablation,” Bio. Opt. Express 4, 831–841 (2013).
[CrossRef]

Bradley, J.

E. Papagiakoumou, A. Bègue, B. Leshem, O. Schwartz, B. M. Stell, J. Bradley, D. Oron, V. Emiliani, “Functional patterned multiphoton excitation deep inside scattering tissue,” Nat. Photonics 7, 274–278 (2013).
[CrossRef]

Brosh, I.

I. Reutsky-Gefen, L. Golan, N. Farah, A. Schejter, L. Tsur, I. Brosh, S. Shoham, “Holographic optogenetic stimulation of patterned neuronal activity for vision restoration,” Nat. Commun. 4, 1509 (2013).
[CrossRef] [PubMed]

Charpak, S.

C. Lutz, T. S. Otis, V. de Sars, S. Charpak, D. A. DiGregorio, V. Emiliani, “Holographic photolysis of caged neurotransmitters,” Nat. Methods 5, 821–827 (2008).
[CrossRef]

Choi, H.

E. Y. S. Yew, H. Choi, D. Kim, P. T. C. So, “Wide-field two-photon microscopy with temporal focusing and hilo background rejection,” in “SPIE BiOS” (International Society for Optics and Photonics, 2011), p. 79031O.

Conti, R.

A. Bègue, E. Papagiakoumou, B. Leshem, R. Conti, L. Enke, D. Oron, V. Emiliani, “Multiphoton excitation in scattering media by holographic beams and their application in optogenetic stimulation,” Biomed. Opt. Express (to be published) (2013).
[CrossRef]

Curtis, J. E.

J. E. Curtis, B. A. Koss, D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

Dana, H.

de Sars, V.

S. Yang, E. Papagiakoumou, M. Guillon, V. de Sars, C.-M. Tang, V. Emiliani, “Three-dimensional holographic photostimulation of the dendritic arbor,” J. Neur. Eng. 8, 046002 (2011).
[CrossRef]

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7, 848–854 (2010).
[CrossRef] [PubMed]

C. Lutz, T. S. Otis, V. de Sars, S. Charpak, D. A. DiGregorio, V. Emiliani, “Holographic photolysis of caged neurotransmitters,” Nat. Methods 5, 821–827 (2008).
[CrossRef]

E. Papagiakoumou, V. de Sars, D. Oron, V. Emiliani, “Patterned two-photon illumination by spatiotemporal shaping of ultrashort pulses,” Opt. Express 16, 22039–22047 (2008).
[CrossRef] [PubMed]

DiGregorio, D. A.

C. Lutz, T. S. Otis, V. de Sars, S. Charpak, D. A. DiGregorio, V. Emiliani, “Holographic photolysis of caged neurotransmitters,” Nat. Methods 5, 821–827 (2008).
[CrossRef]

Durfee, C.

E. Block, M. Greco, D. Vitek, O. Masihzadeh, D. A. Ammar, M. Y. Kahook, N. Mandava, C. Durfee, J. Squier, “Simultaneous spatial and temporal focusing for tissue ablation,” Bio. Opt. Express 4, 831–841 (2013).
[CrossRef]

Durst, M. E.

Emiliani, V.

E. Papagiakoumou, A. Bègue, B. Leshem, O. Schwartz, B. M. Stell, J. Bradley, D. Oron, V. Emiliani, “Functional patterned multiphoton excitation deep inside scattering tissue,” Nat. Photonics 7, 274–278 (2013).
[CrossRef]

D. Oron, E. Papagiakoumou, F. Anselmi, V. Emiliani, “Two-photon optogenetics,” Prog. Brain Res. 196, 119–143 (2012).
[CrossRef] [PubMed]

F. Anselmi, C. Ventalon, A. Bègue, D. Ogden, V. Emiliani, “Three-dimensional imaging and photostimulation by remote-focusing and holographic light patterning,” Proc. Natl. Acad. Sci. U. S. A. 108, 19504–19509 (2011).
[CrossRef] [PubMed]

S. Yang, E. Papagiakoumou, M. Guillon, V. de Sars, C.-M. Tang, V. Emiliani, “Three-dimensional holographic photostimulation of the dendritic arbor,” J. Neur. Eng. 8, 046002 (2011).
[CrossRef]

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7, 848–854 (2010).
[CrossRef] [PubMed]

C. Lutz, T. S. Otis, V. de Sars, S. Charpak, D. A. DiGregorio, V. Emiliani, “Holographic photolysis of caged neurotransmitters,” Nat. Methods 5, 821–827 (2008).
[CrossRef]

E. Papagiakoumou, V. de Sars, D. Oron, V. Emiliani, “Patterned two-photon illumination by spatiotemporal shaping of ultrashort pulses,” Opt. Express 16, 22039–22047 (2008).
[CrossRef] [PubMed]

A. Bègue, E. Papagiakoumou, B. Leshem, R. Conti, L. Enke, D. Oron, V. Emiliani, “Multiphoton excitation in scattering media by holographic beams and their application in optogenetic stimulation,” Biomed. Opt. Express (to be published) (2013).
[CrossRef]

Enke, L.

A. Bègue, E. Papagiakoumou, B. Leshem, R. Conti, L. Enke, D. Oron, V. Emiliani, “Multiphoton excitation in scattering media by holographic beams and their application in optogenetic stimulation,” Biomed. Opt. Express (to be published) (2013).
[CrossRef]

Farah, N.

I. Reutsky-Gefen, L. Golan, N. Farah, A. Schejter, L. Tsur, I. Brosh, S. Shoham, “Holographic optogenetic stimulation of patterned neuronal activity for vision restoration,” Nat. Commun. 4, 1509 (2013).
[CrossRef] [PubMed]

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Glückstad, J.

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7, 848–854 (2010).
[CrossRef] [PubMed]

Golan, L.

I. Reutsky-Gefen, L. Golan, N. Farah, A. Schejter, L. Tsur, I. Brosh, S. Shoham, “Holographic optogenetic stimulation of patterned neuronal activity for vision restoration,” Nat. Commun. 4, 1509 (2013).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Publishers, 2007).

Greco, M.

E. Block, M. Greco, D. Vitek, O. Masihzadeh, D. A. Ammar, M. Y. Kahook, N. Mandava, C. Durfee, J. Squier, “Simultaneous spatial and temporal focusing for tissue ablation,” Bio. Opt. Express 4, 831–841 (2013).
[CrossRef]

Grier, D. G.

J. E. Curtis, B. A. Koss, D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

Guillon, M.

S. Yang, E. Papagiakoumou, M. Guillon, V. de Sars, C.-M. Tang, V. Emiliani, “Three-dimensional holographic photostimulation of the dendritic arbor,” J. Neur. Eng. 8, 046002 (2011).
[CrossRef]

Haist, T.

Isacoff, E. Y.

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7, 848–854 (2010).
[CrossRef] [PubMed]

Kahook, M. Y.

E. Block, M. Greco, D. Vitek, O. Masihzadeh, D. A. Ammar, M. Y. Kahook, N. Mandava, C. Durfee, J. Squier, “Simultaneous spatial and temporal focusing for tissue ablation,” Bio. Opt. Express 4, 831–841 (2013).
[CrossRef]

Kim, D.

E. Y. S. Yew, H. Choi, D. Kim, P. T. C. So, “Wide-field two-photon microscopy with temporal focusing and hilo background rejection,” in “SPIE BiOS” (International Society for Optics and Photonics, 2011), p. 79031O.

Koss, B. A.

J. E. Curtis, B. A. Koss, D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

Leshem, B.

E. Papagiakoumou, A. Bègue, B. Leshem, O. Schwartz, B. M. Stell, J. Bradley, D. Oron, V. Emiliani, “Functional patterned multiphoton excitation deep inside scattering tissue,” Nat. Photonics 7, 274–278 (2013).
[CrossRef]

A. Bègue, E. Papagiakoumou, B. Leshem, R. Conti, L. Enke, D. Oron, V. Emiliani, “Multiphoton excitation in scattering media by holographic beams and their application in optogenetic stimulation,” Biomed. Opt. Express (to be published) (2013).
[CrossRef]

Lutz, C.

C. Lutz, T. S. Otis, V. de Sars, S. Charpak, D. A. DiGregorio, V. Emiliani, “Holographic photolysis of caged neurotransmitters,” Nat. Methods 5, 821–827 (2008).
[CrossRef]

Mandava, N.

E. Block, M. Greco, D. Vitek, O. Masihzadeh, D. A. Ammar, M. Y. Kahook, N. Mandava, C. Durfee, J. Squier, “Simultaneous spatial and temporal focusing for tissue ablation,” Bio. Opt. Express 4, 831–841 (2013).
[CrossRef]

Martinez, O.

O. Martinez, “3000 times grating compressor with positive group velocity dispersion: Application to fiber compensation in 1.3–1.6 μm region,” IEEE J. Quantum Electron. 23, 59–64 (1987).
[CrossRef]

Masihzadeh, O.

E. Block, M. Greco, D. Vitek, O. Masihzadeh, D. A. Ammar, M. Y. Kahook, N. Mandava, C. Durfee, J. Squier, “Simultaneous spatial and temporal focusing for tissue ablation,” Bio. Opt. Express 4, 831–841 (2013).
[CrossRef]

Menon, R.

P. Wang, R. Menon, “Three-dimensional lithography via digital holography,” in “Frontiers in Optics” (Optical Society of America, 2012).

Ogden, D.

F. Anselmi, C. Ventalon, A. Bègue, D. Ogden, V. Emiliani, “Three-dimensional imaging and photostimulation by remote-focusing and holographic light patterning,” Proc. Natl. Acad. Sci. U. S. A. 108, 19504–19509 (2011).
[CrossRef] [PubMed]

Oron, D.

E. Papagiakoumou, A. Bègue, B. Leshem, O. Schwartz, B. M. Stell, J. Bradley, D. Oron, V. Emiliani, “Functional patterned multiphoton excitation deep inside scattering tissue,” Nat. Photonics 7, 274–278 (2013).
[CrossRef]

D. Oron, E. Papagiakoumou, F. Anselmi, V. Emiliani, “Two-photon optogenetics,” Prog. Brain Res. 196, 119–143 (2012).
[CrossRef] [PubMed]

E. Papagiakoumou, V. de Sars, D. Oron, V. Emiliani, “Patterned two-photon illumination by spatiotemporal shaping of ultrashort pulses,” Opt. Express 16, 22039–22047 (2008).
[CrossRef] [PubMed]

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

D. Oron, E. Tal, Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express 13, 1468–1476 (2005).
[CrossRef] [PubMed]

A. Bègue, E. Papagiakoumou, B. Leshem, R. Conti, L. Enke, D. Oron, V. Emiliani, “Multiphoton excitation in scattering media by holographic beams and their application in optogenetic stimulation,” Biomed. Opt. Express (to be published) (2013).
[CrossRef]

Otis, T. S.

C. Lutz, T. S. Otis, V. de Sars, S. Charpak, D. A. DiGregorio, V. Emiliani, “Holographic photolysis of caged neurotransmitters,” Nat. Methods 5, 821–827 (2008).
[CrossRef]

Papagiakoumou, E.

E. Papagiakoumou, A. Bègue, B. Leshem, O. Schwartz, B. M. Stell, J. Bradley, D. Oron, V. Emiliani, “Functional patterned multiphoton excitation deep inside scattering tissue,” Nat. Photonics 7, 274–278 (2013).
[CrossRef]

D. Oron, E. Papagiakoumou, F. Anselmi, V. Emiliani, “Two-photon optogenetics,” Prog. Brain Res. 196, 119–143 (2012).
[CrossRef] [PubMed]

S. Yang, E. Papagiakoumou, M. Guillon, V. de Sars, C.-M. Tang, V. Emiliani, “Three-dimensional holographic photostimulation of the dendritic arbor,” J. Neur. Eng. 8, 046002 (2011).
[CrossRef]

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7, 848–854 (2010).
[CrossRef] [PubMed]

E. Papagiakoumou, V. de Sars, D. Oron, V. Emiliani, “Patterned two-photon illumination by spatiotemporal shaping of ultrashort pulses,” Opt. Express 16, 22039–22047 (2008).
[CrossRef] [PubMed]

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I. Reutsky-Gefen, L. Golan, N. Farah, A. Schejter, L. Tsur, I. Brosh, S. Shoham, “Holographic optogenetic stimulation of patterned neuronal activity for vision restoration,” Nat. Commun. 4, 1509 (2013).
[CrossRef] [PubMed]

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R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Schejter, A.

I. Reutsky-Gefen, L. Golan, N. Farah, A. Schejter, L. Tsur, I. Brosh, S. Shoham, “Holographic optogenetic stimulation of patterned neuronal activity for vision restoration,” Nat. Commun. 4, 1509 (2013).
[CrossRef] [PubMed]

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E. Papagiakoumou, A. Bègue, B. Leshem, O. Schwartz, B. M. Stell, J. Bradley, D. Oron, V. Emiliani, “Functional patterned multiphoton excitation deep inside scattering tissue,” Nat. Photonics 7, 274–278 (2013).
[CrossRef]

Shank, C. V.

A. Vaziri, J. Tang, H. Shroff, C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl Acad. Sci. U. S. A. 105, 20221–20226 (2008).
[CrossRef] [PubMed]

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I. Reutsky-Gefen, L. Golan, N. Farah, A. Schejter, L. Tsur, I. Brosh, S. Shoham, “Holographic optogenetic stimulation of patterned neuronal activity for vision restoration,” Nat. Commun. 4, 1509 (2013).
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A. Vaziri, J. Tang, H. Shroff, C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl Acad. Sci. U. S. A. 105, 20221–20226 (2008).
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E. Block, M. Greco, D. Vitek, O. Masihzadeh, D. A. Ammar, M. Y. Kahook, N. Mandava, C. Durfee, J. Squier, “Simultaneous spatial and temporal focusing for tissue ablation,” Bio. Opt. Express 4, 831–841 (2013).
[CrossRef]

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E. Papagiakoumou, A. Bègue, B. Leshem, O. Schwartz, B. M. Stell, J. Bradley, D. Oron, V. Emiliani, “Functional patterned multiphoton excitation deep inside scattering tissue,” Nat. Photonics 7, 274–278 (2013).
[CrossRef]

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H. Suchowski, D. Oron, Y. Silberberg, “Generation of a dark nonlinear focus by spatio-temporal coherent control,” Opt. Commun. 264, 482–487 (2006).
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S. Yang, E. Papagiakoumou, M. Guillon, V. de Sars, C.-M. Tang, V. Emiliani, “Three-dimensional holographic photostimulation of the dendritic arbor,” J. Neur. Eng. 8, 046002 (2011).
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A. Vaziri, J. Tang, H. Shroff, C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl Acad. Sci. U. S. A. 105, 20221–20226 (2008).
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I. Reutsky-Gefen, L. Golan, N. Farah, A. Schejter, L. Tsur, I. Brosh, S. Shoham, “Holographic optogenetic stimulation of patterned neuronal activity for vision restoration,” Nat. Commun. 4, 1509 (2013).
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A. Vaziri, J. Tang, H. Shroff, C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl Acad. Sci. U. S. A. 105, 20221–20226 (2008).
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F. Anselmi, C. Ventalon, A. Bègue, D. Ogden, V. Emiliani, “Three-dimensional imaging and photostimulation by remote-focusing and holographic light patterning,” Proc. Natl. Acad. Sci. U. S. A. 108, 19504–19509 (2011).
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E. Block, M. Greco, D. Vitek, O. Masihzadeh, D. A. Ammar, M. Y. Kahook, N. Mandava, C. Durfee, J. Squier, “Simultaneous spatial and temporal focusing for tissue ablation,” Bio. Opt. Express 4, 831–841 (2013).
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Bio. Opt. Express (1)

E. Block, M. Greco, D. Vitek, O. Masihzadeh, D. A. Ammar, M. Y. Kahook, N. Mandava, C. Durfee, J. Squier, “Simultaneous spatial and temporal focusing for tissue ablation,” Bio. Opt. Express 4, 831–841 (2013).
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J. Neur. Eng. (1)

S. Yang, E. Papagiakoumou, M. Guillon, V. de Sars, C.-M. Tang, V. Emiliani, “Three-dimensional holographic photostimulation of the dendritic arbor,” J. Neur. Eng. 8, 046002 (2011).
[CrossRef]

Nat. Commun. (1)

I. Reutsky-Gefen, L. Golan, N. Farah, A. Schejter, L. Tsur, I. Brosh, S. Shoham, “Holographic optogenetic stimulation of patterned neuronal activity for vision restoration,” Nat. Commun. 4, 1509 (2013).
[CrossRef] [PubMed]

Nat. Methods (2)

C. Lutz, T. S. Otis, V. de Sars, S. Charpak, D. A. DiGregorio, V. Emiliani, “Holographic photolysis of caged neurotransmitters,” Nat. Methods 5, 821–827 (2008).
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E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7, 848–854 (2010).
[CrossRef] [PubMed]

Nat. Photonics (1)

E. Papagiakoumou, A. Bègue, B. Leshem, O. Schwartz, B. M. Stell, J. Bradley, D. Oron, V. Emiliani, “Functional patterned multiphoton excitation deep inside scattering tissue,” Nat. Photonics 7, 274–278 (2013).
[CrossRef]

Opt. Commun. (3)

M. E. Durst, G. Zhu, C. Xu, “Simultaneous spatial and temporal focusing in nonlinear microscopy,” Opt. Commun. 281, 1796–1805 (2008).
[CrossRef] [PubMed]

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

J. E. Curtis, B. A. Koss, D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[CrossRef]

Opt. Express (5)

Opt. Lett. (2)

Optik (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Proc. Natl Acad. Sci. U. S. A. (1)

A. Vaziri, J. Tang, H. Shroff, C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl Acad. Sci. U. S. A. 105, 20221–20226 (2008).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U. S. A. (1)

F. Anselmi, C. Ventalon, A. Bègue, D. Ogden, V. Emiliani, “Three-dimensional imaging and photostimulation by remote-focusing and holographic light patterning,” Proc. Natl. Acad. Sci. U. S. A. 108, 19504–19509 (2011).
[CrossRef] [PubMed]

Prog. Brain Res. (1)

D. Oron, E. Papagiakoumou, F. Anselmi, V. Emiliani, “Two-photon optogenetics,” Prog. Brain Res. 196, 119–143 (2012).
[CrossRef] [PubMed]

Other (5)

A. Bègue, E. Papagiakoumou, B. Leshem, R. Conti, L. Enke, D. Oron, V. Emiliani, “Multiphoton excitation in scattering media by holographic beams and their application in optogenetic stimulation,” Biomed. Opt. Express (to be published) (2013).
[CrossRef]

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Publishers, 2007).

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005).

P. Wang, R. Menon, “Three-dimensional lithography via digital holography,” in “Frontiers in Optics” (Optical Society of America, 2012).

E. Y. S. Yew, H. Choi, D. Kim, P. T. C. So, “Wide-field two-photon microscopy with temporal focusing and hilo background rejection,” in “SPIE BiOS” (International Society for Optics and Photonics, 2011), p. 79031O.

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Figures (7)

Fig. 1
Fig. 1

Sketch of the TF-CGH setup. An Ultra-short pulse reflects off an SLM and is focused onto a diffraction grating (G) through a lens (L1). The first diffraction order is consequently imaged via a tube lens (L2) and an objective to the front focal plane (FFP) of the objective. The incident angle is such that the first order of diffraction is perpendicular to the grating. The SLM is imaged to the back focal plane (BFP) of the objective via lenses L1 and L2. Equation (1) describes the light distribution at the FFP of the objective.

Fig. 2
Fig. 2

a) Illustration of TF beam impinging on a grating when GVD is applied. The temporal shift between “blue” and “red” portions of the temporal spectrum generates a spatial shift as the pulse scans the grating. This is equivalent to shifting the grating in the z-direction as long as the spectral portions can be considered as replicas of one another. b) The same effect but with TF-CGH beams. The autocorrelation width in the x-direction determines the lateral shift for which the spectral portions can be considered to be replicas of one another, which in turn determines the amount of TFS that can be achieved.

Fig. 3
Fig. 3

Axial profile as a function of the applied GVD for the case: a) σx, σy → ∞. b) σx → ∞, σy = 0.3 μm. c) σy → ∞, σx = 0.3 μm.

Fig. 4
Fig. 4

a) Axial profile of a TF-CGH beam when applying GVD of 40000 fs2 vs. σx (with σy → ∞). The superimposed dashed line is the peak position of a TF Gaussian beam with the same amount of GVD applied and beam waist varying as σx. b) The TFS for which the two-photon signal decreases to half its value with no GVD (denoted Δ z 1 2 ), as a function of σx. In both plots the minimum value of σx is 0.3 μm

Fig. 5
Fig. 5

Schematics of the experimental setup. Laser beam from a Ti:Sapphire laser is passed through a grating compressor/stretcher where GVD is applied. The beam then impinges on an SLM and focused into the TF setup, constituted of a diffraction grating, G, and an imaging system. L: Lens, M: Mirror, BE: Beam Expander, OBJ: Microscope Objectives, FFP: Front Focal Plane.

Fig. 6
Fig. 6

Each plot depicts the analytical results for the two-photon axial profiles for different values of the applied GVD. Plots a–d are for different slit widths corresponding to different spatial lowpass filters. a) No slit. b) 1 mm slit with its short axis in the x-direction. c) 1 mm slit with its short axis in the y-direction. d) 2.5 mm iris. The overlayed TF-CGH patterns are presented here for illustration, they are calculated for a single realization of a speckle pattern with a Gaussian envelope with the same parameters as the analytical calculation.

Fig. 7
Fig. 7

The experimental and numerical results corresponding to the ones presented in Fig. 6. Each plot depicts comparison between experimental (circles) and numerical (solid line) results. The overlayed images are the corresponding experimental TF-CGH patterns.

Equations (15)

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E ( x , y , Δ ω ) = A ( x , y ) exp ( i α Δ ω x i β Δ ω 2 Δ ω 2 2 δ 2 )
A ( x , y ) = S ( x , y ) exp ( x 2 + y 2 2 W 2 )
S ( r i ) S ( r j ) = exp ( ( r i r j ) 2 2 σ 2 )
I 2 p ( z ) = | E ( r , z , t ) | 4 d r d t = | E ( r , z = 0 , t ) * h ( r , z ) | 4 d r d t
E ( x , z , t ) = FT ( Δ ω t ) 1 { S ( x ) exp ( x 2 2 W 2 i α Δ ω x i β Δ ω 2 Δ ω 2 2 δ 2 ) } * h ( x , z ) = S ( x ) G ( x , t ) * h ( x , z )
I x 2 p ( z ) = | E ( x , z , t ) | 4 d x d t = 2 d x d t [ d x 1 d x 2 S ( x 1 ) S ( x 2 ) G ( x 1 , t ) G ( x 2 , t ) h ( x x 1 , z ) h ( x x 2 , z ) ] 2
I x 2 p ( z ) = A x ( ( z Δ z ) 2 + z T F 2 ) 1 2
Δ z = T R ( σ x W ) 2 T S ( 1 + T S 2 + T R 2 ) + ( σ x W ) 2 ( T S 2 + ( 1 + T R ) 2 ) z R
z T F 2 = ( 1 + T S 2 + T R ) [ 2 ( 1 + T S 2 ) ( σ x W ) 2 + ( 1 + T S 2 + T R ) ( σ x W ) 4 ] [ ( ( 1 + T R ) 2 + T S 2 ) ( σ x W ) 2 + 2 ( 1 + T R + T S 2 ) ] 2 z R 2
T R = ( W α ) 2 a , T S = b a , z R = k 0 W 2 , A x = π σ x z R 2 a 3 2 [ ( 1 + T S 2 + T R 2 ) + ( σ x W ) 2 ( T S 2 + ( 1 + T R ) 2 ) ] 1 2 .
I y 2 p ( z ) = A y ( 2 W 2 z 2 σ y 2 + z 2 + z R 2 ) 1 2
I 2 p ( z ) = I x 2 p ( z ) I y 2 p ( z )
z T F 1 + T S 2 + T R ( 1 + T R ) 2 + T S 2 z R , Δ z T S T R T S 2 + ( 1 + T R ) 2 z R
I 2 p ( z ) 1 z 2 + z R 2 1 z 2 + z R 2 ( 1 + T R ) 2
I 2 p ( z ) 1 z 2 + z R 2

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