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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 6 — Mar. 14, 2011
  • pp: 4937–4948
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Numerical evaluation of temporal focusing characteristics in transparent and scattering media

Hod Dana and Shy Shoham  »View Author Affiliations


Optics Express, Vol. 19, Issue 6, pp. 4937-4948 (2011)
http://dx.doi.org/10.1364/OE.19.004937


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Abstract

Temporal focusing is a simple approach for achieving tight, optically sectioned excitation in nonlinear microscopy and multiphoton photo-manipulation. Key applications and advantages of temporal focusing involve propagation through scattering media, but the progressive broadening of the temporal focus has not been characterized. By combining a detailed geometrical optics model with Monte-Carlo scattering simulations we introduce and validate a simulation strategy for predicting temporal focusing characteristics in scattering and non-scattering media. The broadening of the temporal focus width with increasing depth in brain tissue is studied using both simulations and experiments for several key optical geometries, and an analytical approximation is found for the dependence of this broadening on the microscope’s parameters in a transparent medium. Our results indicate that a multiphoton temporal focus has radically different broadening characteristics in deep tissue than those of a spatial focus.

© 2011 OSA

1. Introduction

Temporal focusing (TF) nonlinear microscopy [1

1. D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express 13(5), 1468–1476 (2005). [CrossRef] [PubMed]

4

4. M. E. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing in nonlinear microscopy,” Opt. Commun. 281(7), 1796–1805 (2008). [CrossRef] [PubMed]

] enables optically-sectioned excitation of a thin plane inside a three dimensional (3D) volume without the need to spatially focus the light beam. TF thus allows to benefit from the unique capacity of nonlinear optical methods to achieve microscopic sectioning deep inside scattering biological tissue [5

5. F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2(12), 932–940 (2005). [CrossRef] [PubMed]

] (or other scattering media) without being constrained to near-diffraction-limited excitation spots that have to be scanned across regions of interest. In imaging applications, this allows scan-less illumination of relatively large light spots while obtaining optically sectioned images in conventional [1

1. D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express 13(5), 1468–1476 (2005). [CrossRef] [PubMed]

,2

2. 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]

,6

6. 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]

] and super-resolution [6

6. 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]

] fluorescence, and harmonic generation [7

7. D. Oron and Y. Silberberg, “Harmonic generation with temporally focused ultrashort pulses,” J. Opt. Soc. B 22(12), 2660–2663 (2005). [CrossRef]

] microscopy. Moreover, the ability TF provides to decouple the lateral and axial focal dimensions, that are typically jointly determined by the numerical aperture (∝NA−1 and ∝NA−2 respectively for a focused Gaussian beam), also renders it a powerful method for shaping multiphoton light-matter interaction geometries as in bulk micromachining [8

8. 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. Express 18(17), 18086–18094 (2010). [CrossRef] [PubMed]

,9

9. D. Kim and P. T. C. So, “High-throughput three-dimensional lithographic microfabrication,” Opt. Lett. 35(10), 1602–1604 (2010). [CrossRef] [PubMed]

] and optogenetic neural stimulation [10

10. 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]

12

12. S. Shoham, “Optogenetics meets optical wavefront shaping,” Nat. Methods 7(10), 798–799 (2010). [CrossRef] [PubMed]

].

2. Methods

2.1. Model and simulations

In this section, we present a geometrical optics model for the propagation of a temporally-focused light beam, which analyzes the propagation of individual spectral elements from the objective's front aperture to the focal plane and sums these individual contributions (a conceptually similar decomposition was used in Ref. [4

4. M. E. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing in nonlinear microscopy,” Opt. Commun. 281(7), 1796–1805 (2008). [CrossRef] [PubMed]

].). The effect of light scattering is introduced by convolving the light intensities with appropriate scattering kernels computed by a time-resolved Monte-Carlo simulation [17

17. D. Boas, J. Culver, J. Stott, and A. Dunn, “Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head,” Opt. Express 10(3), 159–170 (2002). [PubMed]

].

The modeled light propagation scheme of a basic TF setup is illustrated in Fig. 1
Fig. 1 Schematic representation of light propagation in a TF setup. Light propagating at an angle α' (with its wavefront tilted by the same angle) hits a diffraction grating, causing each spectral component to diffract at a specific angle and a different tilt angle. After passing through a collimating and a focusing lens each spectral component moves towards the TF plane with a propagation angle β and tilt angle α. Since all optical paths from the grating to the focal plane are equal (Fermat's principle), all the spectral components scan the TF plane simultaneously, and α and β are coupled.
(a two-dimensional coordinate system provides a sufficient description for modeling wide-field TF propagation). A delta pulse beam, tilted by an angle α' with respect to the optical axis (z axis), propagates in the direction α', and impinges upon a diffraction grating. A collimating lens (of focal length f1) and a focusing lens (objective, focal length f2) arranged in a 4f configuration image the grating onto the latter’s focal plane with a magnification factor of M=f1/f2. After undergoing diffraction by the grating, the collection of rays belonging to each spectral component propagates along a different optical path; near the focal plane, each is imaged onto a line (a plane in 3D) tilted at an angle α relative to the optical axis but propagating at another relative angle, β.

To obtain the relation between α and β we observe first that according to Fermat's principle, all impinging spectral components scan the focal plane simultaneously with a scanning speed [1

1. D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express 13(5), 1468–1476 (2005). [CrossRef] [PubMed]

] of c/(nMsinα). On the other hand, from elementary geometrical considerations we obtain that a spectral component which propagates in direction β, tilted by an angle α, scans the focal plane with scanning speed of ccos(αβ)/(nsinα). Equating these two expressions, we get:

α=cot1(1Msinαcosβtanβ).
(1)

To compute the suggested model and simulate the TF performance in a non-scattering medium we allocated a satisfactory number of spectral elements on the front aperture of the focusing lens (21-57 elements): β values were equally spaced between -βmax and βmax, determined by the focusing lens’s numerical aperture, and the laser Gaussian spectral profile was introduced by assigning different weights to each spectral component, α values for every element were computed according to Eq. (1). To optimize the TF optical sectioning properties while maintaining a high laser power transmission efficiency we chose to model the case where the Gaussian beam's 1/e diameter equals the objective's aperture diameter. A more excessive filling would result in better optical sectioning compared to the presented results, while underfilling of the objective's back aperture would result in a lower effective NA and worsen the optical sectioning. This assumption holds across all the presented model calculations, and allows treating the NA independently of the system's other parameters. Experimentally, this means that when the magnification, the beam diameter or the spectral bandwidth (i.e., pulse duration) is changed, the objective's aperture filling must be compensated.

Each spectral component scans the entire focal plane length l (the laser beam diameter divided by M) and, therefore, it is modeled as a segment with length lcosβ/(cos(αβ)). The time delays between different spectral components were set in a way that the center of all spectral components would overlap with the center of the TF plane at a specific time. At each time step all the components are moved forward towards their respective β direction and their intensities summed. The model results for a specific laser source were finally obtained by convolving the light intensity distribution computed for a delta pulse beam and the laser pulse’s temporal profile and then squaring the computed intensity to obtain a signal proportional to the fluorescence resulting from two-photon TF excitation.

To introduce scattering effects into the model, we computed scattering kernels, in advance, for various scattering depths using a time-resolved Monte-Carlo simulation [17

17. D. Boas, J. Culver, J. Stott, and A. Dunn, “Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head,” Opt. Express 10(3), 159–170 (2002). [PubMed]

] for a medium with a scattering mean free path of 200μm, g = 0.9 and negligible absorption. Upon entering the scattering medium, the different spectral elements’ intensity distributions are convolved with the matching scattering kernels. Since each spectral component has a different orientation as it enters the scattering medium, we rotated the matching scattering kernel by the same angle to precisely simulate the scattering directions.

2.2. Experimental methods

Our TF experimental setup for scanningless illumination is illustrated in Fig. 2
Fig. 2 Experimental system outline. (a) TF optical setup: 800nm laser, beam expander (BE), diffraction grating, collimating lens (CL), and focusing objective lens (obj 1). Objective 2 (obj 2) and another lens image the sample onto a CCD. (b) Detailed view of the sample region. Scattering samples were set over a thin layer with 10μm fluorescent beads. Measurements were obtained by axially moving objective 2 and the sample. (c) xz section through a stack of experimental images of beads taken at different distances from the TF focal plane and under different scattering phantom depths, using 60x magnification and NA = 1. (d) Non-scattering optical sectioning cross-section used for pulse duration estimation.
. The experimental setup is based on an upright microscope for illuminating the sample from above and an inverted imaging system for imaging the sample from below without encountering scattering effects on the emitted light. The excitation source was an amplified 800nm ultrafast laser (RegA 9000, pumped and seeded by a Vitesse duo; Coherent), providing 15-150mW of average power at the sample plane at a 150KHz repetition rate (0.1-1µJ/pulse). After passing through a beam expander and an electro-optic modulator (Conoptics), the beam hits a diffraction grating (1200 grooves/mm, Newport Corporation) with α'=30. An f = 200mm tube lens (Nikon) was used as a collimating lens and two interchangeable objective lenses (Nikon 60x, NA = 1 and Nikon 40x, NA = 0.8) as focusing lenses for illuminating TF planes with diameters of 50µm or 75µm, respectively. A scattering tissue phantom (described below) was placed near the objective's focal plane. To measure the fluorescent light intensity on the opposite side of the sample we used a second objective lens (Leica 40x NA = 0.8), an imaging lens and a 768x576 pixels CCD camera (UEye 2220SE-M, IDS). The scattering sample and the second objective lens were mounted onto two micromanipulators (MP-285 and MP-225 respectively, Sutter), which were used to move the sample and the detection system to controlled distances from the TF plane with 1 µm steps.

Coronal cortical brain slices of varying thickness were prepared from 15 to 25 days-old Sprague Dawley rats according to a standard surgical and preparation procedure [21

21. Y. Ikegaya, M. Le Bon-Jego, and R. Yuste, “Large-scale imaging of cortical network activity with calcium indicators,” Neurosci. Res. 52(2), 132–138 (2005). [CrossRef] [PubMed]

] which was approved by the institutional ethics committee. The slices were similarly placed on top of a fluorescent sample of 10 µm fluorescent beads. The typical scattering mean free path and anisotropy factor for near infrared wavelengths in rat cerebral cortex are also approximately 200µm and 0.9 respectively [5

5. F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2(12), 932–940 (2005). [CrossRef] [PubMed]

,22

22. D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, “Fluctuations and stimulus-induced changes in blood flow observed in individual capillaries in layers 2 through 4 of rat neocortex,” Proc. Natl. Acad. Sci. U.S.A. 95(26), 15741–15746 (1998). [CrossRef] [PubMed]

,23

23. M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods 111(1), 29–37 (2001). [CrossRef] [PubMed]

].

A pulse duration of ~200fs was measured at the laser’s output using an autocorrelator (PulseCheck, APE). Pulse duration at the TF focal plane (after passing through all of the optical components) was estimated to be 325fs by fitting the (scatter-free) TF optical sectioning measurements to model predictions for different pulse durations (see Fig. 2d).

3. Results

3.1 Model validation

To examine the model’s accuracy we tested its predictions of TF’s central characteristic – the optical sectioning width – in scattering and non-scattering media. Optical sectioning was experimentally measured by axially scanning across the focal plane 10 µm fluorescent beads that were located underneath biological (rat cortical slices) and non-biological scattering media of various thicknesses (see section 2.2 for details). Results of these measurements and model predictions (τ = 325fs) for two different optical setup parameters (different objective lenses) are shown in Fig. 3
Fig. 3 Evaluation of model accuracy for optical sectioning of 10 µm fluorescent beads in different TF setups and scattering depths. Setup 1 has a magnification of 40, NA = 0.8 and TF plane diameter of 75 µm, while setup 2 has a magnification of 60, NA = 1 and TF plane diameter of 50 µm (τ = 325fs). The experimental error bars indicate the means and standard deviations, while solid lines indicate the model simulations (computed at scattering depth steps of 50µm). Insets: examples of experimental sectioning traces of two individual beads vs. model prediction.
. The underlying optical sectioning FWHM (i.e., without the beads – data not shown) increases from 7.25µm to 52µm for the 60x objective and from 16.5µm to 93µm for the 40x objective.

3.2 Dependence on optical parameters in non-scattering media

The results shown in Fig. 3 demonstrate that picking a specific objective changes not only the illuminated cross-section, but also the axial thickness of the TF focal volume. Therefore, an optical setup's NA and magnification could potentially be used to control the characteristics of TF setups: optical sectioning, illuminated volume dimensions, efficient use of laser source power or robustness to scattering. In order to investigate the magnification’s role, we simulated a situation where a constant-size TF plane is illuminated by setups with different magnifications. This scenario may be realized by adding a beam expander before the diffraction grating, which changes the beam diameter so that the ratio of beam diameter to magnification remains constant. The results, shown in Fig. 4
Fig. 4 The effect of varying magnifications on TF sectioning. Dots show model results for different magnifications and solid lines show a square-root of a Lorentzian fit (optical parameters: NA = 0.8, TF plane diameter of 15μm, pulse duration - 325fs).
, highlight the fact that the magnification has a significant effect on the TF plane’s width.

Arguably, the most interesting question is the importance of using a high NA objective. In contrast to standard scanning techniques, the importance of high NA objectives as a part of TF setup is less clear. Simulation results for TF performance using a constant magnification and different NA objectives are shown in Fig. 5d for scattering and non-scattering media.

3.3 Analytical approximation

3.4 Single-cell excitation optics

As mentioned in the introduction, TF optical systems were recently applied in the development of single-cell optogenetic multiphoton photo-stimulation systems. The experimental setup presented in Ref. [10

10. 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]

]. used a combination of a pulse duration of 140fs, very high magnification (180) and a high NA (1.2) to illuminate a 6μm diameter TF plane with a measured axial width (FWHM) of ≈1.6μm. The possibility of using this system for deep-tissue stimulation is an exciting but as yet unexplored possibility. To study the performance of this system at various depths we studied the model’s behavior inside a brain-like scattering medium with a Henyey-Greenstein phase function (g = 0.9).

The simulation FWHM in a non-scattering medium was calculated to be 1.25 µm, slightly better than the experimental value that was reported (≈1.6 µm). In a scattering medium this value remained almost constant up to a scattering depth of 400μm (Fig. 6a
Fig. 6 Predicted performance of a single-cell TF optogenetic system (Ref. [10].) in a scattering medium. (a) Optical sectioning under different scattering depths. (b) Comparison of signal attenuation of TF based optical systems inside a scattering medium. Blue: simulation results for the single-cell excitation system (dots) and exponential fit (125µm decay constant, solid line); Green: simulation results for setup 2 in Fig. 3(dots) and exponential fit (190 µm decay constant, solid line). Black: expected exponential decay for TPLSM signal (100µm decay constant). (c) and (d) x-z view of fluorescence distribution inside a non-scattering and a 400 µm deep scattering media, respectively.
). However, this parameter alone does not fully describe the excitation distribution, since large tails can be seen to develop outside the focal plane. In addition, the excitation peak decays exponentially with a decay parameter of ≈125μm (Fig. 6b). This decay rate is slower than the expected attenuation rate of a TPLSM signal in the same scattering medium (100μm), but is faster than the expected decay for the 60x wide-field illumination geometry described in section 3.1. The combination of exponential decay and loss of localization due to scattering sets the ultimate limit at which such a system is useful.

4. Discussion and conclusions

A new numerical approach for calculating planar TF performance in transparent and scattering media was introduced, studied and shown to agree well with experimental results, both in scattering phantoms and in ex-vivo brain samples. This model and its analytical approximation for non-scattering media (Eq. (3) are likely to prove useful for in-depth analysis and design in the rapidly growing field of TF-based optical systems. As noted above, our analysis focused on the illumination’s sectioning performance because of its universal importance to all kinds of TF optical systems, but a complete evaluation of the performance of imaging TF systems will clearly also require accounting for the scattering of the emitted light.

Our approach is based on geometrical considerations and ray-tracing and, therefore, does not take into account any phase dependent effects, such as light diffraction. This limitation does not generally play a significant role for the prediction of optical sectioning, as argued previously [1

1. D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express 13(5), 1468–1476 (2005). [CrossRef] [PubMed]

] and as seen in the good agreement between the empirical measurements and the model’s predictions. Recently, methods for Monte-Carlo simulation of optical electrical field propagation were introduced, which allow such diffraction effects to be simulated [25

25. C. K. Hayakawa, E. O. Potma, and V. Venugopalan, “Electric field Monte Carlo simulations of focal field distributions produced by tightly focused laser beams in tissues,” Biomed. Opt. Express 2(2), 278–299 (2011). [CrossRef] [PubMed]

27

27. D. G. Fischer, S. A. Prahl, and D. D. Duncan, “Monte Carlo modeling of spatial coherence: free-space diffraction,” J. Opt. Soc. Am. A 25(10), 2571–2581 (2008). [CrossRef]

]. Extending our approach along those lines may improve the model's precision and extend its applicability to include diffractive optical systems. Another assumption that was used in our model in order to strike a balance between TF optical sectioning and laser transmission, is that the objective back aperture is always filled by the incoming light beam (similar to the overfill of the objective back aperture typically used in TPLSM [5

5. F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2(12), 932–940 (2005). [CrossRef] [PubMed]

]). This assumption effectively couples the TF optical setup parameters, such as the NA, magnification, beam diameter, grating period and collimating lens focal distance, so that a change in a single parameter imposes changes in the others.

Acknowledgments

The authors wish to thank Suhail Matar, Lior Golan, and two anonymous reviewers for their helpful comments on the manuscript, and the financial support of the European Research Council (starting grant #211055) and the Israel Science Foundation (1248/06).

References and links

1.

D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express 13(5), 1468–1476 (2005). [CrossRef] [PubMed]

2.

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]

3.

G. Zhu, J. van Howe, M. Durst, W. Zipfel, and C. Xu, “Simultaneous spatial and temporal focusing of femtosecond pulses,” Opt. Express 13(6), 2153–2159 (2005). [CrossRef] [PubMed]

4.

M. E. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing in nonlinear microscopy,” Opt. Commun. 281(7), 1796–1805 (2008). [CrossRef] [PubMed]

5.

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2(12), 932–940 (2005). [CrossRef] [PubMed]

6.

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]

7.

D. Oron and Y. Silberberg, “Harmonic generation with temporally focused ultrashort pulses,” J. Opt. Soc. B 22(12), 2660–2663 (2005). [CrossRef]

8.

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. Express 18(17), 18086–18094 (2010). [CrossRef] [PubMed]

9.

D. Kim and P. T. C. So, “High-throughput three-dimensional lithographic microfabrication,” Opt. Lett. 35(10), 1602–1604 (2010). [CrossRef] [PubMed]

10.

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]

11.

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. Methods 7(10), 848–854 (2010). [CrossRef] [PubMed]

12.

S. Shoham, “Optogenetics meets optical wavefront shaping,” Nat. Methods 7(10), 798–799 (2010). [CrossRef] [PubMed]

13.

M. E. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing for axial scanning,” Opt. Express 14(25), 12243–12254 (2006). [CrossRef] [PubMed]

14.

D. Kim, and P. T. C. So, “Three-dimensional (3D) high-speed imaging and fabrication system based on ultrafast optical pulse manipulation,” in Multiphoton Microscopy in the Biomedical Sciences IX, A. Periasamy, and P. T. C. So, eds. (SPIE, 2009), pp. 71831B–71838.

15.

A. Vaziri and C. V. Shank, “Ultrafast widefield optical sectioning microscopy by multifocal temporal focusing,” Opt. Express 18(19), 19645–19655 (2010). [CrossRef] [PubMed]

16.

E. Papagiakoumou, V. de Sars, D. Oron, and V. Emiliani, “Patterned two-photon illumination by spatiotemporal shaping of ultrashort pulses,” Opt. Express 16(26), 22039–22047 (2008). [CrossRef] [PubMed]

17.

D. Boas, J. Culver, J. Stott, and A. Dunn, “Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head,” Opt. Express 10(3), 159–170 (2002). [PubMed]

18.

P. Theer and W. Denk, “On the fundamental imaging-depth limit in two-photon microscopy,” J. Opt. Soc. Am. A 23(12), 3139–3149 (2006). [CrossRef]

19.

P. Theer, M. T. Hasan, and W. Denk, “Two-photon imaging to a depth of 1000 µm in living brains by use of a Ti:Al2O3 regenerative amplifier,” Opt. Lett. 28(12), 1022–1024 (2003). [CrossRef] [PubMed]

20.

L. Wang, and H. Wu, Biomedical Optics, (Wiley-Interscience, 2007), pp. 20–34. [PubMed]

21.

Y. Ikegaya, M. Le Bon-Jego, and R. Yuste, “Large-scale imaging of cortical network activity with calcium indicators,” Neurosci. Res. 52(2), 132–138 (2005). [CrossRef] [PubMed]

22.

D. Kleinfeld, P. P. Mitra, F. Helmchen, and W. Denk, “Fluctuations and stimulus-induced changes in blood flow observed in individual capillaries in layers 2 through 4 of rat neocortex,” Proc. Natl. Acad. Sci. U.S.A. 95(26), 15741–15746 (1998). [CrossRef] [PubMed]

23.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods 111(1), 29–37 (2001). [CrossRef] [PubMed]

24.

C. Y. Dong, K. Koenig, and P. So, “Characterizing point spread functions of two-photon fluorescence microscopy in turbid medium,” J. Biomed. Opt. 8(3), 450–459 (2003). [CrossRef] [PubMed]

25.

C. K. Hayakawa, E. O. Potma, and V. Venugopalan, “Electric field Monte Carlo simulations of focal field distributions produced by tightly focused laser beams in tissues,” Biomed. Opt. Express 2(2), 278–299 (2011). [CrossRef] [PubMed]

26.

C. K. Hayakawa, V. Venugopalan, V. V. Krishnamachari, and E. O. Potma, “Amplitude and phase of tightly focused laser beams in turbid media,” Phys. Rev. Lett. 103(4), 043903 (2009). [CrossRef] [PubMed]

27.

D. G. Fischer, S. A. Prahl, and D. D. Duncan, “Monte Carlo modeling of spatial coherence: free-space diffraction,” J. Opt. Soc. Am. A 25(10), 2571–2581 (2008). [CrossRef]

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(180.6900) Microscopy : Three-dimensional microscopy
(190.4180) Nonlinear optics : Multiphoton processes

ToC Category:
Imaging Systems

History
Original Manuscript: December 20, 2010
Revised Manuscript: February 2, 2011
Manuscript Accepted: February 9, 2011
Published: March 1, 2011

Virtual Issues
Vol. 6, Iss. 4 Virtual Journal for Biomedical Optics

Citation
Hod Dana and Shy Shoham, "Numerical evaluation of temporal focusing characteristics in transparent and scattering media," Opt. Express 19, 4937-4948 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-6-4937


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References

  1. D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express 13(5), 1468–1476 (2005). [CrossRef] [PubMed]
  2. 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]
  3. G. Zhu, J. van Howe, M. Durst, W. Zipfel, and C. Xu, “Simultaneous spatial and temporal focusing of femtosecond pulses,” Opt. Express 13(6), 2153–2159 (2005). [CrossRef] [PubMed]
  4. M. E. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing in nonlinear microscopy,” Opt. Commun. 281(7), 1796–1805 (2008). [CrossRef] [PubMed]
  5. F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2(12), 932–940 (2005). [CrossRef] [PubMed]
  6. 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]
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