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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 5 — Mar. 11, 2013
  • pp: 5677–5687
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Line temporal focusing characteristics in transparent and scattering media

Hod Dana, Nimrod Kruger, Aviv Ellman, and Shy Shoham  »View Author Affiliations


Optics Express, Vol. 21, Issue 5, pp. 5677-5687 (2013)
http://dx.doi.org/10.1364/OE.21.005677


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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

1. Introduction

Although TF is often implemented in a widefield temporal-focusing (WITEF) configuration, the implementation of a video-rate TF multiphoton microscope was based on scanning a temporally-focused line perpendicular to its long dimension [3

3. 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]

, 8

8. 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. SPIE 822603 (2012).

]. Line temporal focusing (LITEF) has two main advantages over WITEF. First, since multiphoton processes have a power-law dependence on light intensity, decreasing the illuminated area by a factor N, enhances two-photon excitation efficiency by N2. Second, the optical sectioning of LITEF is expected to be tighter than that of WITEF, because the addition of spatial focusing contributes to the temporal focusing in the perpendicular plane [3

3. 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]

]. Therefore, LITEF may be an attractive alternative to WITEF applications, where a stronger signal and tighter optical sectioning are required. The cost of using line focusing is an additional lateral scanning needed to illuminate a plane, however, in various applications including imaging and microfabrication, such (millisecond-timescale) scanning is acceptable. Two alternative LITEF optical setups were presented. The first design uses a cylindrical lens to focus a laser beam to a line on a diffraction grating (perpendicular to the grooves direction), and tube and objective lenses in a 4f configuration to image the grating surface onto the objective's front focal plane (Fig. 1(a)
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).
) [3

3. 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]

]. Alternatively, the laser beam hits the grating surface directly, and a 4f configuration of a cylindrical and objective lenses is used to image the grating's surface onto the objective lens front focal plane [2

2. 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]

]. In both options, the diffraction grating separates the incoming laser beam to its spectral components (in the x axis), and they re-unite in the objective focal plane where the sample is located and the grating surface is imaged. The spectral separation (in the xz plane, see Fig. 1(a)) results in pulse temporal stretching, which is compressed back to its original duration in the focal plane and re-stretched after it. Since multiphoton processes are sensitive to pulse duration, effective excitation is achieved only near the focal plane and optical sectioning without spatial focusing of the beam is attained. In the perpendicular (yz) plane the beam reaches the objective back aperture collimated and is focused to a line in the objective focal plane.

2. Methods

2.1 Experimental setup

Our experimental setup is illustrated in Fig. 1(a). It is based on an upright LITEF microscope that illuminates a sample from above (optionally, the sample is located under a scattering medium), and an inverted microscope which images the sample from below without encountering scattering effects on the emitted light. The LITEF path uses a dual-prism grating (DPG) which consists of a transmission diffraction grating embedded between two prisms. The prisms angles (48°x42°x90°, BK7 glass) and the diffraction grating groove density (1200 lines/mm) are designed to refract and diffract the laser’s central wavelength (800nnm) toward the same direction of the incoming light propagation. The DPG based design simplifies the optical setup configuration, offers a high efficiency (85% measured efficiency vs. 87% predicted efficiency for both polarization states), and also enables to perform remote scanning of the focal plane [20

20. H. Dana and S. Shoham, “Remotely scanned multiphoton temporal focusing by axial grism scanning,” Opt. Lett. 37(14), 2913–2915 (2012). [CrossRef] [PubMed]

]. The excitation source is an amplified ultrafast laser (RegA 9000, pumped and seeded by a Vitesse duo; Coherent), providing up to 200mW of average power at the sample plane at a 150KHz repetition rate (1.33 μJ/pulse). After passing through a beam expander, an electro-optic modulator (Conoptics), and a cylindrical lens (f = 75mm), the beam hits the DPG and reaches the grating tilted by an angle α’ = 18°. An f = 200mm tube lens (Nikon) was used together with three interchangeable objective lenses (Nikon 60x NA = 1, Nikon 40x NA = 0.8, and Zeiss 10x NA = 0.45. The latter combined with the Nikon tube lens had an actual magnification of 12; all objectives are water immersion) in a 4f configuration to image a temporally focused line onto the sample.

A scattering tissue phantom (prepared as described in ref [5

5. H. Dana and S. Shoham, “Numerical evaluation of temporal focusing characteristics in transparent and scattering media,” Opt. Express 19(6), 4937–4948 (2011). [CrossRef] [PubMed]

].) was placed on top of a 5µm fluorescein layer near the objective's focal plane (see Fig. 1(b); the fluorescein layer thickness was measured using TPLSM axial scanning). This phantom mimics the scattering characteristics of cortical tissue with mean free path (MFP) of 200 µm and scattering anisotropy of g = 0.9 [5

5. H. Dana and S. Shoham, “Numerical evaluation of temporal focusing characteristics in transparent and scattering media,” Opt. Express 19(6), 4937–4948 (2011). [CrossRef] [PubMed]

, 21

21. 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] [PubMed]

]. To measure the fluorescence light intensity from the opposite side of the sample, as well as to estimate the illuminated line waist, we used a second objective lens (Olympus 20x NA = 0.5 water immersion, and Nikon 40x NA = 0.55 air), an imaging lens and a CCD camera (UEye 2220SE-M, IDS). The sample and the second objective lens were mounted on 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. The thickness of the scattering medium above the fluorescein layer was measured by moving the sample from the scattering medium top to the fluorescein layer, measuring the distance, and subtracting the thickness of a cover slip (average thickness of 150 µm) that lies between them. Pulse duration of ~200fs was measured at the laser’s output using an autocorrelator (PulseCheck, APE). At the TF focal plane (after passing through all of the optical components) a similar pulse duration was estimated by fitting a WITEF optical sectioning measurements (i.e. by removing the cylindrical lens) to model predictions [5

5. H. Dana and S. Shoham, “Numerical evaluation of temporal focusing characteristics in transparent and scattering media,” Opt. Express 19(6), 4937–4948 (2011). [CrossRef] [PubMed]

] for different pulse durations. Optical sectioning curves were calculated by integrating the fluorescence signal from an image acquired for each distance from the focal plane. All comparisons of model predictions to experimental measurements were compensated for the broadening introduced by the finite thickness of the fluorescein layer (see example in Fig. 2(d)
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.
).

2.2 Computational model

In this section we present an adaptation of our WITEF light propagation model [5

5. H. Dana and S. Shoham, “Numerical evaluation of temporal focusing characteristics in transparent and scattering media,” Opt. Express 19(6), 4937–4948 (2011). [CrossRef] [PubMed]

] to account for LITEF. The model assumes independent light propagation in the mutually-perpendicular spatial and temporal focusing planes (yz and xz planes, respectively). The original WITEF model geometry is two dimensional and describes light propagation in the optical axis and the spectral distribution axis (z and x axes, respectively). Here, we add an additional description for the propagation in the spatial focusing plane using a cylindrical Gaussian beam model in the y axis. In addition, our experimental setup now includes a DPG made of BK7 glass (see section 2.1 for details), which we incorporated into the model.

When a delta pulse is focused into a line and impinges upon a diffraction grating (Fig. 1(a)), each spectral component is diffracted to a different direction and propagates a different optical path towards the focal plane. The propagation in the xz plane near the focal plane was previously described in detail [5

5. H. Dana and S. Shoham, “Numerical evaluation of temporal focusing characteristics in transparent and scattering media,” Opt. Express 19(6), 4937–4948 (2011). [CrossRef] [PubMed]

]. Briefly, each spectral component propagates in a direction angle β as a tilted line, with tilting angle α (see Fig. 2(a)). All of the spectral components reunite in the focal plane and scan it together within picoseconds. The scanning speed depends on the angle α’ with which the incoming delta pulse phase front is tilted with respect to the diffraction grating, on the system’s magnification M, and on the DPG material (with refraction index nDPG) and is given by [1

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

] c/(nDPGMsinα). On the other hand, the focal plane is located in a medium with refractive index nf, and is scanned by a line that propagates in direction β and is tilted by angle α with a scanning speed ofccos(αβ)/(nfsinα). The focal plane is the image of the grating’s surface, and according to Fermat’s principle, the scanning time is equal. Therefore:
α=cot1(nf/nDPGMsinαcosβtanβ)
(1)
β values correspond to each spectral component propagation direction and their maximal value is limited by the objective’s NA. The spectral component line length is derived from the illuminated line length land from the angles α and β, and is given bylcosβ/(cos(αβ)). The beam spectral profile was assumed to be Gaussian, and its 1/e width before arriving to the objective lens was estimated to be equal to the objective's back aperture diameter.

The propagation scheme in the yz plane is different. In this plane the cylindrical lens and the tube lens generate a telescope and the light reaches the objective lens nearly collimated. We modeled each spectral component as a cylindrical Gaussian beam in the yz plane, with an equal minimal waist (w0) which is obtained in the focal plane (see Fig. 2(b)). The w0 value was experimentally measured for each objective, and was corrected for the imaging PSF. The two-dimensional Gaussian beam formula is given by I(y,z)=I0(w0w(z))exp(2y2w2(z)). Therefore, each spectral component is characterized by its length, its tilting angle α, its propagation direction β, all in the xz plane, and its waist size w0, in the yz plane.

In order to introduce tissue scattering effects into the model, we computed scattering kernels for various scattering depths, using a time-resolved Monte-Carlo simulation [22

22. Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17(22), 20178–20190 (2009). [CrossRef] [PubMed]

]. Medium parameters were: scattering MFP of 200 μm, 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 propagates inside the scattering medium, we rotated the matching scattering kernel by the same angle to simulate the scattering directions.

3. Results

3.1 Model validation

To examine the model’s accuracy in a transparent medium under various optical configurations, we tested its predictions for TF’s main characteristic - the optical sectioning width. Optical sectioning was experimentally measured by axially scanning a 5µm layer of fluorescein solution across the focal plane. Results of these measurements and model predictions for three different optical setup parameters are shown in 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).
. The optical parameters were chosen to demonstrate LITEF capabilities for different applications: the first set of parameters (M = 40, NA = 0.8, line length = 125µm, beam waist = 0.75µm) represents commonly used system parameters for high resolution two-photon imaging, while the second set (M = 12, NA = 0.45, length = 500 µm, waist = 1 µm) is suitable for high resolution large field-of-view imaging. The third set (M = 60, NA = 1, length = 15µm, waist = 1.6µm) was chosen to explore the possibility of ultra-deep imaging that will be discussed in section 3.4.

3.2 Dependence on optical parameters in non-scattering media

Generalizing a similar result previously obtained for WITEF [5

5. H. Dana and S. Shoham, “Numerical evaluation of temporal focusing characteristics in transparent and scattering media,” Opt. Express 19(6), 4937–4948 (2011). [CrossRef] [PubMed]

], we found an approximate formula that fits LITEF optical sectioning in transparent media. The sectioning profile of both our model predictions and the experimental measurements are consistently well fit with an analytical product of two square-roots of Lorentz-Cauchy functions given by:

F=11+(z/zR1)21+(z/zR2)2
(2)

Where F is the (peak-normalized) fluorescence signal and z is the axial distance from the TF focal plane. The optical sectioning parameters zR1 and zR2 depend only on the temporal and spatial focusing, respectively, highlighting the previously-noted separation of the two independent effects [2

2. 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]

, 12

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

, 19

19. 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]

].

3.3 Scattering effects

The use of an amplified laser source enabled the measurement of light penetrating through more than 1mm of the scattering phantom - these measurements and model predictions were compared for two different optical setups (Fig. 6(a)
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.
). Interestingly, according to both the theoretical and experimental results, LITEF exhibits a relatively slow deterioration of the optical sectioning with scattering depth: no significant broadening was measured for the high magnification setup, and a broadening by a factor less than 1.5 was measured in the low magnification configuration at a depth of 6 scattering MFPs. For comparison, WITEF with similar optical parameters to the high magnification setup exhibits a 5-fold broadening of the axial sectioning over a much smaller range of 2.5 MFPs (500µm) [5

5. H. Dana and S. Shoham, “Numerical evaluation of temporal focusing characteristics in transparent and scattering media,” Opt. Express 19(6), 4937–4948 (2011). [CrossRef] [PubMed]

]. This highlights the relative robustness of LITEF over WITEF for tissue scattering effect on sectioning (Fig. 6c).

The Fluorescence signal power as a function of depth in scattering media was also measured (Fig. 6(b)). The fluorescence signal exponential attenuation fit corresponds to a 1/e decay constant of 127 µm for the x12 NA = 0.45 setup and 105 µm for the x40 NA = 0.8 setup. Interestingly, these measured decay constants are intermediate between the spatial focusing MFP (100 µm independent of optical parameters, e.g., ref [23

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

], box 1), and the 190 µm for the x60 NA = 1 simulated WITEF imaging setup [5

5. H. Dana and S. Shoham, “Numerical evaluation of temporal focusing characteristics in transparent and scattering media,” Opt. Express 19(6), 4937–4948 (2011). [CrossRef] [PubMed]

] (Fig. 6(d)).

3.4 Deep tissue penetration

4. Discussion

In this study we combined theoretical and experimental work to expand the understanding of LITEF, and emphasized its unique characteristics and capabilities in comparison with WITEF and spatial focusing. The enhanced sectioning capability of LITEF allows the use of lower magnification objectives, which offer a larger field of view, while still maintaining microscopic-resolution imaging.

Two new analytical expressions were introduced to describe LITEF's sectioning characteristics. Equation (2) describes the axial sectioning profile as a product of two square-roots of Lorentz-Cauchy functions, and highlights the separable role of spatial and temporal focusing in creating this profile (the WITEF temporal-only profile is described by a square-root of a single Lorentz-Cauchy function [5

5. H. Dana and S. Shoham, “Numerical evaluation of temporal focusing characteristics in transparent and scattering media,” Opt. Express 19(6), 4937–4948 (2011). [CrossRef] [PubMed]

, 19

19. 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]

]). Equation (3), which has the same form as the equivalent expression we previously found for WITEF [5

5. H. Dana and S. Shoham, “Numerical evaluation of temporal focusing characteristics in transparent and scattering media,” Opt. Express 19(6), 4937–4948 (2011). [CrossRef] [PubMed]

] (but has different parameter values, due to the change in system’s characteristics), may serve as a basis for approximating the optical sectioning for a given set of optical parameters. The dependence on five different parameters, compared to just one in spatial focusing, offers a relatively high level of flexibility in the optical design process.

LITEF is a hybrid method of spatial and temporal focusing, and it was found here to have intermediate robustness to scattering effects relative to the two “pure” methods (Fig. 6). We have shown that the measured effects of scattering on axial sectioning are relatively minor and enable the use of LITEF deep inside scattering media, for applications like imaging and single-cell excitation, without significant deterioration of the system’s performance. This is in contrast to the rapid deterioration of WITEF's optical sectioning [5

5. H. Dana and S. Shoham, “Numerical evaluation of temporal focusing characteristics in transparent and scattering media,” Opt. Express 19(6), 4937–4948 (2011). [CrossRef] [PubMed]

] - the difference between the relative sectioning deterioration could be of an order of magnitude within less than 1mm of tissue propagation. Thus, LITEF appears to be generally more suitable for deep tissue applications than WITEF [for multiphoton imaging, tissue scattering will also affect the detected light propagation, an effect that can be partially mitigated using descattering algorithms [8

8. 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. SPIE 822603 (2012).

] and customized detection schemes]. Secondly, the signal attenuation rate, shown in Fig. 6(b and d), gives an indication about the expected scattering effects. For standard spatial focusing the decay constant is expected to be 100 µm (MFP/2 [23

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

]), since only ballistic (non-scattered) photons contribute to the nonlinear fluorescence signal. LITEF’s decay constants were slightly longer, which also means that scattered photons contribute to the fluorescence signal (this effect is even stronger for WITEF, where longer decay constants are observed). Interestingly, we note that our results on the relative resilience of TF axial sectioning to scattering are complementary to recent findings on the scattering-resilience of diffractive pattern TF illumination [25

25. 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).

] that were based on a different model describing light wave propagation.

Finally, based on the observation of ultra-deep penetration by very short LITEF lines (Fig. 7), we put forward the idea of combining such micro-line illumination and raster scanning across a volume, as a method that in principle may allow imaging beyond the physical out-of-focus limits [21

21. 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] [PubMed]

]. Although micro-LITEF is demonstrated to have impressive scattering resilience - the expected improvement in penetration depth of the proposed imaging method remains to be verified and the system’s implementation would require additional work.

Acknowledgments

The authors wish to thank Dr. Gali Sela, Einat Binyamin and two anonymous reviewers for their helpful comments on the manuscript. We gratefully acknowledge the financial support of the European Research Council (starting grant #211055), the Niedersachsen-Technion grant #VWZN2632, and the Russell-Berrie Nanotechnology Institute.

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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] [PubMed]

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Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17(22), 20178–20190 (2009). [CrossRef] [PubMed]

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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).

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
(290.5850) Scattering : Scattering, particles

ToC Category:
Microscopy

History
Original Manuscript: October 17, 2012
Revised Manuscript: December 26, 2012
Manuscript Accepted: January 25, 2013
Published: March 1, 2013

Virtual Issues
Vol. 8, Iss. 4 Virtual Journal for Biomedical Optics

Citation
Hod Dana, Nimrod Kruger, Aviv Ellman, and Shy Shoham, "Line temporal focusing characteristics in transparent and scattering media," Opt. Express 21, 5677-5687 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-5677


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References

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