Abstract

Line illumination geometries have advantageous properties for temporal focusing nonlinear microscopy. The characteristics of line temporal focusing (LITEF) in transparent and scattering media are studied here both experimentally and using numerical model simulations. We introduce an approximate analytical formula for the dependence of axial sectioning on the laser and microscope's parameters. Furthermore, we show that LITEF is more robust to tissue scattering than wide-field temporal focusing, and can penetrate much deeper into scattering tissue while maintaining good sectioning capabilities. Based on these observations, we propose a new design for LITEF-based tissue imaging at depths that could potentially exceed the out-of-focus physical excitation limit.

© 2013 OSA

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    [CrossRef] [PubMed]
  24. C. G. Durfee, M. Greco, E. Block, D. Vitek, and J. A. Squier, “Intuitive analysis of space-time focusing with double-ABCD calculation,” Opt. Express20(13), 14244–14259 (2012).
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2012 (4)

2011 (5)

J. Y. Yu, C. H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C. L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16(11), 116009 (2011).
[CrossRef] [PubMed]

H. Dana and S. Shoham, “Numerical evaluation of temporal focusing characteristics in transparent and scattering media,” Opt. Express19(6), 4937–4948 (2011).
[CrossRef] [PubMed]

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]

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods8(4), 327–333 (2011).
[CrossRef] [PubMed]

F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13(8), 083014 (2011).
[CrossRef]

2010 (5)

2009 (2)

2008 (1)

A. Vaziri, J. Tang, H. Shroff, and C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl. Acad. Sci. U.S.A.105(51), 20221–20226 (2008).
[CrossRef] [PubMed]

2006 (2)

2005 (5)

Adams, D. E.

Andrasfalvy, B. K.

B. K. Andrasfalvy, B. V. Zemelman, J. Tang, and A. Vaziri, “Two-photon single-cell optogenetic control of neuronal activity by sculpted light,” Proc. Natl. Acad. Sci. U.S.A.107(26), 11981–11986 (2010).
[CrossRef] [PubMed]

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]

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]

Bellouard, Y.

Blake, G. A.

J. Y. Yu, C. H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C. L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16(11), 116009 (2011).
[CrossRef] [PubMed]

Block, E.

Boas, D. A.

Chang, C. Y.

Chang, N. S.

Chen, S. J.

Chen, Y.

J. Y. Yu, C. H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C. L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16(11), 116009 (2011).
[CrossRef] [PubMed]

Cheng, L. C.

Cheng, Y.

F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13(8), 083014 (2011).
[CrossRef]

Cho, K. C.

Côté, D.

Dana, H.

Davidson, M. W.

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods8(4), 327–333 (2011).
[CrossRef] [PubMed]

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]

E. Papagiakoumou, V. de Sars, V. Emiliani, and D. Oron, “Temporal focusing with spatially modulated excitation,” Opt. Express17(7), 5391–5401 (2009).
[CrossRef] [PubMed]

Denk, W.

Dong, C. Y.

Durfee, C. G.

Durst, M.

Durst, M. E.

Ellman, A.

H. Dana, A. Marom, N. Kruger, A. Ellman, and S. Shoham. “Rapid volumetric temporal focusing multiphoton microscopy of neural activity: theory, image processing, and experimental realization,” Proc. SPIE822603 (2012).

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]

E. Papagiakoumou, V. de Sars, V. Emiliani, and D. Oron, “Temporal focusing with spatially modulated excitation,” Opt. Express17(7), 5391–5401 (2009).
[CrossRef] [PubMed]

Fang, Q.

Ghitani, A.

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods8(4), 327–333 (2011).
[CrossRef] [PubMed]

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]

Greco, M.

Guo, C. L.

J. Y. Yu, C. H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C. L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16(11), 116009 (2011).
[CrossRef] [PubMed]

He, F.

F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13(8), 083014 (2011).
[CrossRef]

Helmchen, F.

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods2(12), 932–940 (2005).
[CrossRef] [PubMed]

Holland, D. B.

J. Y. Yu, C. H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C. L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16(11), 116009 (2011).
[CrossRef] [PubMed]

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.

Kleinfeld, D.

Koninck, P. D.

Kruger, N.

H. Dana, A. Marom, N. Kruger, A. Ellman, and S. Shoham. “Rapid volumetric temporal focusing multiphoton microscopy of neural activity: theory, image processing, and experimental realization,” Proc. SPIE822603 (2012).

Kuo, C. H.

J. Y. Yu, C. H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C. L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16(11), 116009 (2011).
[CrossRef] [PubMed]

Lin, C. Y.

Lin, J.

F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13(8), 083014 (2011).
[CrossRef]

Marom, A.

H. Dana, A. Marom, N. Kruger, A. Ellman, and S. Shoham. “Rapid volumetric temporal focusing multiphoton microscopy of neural activity: theory, image processing, and experimental realization,” Proc. SPIE822603 (2012).

Midorikawa, K.

F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13(8), 083014 (2011).
[CrossRef]

Ni, J.

F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13(8), 083014 (2011).
[CrossRef]

Oron, D.

Ouyang, M.

J. Y. Yu, C. H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C. L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16(11), 116009 (2011).
[CrossRef] [PubMed]

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]

E. Papagiakoumou, V. de Sars, V. Emiliani, and D. Oron, “Temporal focusing with spatially modulated excitation,” Opt. Express17(7), 5391–5401 (2009).
[CrossRef] [PubMed]

Shank, C. V.

A. Vaziri, J. Tang, H. Shroff, and C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl. Acad. Sci. U.S.A.105(51), 20221–20226 (2008).
[CrossRef] [PubMed]

Shoham, S.

Shroff, H.

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods8(4), 327–333 (2011).
[CrossRef] [PubMed]

A. Vaziri, J. Tang, H. Shroff, and C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl. Acad. Sci. U.S.A.105(51), 20221–20226 (2008).
[CrossRef] [PubMed]

Silberberg, Y.

So, P. T. C.

Squier, J. A.

Sugioka, K.

F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13(8), 083014 (2011).
[CrossRef]

Tal, E.

Tang, J.

B. K. Andrasfalvy, B. V. Zemelman, J. Tang, and A. Vaziri, “Two-photon single-cell optogenetic control of neuronal activity by sculpted light,” Proc. Natl. Acad. Sci. U.S.A.107(26), 11981–11986 (2010).
[CrossRef] [PubMed]

A. Vaziri, J. Tang, H. Shroff, and C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl. Acad. Sci. U.S.A.105(51), 20221–20226 (2008).
[CrossRef] [PubMed]

Theer, P.

Therrien, O. D.

Tsai, P. S.

van Howe, J.

Vaziri, A.

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods8(4), 327–333 (2011).
[CrossRef] [PubMed]

B. K. Andrasfalvy, B. V. Zemelman, J. Tang, and A. Vaziri, “Two-photon single-cell optogenetic control of neuronal activity by sculpted light,” Proc. Natl. Acad. Sci. U.S.A.107(26), 11981–11986 (2010).
[CrossRef] [PubMed]

A. Vaziri, J. Tang, H. Shroff, and C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl. Acad. Sci. U.S.A.105(51), 20221–20226 (2008).
[CrossRef] [PubMed]

Vitek, D.

Vitek, D. N.

Xu, C.

Xu, Z.

F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13(8), 083014 (2011).
[CrossRef]

Yen, W. C.

York, A. G.

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods8(4), 327–333 (2011).
[CrossRef] [PubMed]

Yu, J. Y.

J. Y. Yu, C. H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C. L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16(11), 116009 (2011).
[CrossRef] [PubMed]

Zadoyan, R.

J. Y. Yu, C. H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C. L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16(11), 116009 (2011).
[CrossRef] [PubMed]

Zemelman, B. V.

B. K. Andrasfalvy, B. V. Zemelman, J. Tang, and A. Vaziri, “Two-photon single-cell optogenetic control of neuronal activity by sculpted light,” Proc. Natl. Acad. Sci. U.S.A.107(26), 11981–11986 (2010).
[CrossRef] [PubMed]

Zhu, G.

Zipfel, W.

Biomed. Opt. Express (1)

J. Biomed. Opt. (1)

J. Y. Yu, C. H. Kuo, D. B. Holland, Y. Chen, M. Ouyang, G. A. Blake, R. Zadoyan, and C. L. Guo, “Wide-field optical sectioning for live-tissue imaging by plane-projection multiphoton microscopy,” J. Biomed. Opt.16(11), 116009 (2011).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Nat. Methods (3)

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods8(4), 327–333 (2011).
[CrossRef] [PubMed]

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]

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods2(12), 932–940 (2005).
[CrossRef] [PubMed]

New J. Phys. (1)

F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13(8), 083014 (2011).
[CrossRef]

Opt. Express (10)

C. G. Durfee, M. Greco, E. Block, D. Vitek, and J. A. Squier, “Intuitive analysis of space-time focusing with double-ABCD calculation,” Opt. Express20(13), 14244–14259 (2012).
[CrossRef] [PubMed]

Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express17(22), 20178–20190 (2009).
[CrossRef] [PubMed]

M. E. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing for axial scanning,” Opt. Express14(25), 12243–12254 (2006).
[CrossRef] [PubMed]

D. N. Vitek, E. Block, Y. Bellouard, D. E. Adams, S. Backus, D. Kleinfeld, C. G. Durfee, and J. A. Squier, “Spatio-temporally focused femtosecond laser pulses for nonreciprocal writing in optically transparent materials,” Opt. Express18(24), 24673–24678 (2010).
[CrossRef] [PubMed]

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]

L. C. Cheng, C. Y. Chang, C. Y. Lin, K. C. Cho, W. C. Yen, N. S. Chang, C. Xu, C. Y. Dong, and S. J. Chen, “Spatiotemporal focusing-based widefield multiphoton microscopy for fast optical sectioning,” Opt. Express20(8), 8939–8948 (2012).
[CrossRef] [PubMed]

D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express13(5), 1468–1476 (2005).
[CrossRef] [PubMed]

G. 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]

E. Papagiakoumou, V. de Sars, V. Emiliani, and D. Oron, “Temporal focusing with spatially modulated excitation,” Opt. Express17(7), 5391–5401 (2009).
[CrossRef] [PubMed]

H. Dana and S. Shoham, “Numerical evaluation of temporal focusing characteristics in transparent and scattering media,” Opt. Express19(6), 4937–4948 (2011).
[CrossRef] [PubMed]

Opt. Lett. (3)

Proc. Natl. Acad. Sci. U.S.A. (2)

B. K. Andrasfalvy, B. V. Zemelman, J. Tang, and A. Vaziri, “Two-photon single-cell optogenetic control of neuronal activity by sculpted light,” Proc. Natl. Acad. Sci. U.S.A.107(26), 11981–11986 (2010).
[CrossRef] [PubMed]

A. Vaziri, J. Tang, H. Shroff, and C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl. Acad. Sci. U.S.A.105(51), 20221–20226 (2008).
[CrossRef] [PubMed]

Proc. SPIE (1)

H. Dana, A. Marom, N. Kruger, A. Ellman, and S. Shoham. “Rapid volumetric temporal focusing multiphoton microscopy of neural activity: theory, image processing, and experimental realization,” Proc. SPIE822603 (2012).

Other (1)

E. Papagiakoumou, A. Bègue, O. Schwartz, D. Oron, and V. Emiliani, “Shaped two-photon excitation deep inside scattering tissue,” arXiv preprint arXiv:1109.0160 (2011).

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Figures (7)

Fig. 1
Fig. 1

Experimental system outline. (a) LITEF optical setup and inverted detection setup. Laser beam is focused by a cylindrical lens to a line (y axis) on the DPG transmission grating surface; the DPG is designed to diffract the laser beam and maintain the laser’s central wavelength in the same propagation direction. The tube and objective lenses image the grating surface onto the objective focal plane, where the pulse duration is minimal. The detection microscope uses a second objective and another lens to image the fluorescence on a CCD. (b) Detailed view of the sample region. Scattering samples were set over a 5µm layer of fluorescein. Measurements were obtained by axially moving objective 2 and the sample. (c) xz and yz projections of images taken at different distances from the TF focal plane using Nikon 40x NA = 0.8 objective (beam waist 0.75µm, line length 125µm). (d) Measurements (dots) of axial optical sectioning of the data shown in (c).

Fig. 2
Fig. 2

Numerical simulation of LITEF light propagation. (a) Schematic demonstration of light propagation in temporal and spatial focusing planes (xz and yz respectively), near the objective lens focal plane. Different colors in the xz planes represents different spectral components, each one is propagating in a different direction (β) and tilted in a different angle (α). (b) Snapshot of light propagation on the optical axis (in logarithmic scale), taken from the simulation. (c) Projections of simulated LITEF illumination of 5µm fluorescent layer (blurring by the imaging system was not simulated). (d) Optical sectioning curves for thin fluorescent layer (thickness0, blue line) and 5µm fluorescent layer (black line). Optical parameters: M = 40, NA = 0.8, w0 = 0.75µm, l = 50µm.

Fig. 3
Fig. 3

Model validation. Measured axial optical sectioning (dots) and model’s prediction (lines) for three sets of indicated optical parameters (200fsec pulses).

Fig. 4
Fig. 4

Comparison of calculated axial optical sectioning for different beam waists (dots) and best-fit products of two square roots of Lorentz-Cauchy functions (lines). Optical parameters: M = 20, NA = 1, l = 50µm, tau = 100fsec.

Fig. 5
Fig. 5

Comparison of LITEF calculated optical sectioning and its analytical approximation. (a) Scatter plot of the estimated Lorentz-Cauchy parameters, according to Eqs. (2) and (3), and their calculation from fitting the functions to the numerical model results. Error bars in right panel indicates standard deviation. (b) Comparison of model calculated optical sectioning (dots) vs. Equations (2) and (3) (lines). Optical parameters are indicated next to each graph.

Fig. 6
Fig. 6

Scattering effects. (a) Optical sectioning of two optical setups at different scattering depths. Dots represent experimental measurements; rectangles are model calculation results (connected by a dotted line). Insets show model’s prediction vs. experimental measurements for sectioning profile, and xy/xz projection images taken at specific points in the graph. Optical parameters: 1) M = 12, NA = 0.45, l = 500µm, w = 1 µm, tau = 200fsec. 2) M = 40, NA = 0.8, l = 125 µm, w = 0.75 µm, tau = 200fsec. (b) Measured attenuation of the LITEF signal (logarithmic scale) and exponential fit as a function of scattering phantom thickness. (c) Comparison of broadening of optical sectioning FWHM through 500µm of the scattering phantom for the two LITEF setups from (a, b) vs. WITEF broadening for setup 2 (ref [5].) and vs. expected optical sectioning of a spatially-focused beam (TPLSM, ref [23].). (d) TPLSM excitation decay constant [23] vs. decay constant ranges measured in LITEF (panel b), and WITEF [5] in scattering phantoms.

Fig. 7
Fig. 7

Ultra-deep penetration into scattering phantom. A 15µm line is illuminated through more than 9 scattering MFPs without significant loss of optical sectioning. Dots represent experimental measurements, rectangles - model calculations results (connected by a dotted line). Insets show optical sectioning measurements and their model predictions for specific depths.

Equations (3)

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α= cot 1 ( n f / n DPG Msin α cosβ tanβ )
F= 1 1+ ( z/ z R1 ) 2 1+ ( z/ z R2 ) 2
z R1 = k 1 + τ k 2 τ l + k 3 MN A 2 , z R2 = k 4 w 0 2

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